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We analyze the problem of blackbody radiation in the presence of quantum gravity effects encoded in modified dispersion relations. In this context, the spectral radiance and the generalized Stefan-Boltzmann law are studied. Furthermore, the regime of low temperatures is contemplated as well, where features related to the blackbody thermal laws and the thermodynamics quantities such as energy, pressure, entropy, and specific heat are obtained. Possible implications in compact objects such as neutron stars are also discussed., Comment: 5 pages, 3 figures

Nonlinear wave propagation in large extra spatial dimensions (on and above $d=2$) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant $\mathcal{F}\left(=-(1/4)F_{\mu\nu}F^{\mu\nu}\right)$. In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan-Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien's displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well., Comment: 9 pages, 3 figures

We study the blackbody properties and the thermodynamic equilibrium quantities of a photon gas in the framework of nonlinear electrodynamics. In this vein, we take into account the photon propagation in a uniform external magnetic field in the weak field approximation, where an angular anisotropic energy density distribution appears in the frequency spectrum. The particular case when the photon propagates perpendicular to the background magnetic field is also discussed, which allows us to probe the strong field regime. We then derive a modified blackbody spectral distribution and the Stefan-Boltzmann law in this situation. Considerations about Wien's displacement law and the Rayleigh-Jeans formula are contemplated as well. Deviations from the thermodynamic quantities at thermal equilibrium such as energy, pressure, entropy, and heat capacity densities are obtained from the Helmholtz free energy. As an application, we study three nonlinear electrodynamics, namely, the Euler-Heisenberg, the generalized Born-Infeld, and the logarithmic electrodynamics. Possible implications on stellar systems with strong magnetic fields such as magnetars are discussed., Comment: 11 pages, 1 figure

We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $\rho_0$ in the initial data. For the range of $\rho_0$ examined ($3^{\circ} \leq \rho_0 \leq 110^{\circ}$) the kick distributions as a function of the symmetric mass parameter $\eta$ satisfy a law obtained from an empirical modification of the Fitchett law, with a parameter $C$ that accounts for the non-zero net gravitational momentum wave fluxes for the equal mass case. The law fits accurately the kick distributions for the range of $\rho_0$ examined, with a rms normalized error of the order of $5 \%$. For the equal mass case the nonzero net gravitational wave momentum flux increases as $\rho_0$ increases, up to $\rho_0 \simeq 55^{\circ}$ beyond which it decreases. The maximum net kick velocity is about $190 {\rm km/s}$ for for the boost parameter considered. For $\rho_0 \geq 50^{\circ}$ the distribution is a monotonous function of $\eta$. The angular patterns of the gravitational waves emitted are examined. Our analysis includes the two polarization modes present in wave zone curvature., Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.1223

We examine numerically the gravitational wave recoil in non-axisymmetric Robinson-Trautman spacetimes. We construct characteristic initial data for the Robinson-Trautman dynamics which are interpreted as corresponding to the early post-merger state of two boosted colliding black holes with a common apparent horizon. Our analysis is based on the Bondi-Sachs energy-momentum conservation laws which regulate the radiative transfer processes involved in the emission of gravitational waves. We evaluate the Bondi-Sachs momentum flux carried out by gravitational waves and the associated net kick velocity defined (in a zero-initial-Bondi-momentum frame) as proportional to the total gravitational wave impulse imparted on the system. The kick velocity distributions are obtained and analyzed for two distinct classes of initial data corresponding to the early post-merger state of (i) non-head-on collisions and (ii) head-on collisions of black holes. For the first class (i), the net gravitational wave momentum fluxes and associated kicks are evaluated for a given domain of parameters (incidence angle and mass ratio). Typically for the equal mass case the net gravitational wave momentum flux carried is nonzero. This last result indicates that these configurations are not connected with black hole binary inspirals or head-on collisions. We suggest that these systems might be a candidate to an approximate description of the post-merger phase of a non-head-on collision of black holes not preceded by a pre-merger inspiral phase, as for instance colliding black holes in pre-merger unbounded trajectories. For the second class (ii), head-on collisions, we compare our results, and discuss the analogies, with $1+3$ numerical relativity simulations of binary black hole inspirals and head-on collisions., Comment: 10 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1202.1271

