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The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximum electric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnet gravity as well as general relativity. The charged gravitational collapse process is also similar for all dimensions N ≥ 5 unlike in the neutral scenario where there is a marked difference between the N = 5 and N > 5 cases. In the case where N = 5 uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, before succumbing to an event horizon. The similarity of charged collapse for all higher dimensions is a unique feature in the theory. The sufficient conditions for the formation of a naked singularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein–Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested and it is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible. [ABSTRACT FROM AUTHOR]

In gravitational collapses, the horizon and singularity's realisation in the finite future of the proper time used co-moving observer happens in the future of infinitely far away future of the normal time used outside probe. To the latter the horizon and singularity defined in the singularity theorem are physical realities only in the sense of uncertainty principle and ensemble interpretation. We provide two exact time dependent solution families to the Einstein equation and show that they form a pair of complementary description for the microscopic state of black holes by showing that the Bekenstein–Hawking entropy formula follows properly from their canonical wave function's degeneracy. We also develop an eXact One Body method for general relativity two-body dynamics whose conservative part calls no post newtonian approximation as input and applies to the full three stages of black hole binary merger events. By this method, we analytically calculate the gravitational wave forms following from such merger processes. In the case black holes carry exact and apriori horizon and singularity our wave forms agree with those following from conventional effective one body method but exhibit more consistent late time behaviour. In the case black holes carry only asymptotic horizon and extended inner structure thus experiencing banana shape deformation as the merger occurs, our wave forms exhibit all features especially the late time quasi-normal mode type oscillation seen in real observations. [ABSTRACT FROM AUTHOR]

Primordial black holes (PBHs) are known as one of the potential candidates for dark matter. They are expected to have formed due to the direct gravitational collapse of density fluctuations in the early Universe. In this regard, examining the merger rate of PBHs within modified theories of gravity can offer a deeper insight into their abundance. In this work, we delve into the calculation of the merger rate of PBHs within the theoretical framework of f (R) gravity. Our analysis reveals an enhancement in the merger rate of PBHs compared to that obtained from general relativity. Additionally, modulating the field strength f R0 induces shifts in the PBH merger rate, presenting a potential observational signature of modified gravity. We also explore the upper bounds on the abundance of PBHs obtained from f (R) gravity models by comparing the results with gravitational-wave and observational data. The results indicate that in certain regions not excluded by benchmarking data, the parameter space for these upper bounds may be considered reliable. [ABSTRACT FROM AUTHOR]

In this paper, we present some new static and spherically symmetric solutions of the Einstein equation in which the matter sector is accounted for by a free Dirac–Born–Infeld field. Our novel spacetimes can describe either a black hole, a wormhole, or a naked singularity depending on certain boundary conditions. By tracking the dynamical gravitational collapse, we enlighten the importance of the isotropy of the pressure for having an horizon as a result, as required by the Cosmic Censorship Conjecture. Our new spacetime solutions, the amount of exotic matter, its "complexity", and the equation of state along the tangential direction are analytical and written in closed forms. We identify a taming of the breaking of the null energy condition, customary for wormhole spacetimes in General Relativity, along both the radial and tangential direction. We assess the astrophysical applicability and perform a comparative analysis between our solutions and other literature ones, by identifying an ISO-like density profile of the matter field, which provides a flattening of the rotation curves, by discussing the motion of test particles, and the shadow properties. In our model, those effects are interpreted as a manifestation of a topological defect, and since they can observationally mimic the signatures of other spacetimes, a study of the perturbations is performed within the quasi-normal modes formalism. Having identified the Reissner–Nordström-like quasi-resonance, our paper is intended also to provide some insights on which combinations of background and perturbation properties should be observed, for claiming the nature of astrophysical compact objects. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class. Leveraging a profile root-finding technique based on General Relativity we describe an ANN solver to directly tackle the system of ordinary differential equations. Through our extensive numerical analysis, we demonstrate, for the first time, that there is no self-similar critical solution for the parabolic class in the high dimensions of space-time. Specifically, we develop 95% ANN-based confidence intervals for all the solutions in their domains. At the 95% confidence level, our ANN estimators confirm that there is no black hole solution in higher dimensions, hence the gravitational collapse does not occur. Results provide some doubts about the universality of the Choptuik phenomena. Therefore, we conclude that the fastest-growing mode of the perturbations that determine the critical exponent does not exist for the parabolic class in the high dimensions. [ABSTRACT FROM AUTHOR]

