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We revisit Duff, Okun, and Veneziano's divergent views on the number of fundamental constants and argue that the issue can be set to rest by having spacetime as the starting point. This procedure disentangles the resolution in what depends on the assumed spacetime (whether relativistic or not) from the theories built over it. By defining that the number of fundamental constants equals the minimal number of independent standards necessary to express all observables, as assumed by Duff, Okun, and Veneziano, it is shown that the same units fixed by the apparatuses used to construct the spacetimes are enough to express all observables of the physical laws defined over them. As a result, the number of fundamental constants equals two in Galilei spacetime and one in relativistic spacetimes., Comment: 17 pages and 4 figures. Extra appendix, figure, and clarifications included

We introduce the relativistic version of the well-known Henon's isochrone spherical models: static spherically symmetrical spacetimes in which all bounded trajectories are isochrone in Henon's sense, i.e., their radial periods do not depend on their angular momenta. Analogously to the Newtonian case, these "isochrone spacetimes" have as particular cases the so-called Bertrand spacetimes, in which all bounded trajectories are periodic. We propose a procedure to generate isochrone spacetimes by means of an algebraic equation, present explicitly several families of these spacetimes, and discuss briefly their main properties. We identify, in particular, the family whose Newtonian limit corresponds to the Henon's isochrone potentials and that could be considered as the relativistic extension of the original Henon's proposal for the study of globular clusters. Nevertheless, isochrone spacetimes generically violate the weak energy condition and may exhibit naked singularities, challenging their physical interpretation in the context of General Relativity., Comment: 14 pages, 2 figures. Final version accepted for publication in GRG

We revisit in this note the H\'enon's isochrone problem. By using the standard Abel inversion technique for one-dimensional motion, we recover in a simple way the H\'enon's parabolae and get all isochrone central potentials under mild smoothness assumptions on the potential function. Our approach also allows us to conclude that isochronous radial periods with explicit energy dependence are necessarily Keplerian, i.e., $T^{2}\propto|E|^{-3}$, and that their corresponding orbits can be easily integrated by mapping them into the usual Kepler problem. It can also be employed to study some other inverse central-force problems and, in particular, it provides a proof of Bertrand's theorem., Comment: 7 pages. Text revised, new figure, conclusions unchanged. Final version to appear in Can. J. Phys

We show that a recent proposal for simulating planar hyperbolic lattices with circuit quantum electrodynamics can be extended to accommodate also higher dimensional lattices in Euclidean and non-Euclidean spaces if one allows for circuits with more than three polygons at each vertex. The quantum dynamics of these circuits, which can be constructed with present-day technology, are governed by effective tight-binding Hamiltonians corresponding to higher-dimensional Kagom\'{e}-like structures ($n$-dimensional zeolites), which are well known to exhibit strong frustration and flat bands. We analyze the relevant spectra of these systems and derive an exact expression for the fraction of flat-band states. Our results expand considerably the range of non-Euclidean geometry realizations with circuit quantum electrodynamics., Comment: 8 pages, 6 figures

Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively uncommon, being restricted basically to the case of N-body problems. Here, we present a consistent Hamiltonian formalism for the dynamics of test particles in spacetimes with arbitrary energy-momentum distributions in the first post-Newtonian (1PN) approximation. We apply our formalism to orbital motion in stationary axisymmetric spacetimes and obtain the 1PN relativistic corrections to the radial and vertical epicyclic frequencies for quasi-circular equatorial motion, a result potentially interesting for galactic dynamics. For the case of razor-thin disk configurations, we obtain an approximated third integral which could be used to determine analytically the envelope of nearly equatorial orbits. One of the main advantages of this 1PN analysis is the explicit presence of frame-dragging effects in all pertinent expressions, allowing some qualitative predictions in rotating spacetimes. We finish discussing the 1PN collisionless Boltzmann equation in terms of the Hamiltonian canonical variables and its relation with previous results in the literature., Comment: 9 pages, no figures