We examine numerically the process of gravitational wave recoil in the merger of two black holes in non head-on collision, in the realm of Robinson-Trautman spacetimes. Characteristic initial data for the system are constructed, and the evolution covers the post-merger phase up to the final configuration of the remnant black hole. The net momentum flux carried out by gravitational waves and the associated impulses are evaluated. Our analysis is based on the Bondi-Sachs conservation laws for the energy momentum of the system. The net kick velocity $V_{k}$ imparted to the merged system by the total gravitational wave impulse is also evaluated. Typically for a non head-on collision the net momentum flux carried out by gravitational waves is nonzero for equal-mass colliding black holes. The distribution of $V_{k}$ as a function of the symmetric mass ratio $\eta$ is well fitted by a modified Fitchett $\eta$-scaling law, the additional parameter modifying the law being a measure of the nonzero gravitational wave momentum flux for equal-mass initial black holes. For an initial infalling velocity $v/c \simeq 0.462$ of the colliding black holes, and incidence angle of collision $\rho_0=21^{o}$, we obtain a maximum $V_{k} \sim 121 {\rm km/s}$ located at $\eta \simeq 0.226$. For initial equal-mass black holes ($\eta=0.25$) we obtain $V_{k} \sim 107 {\rm km/s}$. Based on the integrated Bondi-Sachs momentum conservation law we discuss a possible definition of the center-of-mass velocity of the binary merged system and show that -- in an appropriate inertial frame -- it approaches asymptotically the net kick velocity, which is the velocity of the remnant black hole in this inertial frame. For larger values of $v/c$ we obtain substantially larger values of the net kick velocity, e.g., for $v/c \simeq 0.604$ a maximum $V_{k} \sim 610 {\rm km/s}$ is obtained., Comment: 11 pages, 7 figures

We examine numerically the post-merger regime of two Schwarzschild black holes in non head-on collision. Our treatment is made in the realm of non-axisymmetric Robinson-Trautman spacetimes which are appropriate for the description of the system. Characteristic initial data for the system are constructed and the Robinson-Trautman equation is integrated using a numerical code based on the Galerkin spectral method. The collision is planar, restricted to the plane determined by the directions of the two initial colliding black holes, with the net momentum fluxes of gravitational waves confined to this plane. We evaluate the efficiency of mass-energy extraction, the total energy and momentum carried out by gravitational waves and the momentum distribution of the remnant black hole. Our analysis is based on the Bondi-Sachs four momentum conservation laws. Head-on collisions and orthogonal collisions constitute, respectively, upper and lower bounds to the power emission and to the efficiency of mass-energy extraction by gravitational waves. The momentum extraction and the pattern of the momentum fluxes, as a function of the incidence angle, are examined. The momentum extraction characterizes a regime of strong deceleration of the system. The angular pattern of gravitational wave signals is also examined. They are typically bremsstrahlung for early times emission. Gravitational waves are also emitted outside the plane of collision but this component has a zero net momentum flux. The relation between the incidence angle of collision and the exit angle of the remnant closely approximates a relation for inelastic collisions of classical particles in Newtonian dynamics., Comment: 18 pages, 12 Figures, published with slight modifications in Phys. Rev. D 85, 024003 (2012)

We present an alternative scheme of finding apparent horizons based on spectral methods applied to Robinson-Trautman spacetimes. We have considered distinct initial data such as representing the spheroids of matter and the head-on collision of two non-rotating black holes. The evolution of the apparent horizon is presented. We have obtained in some cases a mass gap between the final Bondi and apparent horizon masses, whose implications were briefly commented in the light of the thermodynamics of black holes., Comment: 9 pages, 7 figures