Magnetic fields are a very special form of elastic medium. Within astrophysical environments (magnetized stars and protogalaxies) they counteract shear and rotational distortions as well as gravitational collapse. Their vector nature allows for their extraordinary coupling with space–time curvature in the framework of general relativity. This particular coupling points out the way to study magnetic elasticity under gravitational deformation. In this context, we reveal their law of elasticity, calculate their fracture limit and subsequently argue that they ultimately lose the battle against gravitational contraction of magnetized matter. Two illustrative applications, in a neutron star and a white dwarf, accompany the results. [ABSTRACT FROM AUTHOR]

We study gravitational collapse for the Starobinsky R2 model, a particular example of an f(r) theory, in a spherically symmetric spacetime. We add a massless scalar field as matter content to the spacetime. We work in the Einstein frame, where an additional scalar field arises due to the conformal transformation. As in general relativity, depending on the initial data, we found that the gravity scalar field and the physical scalar field can collapse, forming a black hole, in which the final solution is the Schwarzschild metric. We found the threshold of black hole formation through a fine-tuning method and studied critical collapse near this regime. [ABSTRACT FROM AUTHOR]

In this paper, we treat 4-dimensional Einstein–Gauss–Bonnet (EGB) gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer–Snyder–Datt model of the gravitational collapse of a star in a 4-dimensional EGB black hole (BH). The inside geometry of the star is described by the spatially flat Friedmann–Robertson–Walker metric and the matter is distributed uniformly without any pre-assumption about its equation of state. The exterior EGB BH is smoothly matched to the interior geometry without the requirement of any thin shell. This gives the energy density, pressure, and the equation of state of collapsing matter. At the end, we study the time evolution of event and apparent horizons. [ABSTRACT FROM AUTHOR]

In this paper, we investigate spherically symmetric gravitational collapse of thick matter shell without radiation in the Einstein gravity with cosmological constant. The orbit of the infalling thick matter is determined by imposing an equation of state for the matter near interface, where pressure constituted of the transverse component and the longitudinal one is proportional to energy density. We present analytic solutions for the equation of state and discuss parameter region to satisfy physical conditions such as the absence of the shell crossing singularity, the monotonic increase of the emergent infinite redshift surface and energy conditions. We finally show that adopting the definition presented in arXiv:2005.13233 the total energy in this time-dependent system is invariant under the given time evolution. [ABSTRACT FROM AUTHOR]

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein's equations is obtained, characterized by an interior de Sitter region of p = − ρ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order k B ℓ M c / ℏ , instead of the Bekenstein–Hawking entropy, S B H = 4 π k B G M 2 / ℏ c . Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox. [ABSTRACT FROM AUTHOR]

In this paper, we make a close comparison of a covariant definition of an energy/ entropy in general relativity, recently proposed by a collaboration including the present authors, with existing definitions of energies such as the one from the pseudo-tensor and the quasi-local energy. We show that existing definitions of energies in general relativity are conserved charges from Noether's second theorem for the general coordinate transformation, whose conservations are merely identities implied by the local symmetry and always hold without using equations of motion. Thus, none of the existing definitions in general relativity reflects the dynamical properties of the system, and the need for a physical definition of an energy. In contrast, our new definition of the energy/ entropy in general relativity is generically a conserved non-Noether charge and gives physically sensible results for various cases such as the black hole mass, the gravitational collapse and the expanding universe, while existing definitions sometimes lead to unphysical ones including zero and infinity. We conclude that our proposal is more physical than existing definitions of energies. Our proposal makes it possible to define almost uniquely the covariant and conserved energy/ entropy in general relativity, which brings some implications to future investigations. [ABSTRACT FROM AUTHOR]