We revisit here the analytical continuation approach usually employed to compute quasinormal modes (QNM) and frequencies of a given potential barrier $V$ starting from the bounded states and respective eigenvalues of the Schroedinger operator associated with the potential well corresponding to the inverted potential $-V$. We consider an exactly soluble problem corresponding to a potential barrier of the Poschl-Teller type with a well defined and behaved QNM spectrum, but for which the associated Schroedinger operator $\cal H$ obtained by analytical continuation fails to be self-adjoint. Although $\cal H$ admits self-adjoint extensions, we show that the eigenstates corresponding to the analytically continued QNM do not belong to any self-adjoint extension domain and, consequently, they cannot be interpreted as authentic quantum mechanical bounded states. Our result challenges the practical use of the this type of method when $\cal H$ fails to be self-adjoint since, in such cases, we would not have in advance any reasonable criterion to choose the initial eigenstates of $\cal H$ which would correspond to the analytically continued QNM., Comment: & pages, 1 Figure. Accepted for its publication in Physical Review D

We consider the stationary spherical accretion process of perfect fluids onto a class of spherically symmetric regular black holes corresponding to quantum-corrected Schwarzschild spacetimes. We show that the accretion rates can differ from the Schwarzschild case, suggesting that the de Sitter core inside these regular black holes, which indeed precludes the central singularity, can act for some cases as a sort of antigravitational source, decreasing the fluid's radial infall velocity in the accretion process, and for others as a gravitational enhancer, increasing the fluid flow into the black hole horizon. Our analysis and results can be extended and also applied to the problem of black hole evaporation in cosmological scenarios with phantom fluids. In particular, we show that the mass of typical regular black holes can be used in order to constrain turnaround events in cyclic cosmologies., Comment: 9 pages, 1 figure and 1 table. V3 with minor changes. Published in Annals of Physics

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies $\omega_i$, such that a fraction of them is subject to an external periodic force with frequency $\Omega$, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that $|\omega_i-\Omega|$ is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization are desired properties. Some properties of the optimal forced networks and its relation to recent results in the literature are also discussed., Comment: 8 pages, 3 figures. Final version accepted for publication in Chaos. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

We extend to the $n$-dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometry. For the sake of illustration, we consider two explicit examples motivated by recent experimental results: surface waves in flumes and vortices. For both examples, we have distinctive directional spacetime structures, namely horizons and ergospheres, respectively. We show that both structures are associated with certain directional divergences in the underlying Finslerian (Randers) geometry. Our results show that Finsler geometry may provide a fresh view on the causal structure of spacetime, not only in analogue models but also for General Relativity., Comment: 17 pages, 3 figures. Final version accepted for publication in CQG. Animations in Supplementary Material available at http://vigo.ime.unicamp.br/Huygens/

We investigate the dynamics of $f(R)$ gravity in Jordan and Einstein frames. First, we perform a phase-space singularities analysis in both frames. We show that, typically, anisotropic singularities are absent in the Einstein frame, whereas they may appear in the Jordan frame. We conciliate this apparent inconsistency by showing that the necessary conditions for the existence of the Einstein frame are namely the same ones assuring the absence of the anisotropic singularities in the Jordan frame. In other words, we show that, at least in the context of Bianchi I cosmologies, the Einstein frame is available only when the original formulation in the Jordan frame is free of anisotropic singularities. Furthermore, we present a novel dynamical system formulation for anisotropic cosmologies in which both frames, provided they exist, will be manifestly equivalent from the dynamical point of view, even though they fail to be diffeomorphic in general. Our results could help not only the construction of viable (free of anisotropic singularities) $f(R)$ cosmological models, but also contribute to the still active debate on the physical interpretation of the two frames., Comment: 9 pages. Final version accepted for publication in the PRD

We investigate the dynamics of scalar fields in the near-horizon exterior region of a Schwarzschild black hole. We show that low-energy modes are typically long-living and might be considered as being confined near the black hole horizon. Such dynamics are effectively governed by a Schroedinger operator with infinitely many self-adjoint extensions parameterized by $U(1)$, a situation closely resembling the case of an ordinary free particle moving on a semiaxis. Even though these different self-adjoint extensions lead to equivalent scattering and thermal processes, a comparison with a simplified model suggests a physical prescription to chose the pertinent self-adjoint extensions. However, since all extensions are in principle physically equivalent, they might be considered in equal footing for statistical analyses of near-horizon modes around black holes. Analogous results hold for any non-extremal, spherically symmetric, asymptotically flat black hole., Comment: 10 pages, 1 fig, contribution submitted to the volume "Classical and Quantum Physics: Geometry, Dynamics and Control. (60 Years Alberto Ibort Fest)" Springer (2018)