The dynamics of the gravitational collapse is examined in the realm of string based formalism of D-branes that encompass General Relativity as a low energy limit. A complete analytical solution is given to the spherically symmetric collapse of a pure dust star, including its matching with a corrected Schwarzschild exterior spacetime. The collapse forms a black hole (an exterior event horizon) enclosing not a singularity but perpetually bouncing matter in the infinite chain of spacetime maximal analytical extensions inside the outer event horizon. This chain of analytical extensions has a structure analogous to that of the Reissner-Nordstrom solution, except that the timelike singularities are avoided by bouncing barriers. The interior trapped bouncing matter has the possibility of being expelled by disruptive nonlinear resonance mechanisms., Comment: 4 pages, 2 figures

We examine the efficiency of gravitational bremsstrahlung production in the process of head-on collision of two boosted Schwarzschild black holes. We constructed initial data for the characteristic initial value problem in Robinson-Trautman spacetimes, that represent two instantaneously stationary Schwarzschild black holes in motion towards each other with the same velocity. The Robinson-Trautman equation was integrated for these initial data using a numerical code based on the Galerkin method. The final resulting configuration is a boosted black hole with Bondi mass greater than the sum of the individual mass of each initial black hole. Two relevant aspects of the process are presented. The first relates the efficiency $\Delta$ of the energy extraction by gravitational wave emission to the mass of the final black hole. This relation is fitted by a distribution function of non-extensive thermostatistics with entropic parameter $q \simeq 1/2$; the result extends and validates analysis based on the linearized theory of gravitational wave emission. The second is a typical bremsstrahlung angular pattern in the early period of emission at the wave zone, a consequence of the deceleration of the black holes as they coalesce; this pattern evolves to a quadrupole form for later times., Comment: 16 pages, 4 figures, to appear in Int. J. Modern Phys. D (2008)

In this paper we explore one of the most important features of the Galerkin method, which is to achieve high accuracy with a relatively modest computational effort, in the dynamics of Robinson-Trautman spacetimes., Comment: 7 pages, 5 figures

We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin method that allows us to reduce the equations governing the dynamics to a finite-dimensional dynamical system, after a proper truncation procedure. Amongst the obtained results of the nonlinear evolution, one of the most impressive is the fact that the distribution of the mass fraction extracted by gravitational wave emission satisfies the distribution law of nonextensive statistics and this result is independent of the initial configurations considered., Comment: 3 page, 1 figure, proceedings of the X Marcel Grossmann Meeting 22-26 July, 2003, Rio de Janeiro

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer., Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev. D

We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary differential equations for modal coefficients, after a convenient truncation procedure, largely applied to problems of turbulence. In the present case, we have generated a finite dynamical system that reproduces the essential features of the dynamics of the gravitational collapse, even for a lower order of truncation. Each initial condition in the space of modal coefficients corresponds to a well definite spatial distribution of scalar field. Numerical experiments with the dynamical system show that depending on the strength of the scalar field packet, the formation of black-holes or the dispersion of the scalar field leaving behind flat spacetime are the two main outcomes. We also found numerical evidence that between both asymptotic states, there is a critical solution represented by a limit cycle in the modal space with period $\Delta u \approx 3.55$., Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in press

We describe a new statistical pattern in the chaotic dynamics of closed inflationary cosmologies, associated with the partition of the Hamiltonian rotational motion energy and hyperbolic motion energy pieces, in a linear neighborhood of the saddle-center present in the phase space of the models. The hyperbolic energy of orbits visiting a neighborhood of the saddle-center has a random distribution with respect to the ensemble of initial conditions, but the associated histograms define a statistical distribution law of the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered. We present numerical evidence that $\gamma$ determines the dimension of the fractal basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense that it does not depend on the parameters of the models and is scale invariant. We discuss possible physical consequences of this universality for the physics of inflation.tribution law of the form $p(x) = C x^{-\gamma}$, for almost the whole range of hyperbolic energies considered. We present numerical evidence that $\gamma$ determines the dimension of the fractal basin boundaries in the ensemble of initial conditions. This distribution is universal in the sense that it does not depend on the parameters of the models and is scale invariant. We discuss possible physical consequences of this universality for the physics of inflation., Comment: 5 pages, 4 figures, submitted to Physical Review D