Spherical energy shells in General Relativity tend to collapse due to gravitational effects and/or due to tension effects. Shell stabilization may be achieved by modifying the gravitational properties of the background spacetime. Thus, gravastars consist of stiff matter shells with an interior deSitter space and an exterior Schwarzshild spacetime whose attractive gravity balances the interior repulsive gravity of the interior deSitter spacetime leading to a stable stiff matter shell. Similar stabilization effects may be achieved by considering rotating shells. Here we study the stability of slowly rotating fluid shells. We show that the angular velocity of the shell has stabilizing properties analogous to the repulsive deSitter gravity of the interior of a gravastar. We thus use the Israel junction conditions [W. Israel, Nuovo Cim. B44S10 (1966) 1, Erratum: Nuovo Cim. B48 (1967) 463; N. Deruelle, M. Sasaki and Y. Sendouda, Prog. Theor. Phys.119 (2008) 237, arXiv:0711.1150 [gr-qc]] and the fluid equation of state of the rotating shell to construct the dynamical equations that determine the evolution of the rotating shell radius. These dynamical equations depend on the parameters of the background spacetime and on the angular velocity of the shell. Assuming a rotating interior and a Schwarzschild exterior spacetime we show that the angular velocity of the shell has interesting stabilizing properties on the evolution of its radius R. Thus, rotating matter (or vacuum) shells can imitate black holes while avoiding the presence of a singularity and without the presence of an interior deSitter space. [ABSTRACT FROM AUTHOR]

By following up on three papers that (1) were previously published, and (2) following Einstein's 1954 speculations, it is possible physics is based on a discontinuum theory, and the continuum concept along with space and time must be discarded, a table of realities is developed and used for making predictions. These predictions include (1) discontinuum gravity is required to detail a gravitational collapse, which means (2) general relativity is falsified, and (3) there are discontinuum gravity blackholes, not general relativity blackholes, and (4) there are no general relativity singularities. [ABSTRACT FROM AUTHOR]

We analyze the Wheeler–DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Robertson–Walker metric in which the WDW equation takes the form of a times-less Schrödinger equation. We set up the corresponding WDW potential for the collapse and study the solutions of the wave function. The results show that the central singularity appearing in classical general relativity is avoided, the density is quantized in terms of the Planck density and the expectation value of the scale factor exhibits a discrete behavior. • Wheeler–DeWitt equation applied to gravitational collapse reveals quantum effects inside black holes. • Classical central singularity in gravitational collapse avoided through quantum mechanics. • Quantization of matter density in gravitational collapse, linked to Planck density. • Wave function behavior indicates discrete quantum dynamics in gravitational collapse scenarios. • Study explores quantum gravity's impact on the late stages of astrophysical system collapse. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of f (ℛ , μ ν μ ν) gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory. [ABSTRACT FROM AUTHOR]

The current work is a review, dedicated to the study of semiclassical aspects of black holes. We begin by briefly looking at the main statements of general relativity. We then consider the Schwarzschild, Kerr, and Reissner-Nordstrom black hole solutions and discuss their geometrical properties. Later, the thermodynamic nature of black holes is established. In light of this, we formulate the information loss problem and present the most promising approaches for addressing it with emphasis on introducing low-energy quantum corrections to the classical general relativity picture. Finally, in the context of multimessenger astronomy, we look at naked singularities as possible gravitational collapse endstates and their role in the unitarity of quantum mechanics and discuss their observational prospects. [ABSTRACT FROM AUTHOR]

The concept of black holes or completely collapsed gravitational objects as they were originally called has fascinated the scientific community and writers of science fiction for centuries. The mathematical proof of the existence of black holes came from the collation of multiple lines of evidence, some of which were highly debated and was derived from both indirect and direct sources. The measurement of gravitational waves and the observation of a black hole represent one of the most astounding achievements in astrophysics which will open up new areas of investigation for the role that black holes play in the formation, maintenance and evolution of galactic structure. [ABSTRACT FROM AUTHOR]