We present a dynamical analysis in terms of new expansion-normalized variables for homogeneous and anisotropic Bianchi-I spacetimes in $f(R)$ gravity in the presence of anisotropic matter. With a suitable choice of the evolution parameter, the Einstein's equations are reduced to an autonomous 5-dimensional system of ordinary differential equations for the new variables. Further restrictions lead to considerable simplifications. For instance, we show that for a large class of functions $f(R)$, which includes several cases commonly considered in the literature, all the fixed points are polynomial roots, and hence they can be determined with good accuracy and classified for stability. Moreover, typically for these cases, any fixed point corresponding to isotropic solutions in the presence of anisotropic matter will be unstable. The assumption of a perfect fluid as source and or the vacuum cases imply some dimensional reductions and even more simplifications. In particular, we find that the vacuum solutions of $f(R) = R^{1+\delta}$, with $\delta$ a constant, are governed by an effective bi-dimensional phase space which can be analytically constructed, leading to an exactly soluble dynamics. Finally, we demonstrate that several results already reported in the literature can be re-obtained in a more direct and easy way by exploring our dynamical formulation., Comment: 9 pages. 2 Figures. Extensive revision was done. Errors were corrected. Title has changed. A new author was added. Final version accepted for publication in the PRD

In the light of the recently proposed scenario of asymmetry-induced synchronization (AISync), in which dynamical uniformity and consensus in a distributed system would demand certain asymmetries in the underlying network, we investigate here the influence of some regularities in the interlayer connection patterns on the synchronization properties of multilayer random networks. More specifically, by considering a Stuart-Landau model of complex oscillators with random frequencies, we report for multilayer networks a dynamical behavior that could be also classified as a manifestation of AISync. We show, namely, that the presence of certain symmetries in the interlayer connection pattern tends to diminish the synchronization capability of the whole network or, in other words, asymmetries in the interlayer connections would enhance synchronization in such structured networks. Our results might help the understanding not only of the AISync mechanism itself, but also its possible role in the determination of the interlayer connection pattern of multilayer and other structured networks with optimal synchronization properties., Comment: 11 pages, 9 figure, final version accepted for publication in the PRE

We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely supported by surface polar currents on the disk. Our starting point is the Gutsunaev-Manko axisymmetric solution describing massive magnetic dipoles in General Relativity, from which we obtain a continuous three-parameter family of asymptotically flat static magnetized disks with finite mass and energy. For strong magnetic fields, the disk surface density profile resembles some well known self-gravitating ring-like structures. We show that many of these solutions can be indeed stable and, hence, they could be in principle useful for the study of the abundant astrophysical situations involving disks of matter and magnetic fields., Comment: 9 pages, 7 figures; Accepted for publication in Physical Review D

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow., Comment: 13 pages, 4 figures; Accepted for publication in Physical Review D

Soap bubbles are thin liquid films enclosing a fixed volume of air. Since the surface tension is typically assumed to be the only responsible for conforming the soap bubble shape, the realized bubble surfaces are always minimal area ones. Here, we consider the problem of finding the axisymmetric minimal area surface enclosing a fixed volume $V$ and with a fixed equatorial perimeter $L$. It is well known that the sphere is the solution for $V=L^3/6\pi^2$, and this is indeed the case of a free soap bubble, for instance. Surprisingly, we show that for $V<\alpha L^3/6\pi^2$, with $\alpha\approx 0.21$, such a surface cannot be the usual lens-shaped surface formed by the juxtaposition of two spherical caps, but rather a toroidal surface. Practically, a doughnut-shaped bubble is known to be ultimately unstable and, hence, it will eventually lose its axisymmetry by breaking apart in smaller bubbles. Indisputably, however, the topological transition from spherical to toroidal surfaces is mandatory here for obtaining the global solution for this axisymmetric isoperimetric problem. Our result suggests that deformed bubbles with $V<\alpha L^3/6\pi^2$ cannot be stable and should not exist in foams, for instance., Comment: 5 pages. 5 figures and 1 animation available at http://vigo.ime.unicamp.br/bubble/