We exhibit a resonance mechanism of amplification of density perturbations in inflationary mo-dels, using a minimal set of ingredients (an effective cosmological constant, a scalar field minimally coupled to the gravitational field and matter), common to most models in the literature of inflation. This mechanism is based on the structure of homoclinic cylinders, emanating from an unstable periodic orbit in the neighborhood of a saddle-center critical point, present in the phase space of the model. The cylindrical structure induces oscillatory motions of the scales of the universe whenever the orbit visits the neighborhood of the saddle-center, before the universe enters a period of exponential expansion. The oscillations of the scale functions produce, by a resonance mechanism, the amplification of a selected wave number spectrum of density perturbations, and can explain the hierarchy of scales observed in the actual universe. The transversal crossings of the homoclinic cylinders induce chaos in the dynamics of the model, a fact intimately connected to the resonance mechanism occuring immediately before the exit to inflation., Comment: 4 pages. This essay received an Honorable Mention from the Gravity Research Foundation, 1998-Ed. To appear in Mod. Phys. Lett. A

We show that homogeneous and isotropic cosmological models with radiation and scalar field have, in general, two possible chaotic exits to inflation. These models may describe the early stages of inflation. The central point of our analysis is based on the possible existence of one or two saddle-centers points in the phase space of the models., Comment: 3 pages, 4 figures, lateX (mprocl.sty). To appear in the proceedings of the Eighth Marcel Grossmann Meeting, Jeruslaem, June 1997

We show that anisotropic Bianchi type-IX models, with matter and cosmological constant have chaotic dynamics, connected to the presence of a saddle-center in phase space. The topology of cylinders emanating from unstable periodic orbits about the saddle-center provides an invariant characterization of chaos in the models. The model can be thought to describe the early stages of inflation, the way out to inflation being chaotic., Comment: 3 pages, Latex (mprocl.sty), 4 figures. To appear in the proceedings of the Eighth Marcel Grossmann Meeting, Jerusalem, June 1997

A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational perturbations of the Robinson-Trautman type on the Schwarzschild spacetime. In our scheme of perturbation, gravitational waves may extract mass from the collapsing configuration. Robinson-Trautmann perturbations also include another mode of emission of mass, which we denote shell emission mode: in the equatorial plane of the configuration, a timelike $(1+2)$ shell of matter may be present, whose stress-energy tensor is modelled by neutrinos and strings emitted radially on the shell; no gravitational waves are present in this mode. The invariant characterization of gravitational wave perturbations and of the gravitational wave zone is made through the analysis of the structure of the curvature tensor and the use of the Peeling Theorem., Comment: 26 pages, LaTex, no figures

We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation. The concurrence of the cosmological constant and anisotropy are sufficient to produce a chaotic dynamics in the gravitational degrees of freedom, connected to the presence of a critical point of saddle-center type in the phase space of the system. The invariant character of chaos is guaranteed by the topology of the cylinders emanating from unstable periodic orbits in the neighborhood of the saddle-center. We discuss a possible mechanism for amplification of specific wavelengths of inhomogeneous fluctuations in the models. A geometrical interpretation is given for Wald's inequality in terms of invariant tori and their destruction by increasing values of the cosmological constant., Comment: 14 pages, figures available under request. submitted to Physical Review D

The gravitational properties of the {\em only} static plane-symmetric vacuum solution of Einstein's field equations without cosmological term (Taub's solution, for brevity) are presented: some already known properties (geodesics, weak field limit and pertainment to the Schwarzschild family of spacetimes) are reviewed in a physically much more transparent way, as well as new results about its asymptotic structure, possible matchings and nature of the source are furnished. The main results point to the fact that the solution must be interpreted as representing the exterior gravitational field due to a {\em negative} mass distribution, confirming previous statements to that effect in the literature. Some analogies to Kasner's spatially homogeneous cosmological model are also referred to., Comment: plain LaTex, four Postscript figures