Although it is not a fundamental question, determining exact and general solutions for a given theory has advantages over a numerical integration in many specific cases. Of course, respecting the peculiarities of the problem. Revisiting the integration of the General Relativity Theory field equations for the Kantowski–Sachs spacetime describes a homogeneous but anisotropic universe whose spatial section has the topology of R × S 2 , we integrate the equations for arbitrary curvature parameter and write the solutions considering the process of gravitational collapse. We took the opportunity and made some comments involving some features of the model such as energy density, shear, viscosity and the production of gravitational waves via Petrov classification. [ABSTRACT FROM AUTHOR]

Scientific discoveries are not made in vacuum; they all have a background (or shoulders of Giants to stand on in Newton's pronouncement) to anchor and build on. The famous and powerful singularity theorems of Hawking and Penrose of mid-1960s were strongly anchored on the remarkable Raychaudhri equation discovered in 1953. The most remarkable and profound prediction that followed from the equation was that gravitational collapse would inevitably lead to singularity in Einstein's theory of gravitation - general relativity. Hawking and Penrose generalized and located this result to a more general setting that Einstein's equation under very general conditions cannot admit a solution that has no singularity. They proved powerful rigorous mathematical theorems employing the techniques of global analysis that gravitational collapse would not only end up in singularity but before that a black hole would be formed. It is this robust prediction that has won Roger Penrose the 2020 Nobel Prize in Physics. In this note, I will recount the Indian contributions that have gone into making the background. [ABSTRACT FROM AUTHOR]

We present a method for solving the constraint equations in the Hassan–Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane–Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen–Birkhoff theorem in bimetric relativity. [ABSTRACT FROM AUTHOR]

In general relativity, the endpoint of spherically symmetric gravitational collapse is a Schwarzschild–[(A)dS] black hole. In bimetric gravity, it has been speculated that a static end state must also be Schwarzschild–[(A)dS]. To this end, we present a set of exact solutions, including collapsing massless dust particles. For these, the speculation is confirmed. [ABSTRACT FROM AUTHOR]

In this paper, we employ the Karmarkar condition to model a spherically symmetric radiating star undergoing dissipative gravitational collapse within the framework of classical general relativity. The collapse ensues from an initial static core satisfying the Karmarkar condition in isotropic coordinates and proceeds nonadiabatically by emitting energy in the form of a radial heat flux to the exterior Vaidya spacetime. We show that the dynamical nature of the collapse is sensitive to the initial static configuration that inherently links the embedding to the final remnant. Our model considered several physical tests on how an initially static stellar structure onset to a radiative collapse. [ABSTRACT FROM AUTHOR]

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein's theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein's field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes. [ABSTRACT FROM AUTHOR]

The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses that result in the formation of black holes. If singularities — except the one at the Big Bang — ever become "naked," i.e. not shrouded by black hole horizons, then it is expected that problems would arise and render general relativity indeterministic. For this reason, Penrose proposed the cosmic censorship conjecture, which states that singularities should never be naked. Various counterexamples to the conjecture have since been discovered, but it is still not clear under which kind of physical processes one can expect violation of the conjecture. In this short review, I briefly examine some progresses in space–time singularities and cosmic censorship conjecture. In particular, I shall discuss why we should still care about the conjecture, and whether we should be worried about some of the counterexamples. This is not meant to be a comprehensive review, but rather to give an introduction to the subject, which has recently seen an increase of interest. [ABSTRACT FROM AUTHOR]