A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function $\omega^T L \omega$, where $\omega$ stands for the vector of the natural frequencies of the oscillators, and $L$ for the network Laplacian matrix. Many recently obtained numerical results can be re-obtained analytically and in a simpler way from our maximization condition. A computationally efficient {hill climb} rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner., Comment: 6 pages, 6 figures, final version to appear in PRE

We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order to enhance its synchronization capacity. We show that the the synchrony-optimized networks generated by our algorithm have some interesting topological and dynamical properties. In particular, they typically exhibit an anticipation of the synchronization onset and are more robust against certain types of perturbations. We consider synthetic random networks and also a network with a topology based in an approximated model of the (high voltage) power grid of Spain, since networks of Kuramoto oscillators with inertia have been used recently as simplified models for power grids, for which synchronization is obviously a crucial issue. Despite the extreme simplifications adopted in these models, our results, among others recently obtained in the literature, may provide interesting principles to guide the future growth and development of real-world grids, specially in the case of a change of the current paradigm of centralized towards distributed generation power grids., Comment: 21 pages, 9 figures. Final version to appear in Physica A. Title and several parts of the text have changed, results and conclusions are unaltered. Some online material is available at http://vigo.ime.unicamp.br/PowerGrids/

Networks of Kuramoto oscillators with a positive correlation between the oscillators frequencies and the degree of the their corresponding vertices exhibits the so-called explosive synchronization behavior, which is now under intensive investigation. Here, we study and report explosive synchronization in a situation that has not yet been considered, namely when only a part, typically small, of the vertices is subjected to a degree frequency correlation. Our results show that in order to have explosive synchronization, it suffices to have degree-frequency correlations only for the hubs, the vertices with the highest degrees. Moreover, we show that a partial degree-frequency correlation does not only promotes but also allows explosive synchronization to happen in networks for which a full degree-frequency correlation would not allow it. We perform exhaustive numerical experiments for synthetic networks and also for the undirected and unweighted version of the neural network of the worm Caenorhabditis elegans. The latter is an explicit example where partial degree-frequency correlation leads to explosive synchronization with hysteresis, in contrast with the fully correlated case, for which no explosive synchronization is observed., Comment: 10 pages, 6 figures, final version to appear in PRE

We revisit here a recent work on regular rotating black holes. We introduce a new mass function generalizing the commonly used Bardeen and Hayward mass functions and extend the recently proposed solutions in order to accommodate a cosmological constant $\Lambda$. We discuss some aspects of the causal structure (horizons) and the ergospheres of the new proposed solutions. We also show that, in contrast with the spherically symmetrical case, the black hole rotation will unavoidably lead to the violation of the weak energy condition for any physically reasonable choice of the mass function, reinforcing the idea the description of the interior region of a Kerr black hole is much more challenging than in the Schwarzschild case., Comment: 8 pages, 3 figures

We use the Melnikov integral method to prove that the Hamiltonian flow on the zero-energy manifold for the Kepler problem perturbed by a quadrupole moment is chaotic, irrespective of the perturbation being of prolate or oblate type. This result helps to elucidate some recent conflicting works in the physical literature based on numerical simulations., Comment: 6 pages, 1 figure. Contribution submitted to the volume "Geometry, Mechanics and Dynamics: the Legacy of Jerrold E. Marsden", Springer (2013)

We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to accurately compute it together with its Lyapunov exponent. We then investigate the occurrence of chaos by varying the parameters of the system, with especial emphasis on the simplest possible chaotic oscillations. Our results corroborate and complement some recent works on bifurcations and routes to chaos in certain particular cases corresponding to piecewise linear FitzHugh-Nagumo-like systems., Comment: 16 pages, 6 figures, final version to appear in Chaos, Solitons & Fractals

Superradiant scattering processes are studied in general relativistic systems which, unlike rotating and/or charged black holes, do not exhibit an event horizon. Inspired by Zel'dovich's seminal works on the amplification of waves by a rotating cylinder, we analyse, in the context of General Relativity, the possibility of superradiance for electromagnetic waves reflecting off a rotating star and for charged scalar perturbations impinging on a charged sphere. The role of energy dissipation in these systems is analysed and compared with the role of the event horizon in black hole superradiance., Comment: 5 pages; typos corrected; revised assumptions and revised argument in section II, results unchanged

We revisit here the mathematical model for ATP production in mitochondria introduced recently by Bertram, Pedersen, Luciani, and Sherman (BPLS) as a simplification of the more complete but intricate Magnus and Keizer's model. We identify some inaccuracies in the BPLS original approximations for two flux rates, namely the adenine nucleotide translocator rate $J_{\rm ANT}$ and the calcium uniporter rate $J_{\rm uni}$. We introduce new approximations for such flux rates and then analyze some of the dynamical properties of the model. We infer, from exhaustive numerical explorations, that the enhanced BPLS equations have a unique attractor fixed point for physiologically acceptable ranges of mitochondrial variables and respiration inputs, as one would indeed expect from homeostasis. We determine, in the stationary regime, the dependence of the mitochondrial variables on the respiration inputs, namely the cytosolic concentration of calcium ${\rm Ca}_{\rm c}$ and the substrate fructose 1,6-bisphosphate FBP. The same dynamical effects of calcium and FBP saturations reported for the original BPLS model are observed here. We find out, however, a novel non-stationary effect which could be, in principle, physiologically interesting: some response times of the model tend to increase considerably for high concentrations of calcium and/or FBP. In particular, the larger the concentrations of ${\rm Ca}_{\rm c}$ and/or FBP, the larger the necessary time to attain homeostasis., Comment: 16 pages, 6 figures. Final version to appear in the Bulletin of Mathematical Biology. Scilab codes available at http://vigo.ime.unicamp.br/atp/

We explore the question of what happens with the asymptotically highly damped quasi-normal modes ($\ell$ fixed, $|\omega_{I}|\to\infty$) when the underlying spacetime has no event horizons. We consider the characteristic oscillations of a scalar field in a large class of asymptotically flat spherically symmetric static spacetimes without (absolute) horizons, such that the class accommodates the cases that are known to be of some sort of physical interest. The question of the asymptotic quasi-normal modes in such spacetimes is relevant to elucidate the connection between the behavior of the asymptotic quasi-normal modes and the quantum properties of event horizons, as put forward in some recent important conjectures. We prove for a large class of asymptotically flat spacetimes without horizons that the scalar field asymptotically highly damped modes do not exist. This provides in our view additional evidence that there is indeed a close link between the asymptotically highly damped modes and the existence of spacetime horizons (and their properties)., Comment: 5 pages, v2: the final version accepted for publication in Phys.Rev.D

What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner-Nordstr\"om spacetime with $|q| > m$. We show that there is a qualitative difference between cases with $1 < q^2/m^2 \lesssim 9/8$ and cases with $q^2/m^2 \gtrsim 9/8$. We discuss the necessary conditions for the well-posedness of the problem, and present results for the low damped modes in the low $l$ and large $l$ limit. We also consider the asymptotically highly damped quasinormal modes. We present strong evidence that such modes are absent in the case of a naked Reissner-Nordstr\"om singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons., Comment: v3: final version to appear in Physical Review D, 17 pages, 10 figures, v3: only minor cosmetic changes (few typos corrected) with respect to v2, v1: the same physics, but missing one section

The recently proposed Horava-Lifshitz (HL) theory of gravity is analyzed from the quantum cosmology point of view. By employing usual quantum cosmology techniques, we study the quantum Friedmann-Lemaitre-Robertson-Walker (FLRW) universe filled with radiation in the context of HL gravity. We find that this universe is quantum mechanically nonsingular in two different ways: the expectation value of the scale factor $(t)$ never vanishes and, if we abandon the detailed balance condition suggested by Horava, the quantum dynamics of the universe is uniquely determined by the initial wave packet and no boundary condition at $a=0$ is indeed necessary., Comment: 13 pages, revtex, 1 figure. Final version to appear in PRD

We present here the field equations describing a non-stationary spherically symmetric n-dimensional charged black hole with varying mass m(v) and/or electric charge q(v), described by a generic charged Vaidya metric with cosmological constant Lambda in double null coordinates. This formulation of the metric has been shown to be particularly useful for perturbative studies and it was used in some recent works. Here we also discuss some issues related to the apparent and event horizons of the black hole., Comment: 13 pages, 5 figures, final version to appear in CQG

We address here the problem of extending the Pesin relation among positive Lyapunov exponents and the Kolmogorov-Sinai entropy to the case of dynamical systems exhibiting subexponential instabilities. By using a recent rigorous result due to Zweim\"uller, we show that the usual Pesin relation can be extended straightforwardly for weakly chaotic one-dimensional systems of the Pomeau-Manneville type, provided one introduces a convenient subexponential generalization of the Kolmogorov-Sinai entropy. We show, furthermore, that Zweim\"uller's result provides an efficient prescription for the evaluation of the algorithm complexity for such systems. Our results are confirmed by exhaustive numerical simulations. We also point out and correct a misleading extension of the Pesin relation based on the Krengel entropy that has appeared recently in the literature., Comment: 10 pages, 4 figures. Final version to appear in Journal of Statistical Mechanics (JSTAT)

Motivated by the recent attempts to violate the weak cosmic censorship conjecture for near-extreme black-holes, we consider the possibility of overcharging a near-extreme Reissner-Nordstr\"om black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-1/2 particles by the black hole in a unified framework and obtain analytically, for the first time, the pertinent reflection and transmission coefficients without any small charge approximation. Based on these results, we propose some gedanken experiments that could lead to the violation of the weak cosmic censorship conjecture due to the (classically forbidden) absorption of small energy charged particles by the black hole. As for the case of scattering in Kerr spacetimes, our results demonstrate explicitly that scalar fields are subject to (electrical) superradiance phenomenon, while spin-1/2 fields are not. Superradiance impose some limitations on the gedanken experiments involving spin-0 fields, favoring, in this way, the mechanisms for creation of a naked singularity by the quantum tunneling of spin-1/2 charged fermions. We also discuss the implications that vacuum polarization effects and quantum statistics might have on these gedanken experiments. In particular, we show that they are not enough to prevent the absorption of incident small energy particles and, consequently, the formation of a naked singularity., Comment: 9 pages; Final version to appear in PRD

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a generic class of maps of the Pomeau-Manneville type. We show further that, typically, the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes. Our approaches are firmly based on rigorous results, particularly the Aaronson-Darling-Kac theorem, and are also confirmed by exhaustive numerical simulations., Comment: 7 pages, 5 figures, to appear in PRE

We consider here the recently proposed closed form formula in terms of the Meijer G-functions for the probability density functions $g_\alpha(x)$ of one-sided L\'evy stable distributions with rational index $\alpha=l/k$, with $0<\alpha<1$. Since one-sided L\'evy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions $\rho_\alpha(x)$ of the latter. We show, however, that the formula is computationally inviable for fractions with large denominators, being unpractical even for some modest values of $l$ and $k$. We present a fast and accurate numerical scheme, based on an early integral representation due to Mikusinski, for the evaluation of $g_\alpha(x)$ and $\rho_\alpha(x)$, their cumulative distribution function and their derivatives for any real index $\alpha\in (0,1)$. As an application, we explore some properties of these probability density functions. In particular, we determine the location and value of their maxima as functions of the index $\alpha$. We show that $\alpha \approx 0.567$ and $\alpha \approx 0.605$ correspond, respectively, to the one-sided L\'evy and Mittag-Leffler distributions with shortest maxima. We close by discussing how our results can elucidate some recently described dynamical behavior of intermittent systems., Comment: 6 pages, 5 figures. New references added, final version to appear in PRE. Numerical code available at http://vigo.ime.unicamp.br/distr

We revisit here a previous argument due to Wald showing the impossibility of turning an extremal Kerr-Newman black hole into a naked singularity by plunging test particles across the black hole event horizon. We extend Wald's analysis to the case of near-extremal black holes and show that it is indeed possible to destroy their event horizon, giving rise to naked singularities, by pushing test particles towards the black hole as, in fact, it has been demonstrated explicitly by several recent works. Our analysis allows us to go a step further and to determine the optimal values, in the sense of keeping to a minimum the backreaction effects, of the test particle electrical charge and angular momentum necessary to destroy a given near-extremal Kerr-Newman black hole. We describe briefly a possible realistic scenario for the creation of a Kerr naked singularity from some recently discovered candidates to be rapidly rotating black holes in radio galaxies., Comment: 5 pages, 2 figures. New references added, final version accepted for publication in PRD

We consider non-stationary spherically symmetric $n$-dimensional charged black holes with varying mass $m(v)$ and/or electric charge $q(v)$, described by generic charged Vaidya metrics with cosmological constant $\Lambda$ in double null coordinates, and perform a comprehensive numerical analysis of the fundamental quasinormal modes (QNM) for minimally coupled scalar fields. We show that the "instantaneous" quasinormal frequencies exhibit the same sort of non-stationary behavior reported previously for the four-dimensional uncharged case with $\Lambda=0$. Such property seems to be very robust, independent of the spacetime dimension and of the metric parameters, provided they be consistent with the existence of an event horizon. The study of time dependent Reissner-Nordstr\"om black holes allows us to go a step further and quantify the deviation of the stationary regime for QNM with respect to charge variations as well. We also look for signatures in the quasinormal frequencies from the creation of a Reissner-Nordstr\"om naked spacetime singularity. Even though one should expect the breakdown of our approach in the presence of naked singularities, we show that it is possible, in principle, to obtain some information about the naked singularity from the QNM frequencies, in agreement with the previous results of Ishibashi and Hosoya showing that it would be indeed possible to have regular scattering from naked singularities., Comment: 8 pages, 6 figures, final version to appear in PRD

Bunster and Henneaux and, separately, Deser have very recently considered the possibility of gauging the usual electromagnetic duality of Maxwell equations. By using off-shell manipulations in the context of the Principle of least action, they conclude that this is not possible, at least with the conventional compensating gauge fields scheme. Such a conclusion contradicts, however, an old result of Malik and Pradhan, who showed that it is indeed possible to introduce an extra abelian gauge field directly in the vacuum Maxwell equations in order to render them covariant under local duality transformations. Since it is well known that the equations of motion can, in general, admit more symmetries than the associate Lagrangian, this would not be a paradoxal result, in principle. Here, we revisit these works and identify the source of the different conclusions. We show that the Malik-Pradhan procedure does not preserve the original Maxwell gauge invariance, while Bunster, Henneaux, and Deser sought for generalizations which are, by construction, invariant under the Maxwell gauge transformation. Further, we show that the Malik-Pradhan construction cannot be adapted or extended in order to preserve the Maxwell gauge invariance, reinforcing the conclusion that it is not possible to gauge the electromagnetic duality., Comment: 4 pages. New reference. Final version to appear in CQG

Non-electromagnetic emissions from high energy particles in extreme environments has been studied in the literature by using several variations of the semi-classical formalism. The detailed mechanisms behind such emissions are of great astrophysical interest since they can alter appreciably the associated energy loss rates. Here, we review the role played by the source proper acceleration $a$ in the particle production process. The acceleration $a$ determines the typical scale characterizing the particle production and, moreover, if the massive particle production is inertially forbidden, it will be strongly suppressed for $a$ below a certain threshold. In particular, we show that, for the case of accelerated protons in typical pulsar magnetospheres, the corresponding accelerations $a$ are far below the pion production threshold., Comment: 3 pages. Prepared for the proceedings of the 4th School on Cosmic Rays and Astrophysics, August 25-September 04 2010, Sao Paulo Brazil

By using rather conservative estimates based on the simplest polar cap model, we search the ATNF Pulsar Catalogue for strongly magnetized stars that could accelerate relativistic protons up to the curvature pion production threshold. The best candidate turns out to be the 16 ms pulsar J0537-6910, but the corresponding characteristic parameter $\chi=a/m_p$ is yet too small to give origin to observable signals. We show that, for pulsars with period $P\approx 1\,$ms, a surface polar magnetic field $B \approx 10^{12}$G is required in order to induce detectable curvature pion radiation from accelerated protons in the magnetosphere. Some other emission processes are also considered., Comment: 5 pages, aastex style, accepted for publication in Astrophysics & Space Science

The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates $(u,v)$ describing a non-stationary charged black hole with varying mass $m(v)$ and charge $q(v)$. The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity., Comment: 4 pages. Prepared for the proceedings of the Spanish Relativity meeting (ERE2010), Granada, Spain, September 6-10, 2010

The Weierstrass random walk is a paradigmatic Markov chain giving rise to a L\'evy-type superdiffusive behavior. It is well known that Special Relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive behavior in any process occurring in Minkowski spacetime, implying, in particular, that any relativistic Markov chain describing spacetime phenomena must be essentially Gaussian. Here, we introduce a simple relativistic extension of the Weierstrass random walk and show that there must exist a transition time $t_c$ delimiting two qualitative distinct dynamical regimes: the (non-relativistic) superdiffusive L\'evy flights, for $ t < t_c$, and the usual (relativistic) Gaussian diffusion, for $t>t_c$. Implications of this crossover between different diffusion regimes are discussed for some explicit examples. The study of such an explicit and simple Markov chain can shed some light on several results obtained in much more involved contexts., Comment: 5 pages, final version to appear in PRE

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent results presented in the literature. For the case where sojourn times are identically distributed independent random variables, our results shed some light on the recently proposed transitions between ergodic and weakly nonergodic regimes. On the other hand, for the case of non-identical trapping time densities over the lattice points, the distribution of time-averaged observables reveals that such systems are typically nonergodic, in agreement with some recent experimental evidences on the statistics of blinking quantum dots. Some explicit examples are considered in detail. Our results are independent of the lattice topology and dimensionality., Comment: 8 pages, final version to appear in PRE

By using a quasi-stationary approach, we consider the mass evolution of Schwarzschild black holes in the presence of a nonminimally coupled cosmological scalar field. The mass evolution equation is analytically solved for generic coupling, revealing a qualitatively distinct behavior from the minimal coupling case. In particular, for black hole masses smaller than a certain critical value, the accretion of the scalar field can lead to mass decreasing even if no phantom energy is involved. The physical validity of the adopted quasi-stationary approach and some implications of our result for the evolution of primordial and astrophysical black holes are discussed. More precisely, we argue that black hole observational data could be used to place constraints on the nonminimally coupled energy content of the universe., Comment: 6 pages, final version to appear in PRD

We show that the common singularities present in generic modified gravity models governed by actions of the type $S=\int d^4x \sqrt{-g}f(R,\phi,X)$, with $X= -{1/2}g^{ab}\partial_a\phi\partial_b\phi$, are essentially the same anisotropic instabilities associated to the hypersurface $F(\phi)=0$ in the case of a non-minimal coupling of the type $F(\phi)R$, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface $\frac{\partial f}{\partial R}=0$ exists. Some examples are explicitly discussed., Comment: 6 pages, final version to appear in PRD

The study of chaos in relativistic systems has been hampered by the observer dependence of Lyapunov exponents (LEs) and of conditions, such as orbit boundedness, invoked in the interpretation of LEs as indicators of chaos. Here we establish a general framework that overcomes both difficulties and apply the resulting approach to address three fundamental questions: how LEs transform under Lorentz and Rindler transformations and under transformations to uniformly rotating frames. The answers to the first and third questions show that inertial and uniformly rotating observers agree on a characterization of chaos based on LEs. The second question, on the other hand, is an ill-posed problem due to the event horizons inherent to uniformly accelerated observers.

We consider the gravitational recoil due to non-reflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black-hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black-hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have been appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the non-linear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the non-axisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed., Comment: 9 pages, 6 figures, final version to appear in PRD

We revisit here the recent proposal for overspinning a nearly extreme black hole by means of a quantum tunneling process. We show that electrically neutral massless fermions evade possible back reactions effects related to superradiance, confirming the view that it would be indeed possible to form a naked singularity due to quantum effects., Comment: 4 pages. Final version to appear in PRD as a Rapid Communication