We revisit the accretion-induced collapse (AIC) process, in which a white dwarf collapses into a neutron star. We are motivated by the persistent radio source associated with the fast radio burst FRB 121102, which was explained by Waxman as a weak stellar explosion with a small (∼10−5 M⊙) mildly relativistic mass ejection that may be consistent with AIC. Additionally, the interaction of the relatively low ejected mass with a pre-collapse wind might be related to fast optical transients. The AIC is simulated with a one-dimensional, Lagrangian, Newtonian hydrodynamic code. We put an emphasis on accurately treating the equation of state and the nuclear burning, which is required for any study that attempts to accurately simulate AIC. We leave subjects such as neutrino physics and general relativity corrections for future work. Using an existing initial profile and our own initial profiles, we find that the ejected mass is ∼10−2 to 10−1 M⊙ over a wide range of parameters, and we construct a simple model to explain our results. [ABSTRACT FROM AUTHOR]

In this investigation, we study the structure of ultra‐compact stars in the framework of semiclassical gravity, an extension of Einstein's general relativity (GR), in which a classical spacetime metric is coupled to the quantum expectation value of the stress tensor and that incorporates the polarization of the quantum vacuum in the presence of a gravitational field. In this approach, a generalization of the classical Tolman–Oppenheimer–Volkoff (TOV) equations may be derived. Unlike most theoretical treatments based on GR, this formulation allows a wider range of consistent equation of state (EoS) solutions with enough compactness to produce a photon sphere without violating the Buchdahl limit, an upper bound on the compactness, thus motivating future studies to investigate if ultra‐compact stars could act as black hole mimickers. The main novelty of this extended formalism, when compared to the conventional form of the TOV equations, is the presence of an additional repulsive term—due to quantum corrections originated by the phenomenon of quantum vacuum polarization—that can withstand, under certain conditions, the gravitational collapse. Although the quantum corrections furnished by semiclassical gravity are negligible in most compact stars scenarios, for ultra‐compact configurations, where the star radius is not much larger than its gravitational radius, such effects may be relevant. [ABSTRACT FROM AUTHOR]

We present a study of dissipative gravitational collapse in spherically symmetric gravitating spacetime by applying the Misner–Sharp approach in metric f(R, T) gravity. This work is an extension of the study by Herrera, Di Prisco, Fuenmayor, and Troconis, Int. J. Mod. Phys. D, 18, 129 (2009), that was already done with the general theory of relativity. To this end, we have formulated a set of equations of motion by using f(R, T) = R + λT (where R is the Ricci scalar, T is the trace of stress–energy tensor, and λ is the coupling constant), as well as a stress–energy tensor of viscous and heat conducting fluid. The conservation equations have been also derived for such setup. Both the conservation equations and equation of motion provide the dynamical equations in terms of the theory of gravity. Furthermore, the causal thermodynamic approach introduced by Müller–Israel–Stewart has been used to formulate the transportation equations of heat flux and bulk viscosity. Then, we perform the coupling of dynamical equations and transportation equations. The effects of bulk and shear viscosities have been investigated in detail. Finally, we studied the impact of the matter curvature coupling parameter λ on the dynamics of the gravitating source. [ABSTRACT FROM AUTHOR]

We study spherically symmetric gravitational collapse of a homogeneous perfect fluid in Rastall gravity. Considering a linear equation of state (EoS) for the fluid profiles, we examine the conditions under which the collapse scenario could end in a spacetime singularity. Depending on the model parameters, the singularity could be either naked or covered by a horizon. We find that a non-vanishing Rastall parameter could affect the formation of apparent horizon so that, naked singularities may form for those values of EoS parameter for which a homogeneous perfect fluid collapse in general relativity (GR) terminates at the black hole formation. Hence the visibility of the resulting singularity depends on the Rastall parameter. The solutions we obtain respect the weak energy condition (WEC) which is crucial for physical validity of the model. [ABSTRACT FROM AUTHOR]

Abstract We calculate the interior volume for the three-dimensional Banados–Teitelboim–Zanelli black hole in this paper. To that end, we obtain the volume functional and numerically find a path to extremize it, before choosing a spacelike hypersurface to get an asymptotic analytical expression for the interior volume based on the characteristics of the path. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of perfect fluid spherical collapse in curvature-matter coupled gravity. Using Darmois junction conditions, we derive smooth matching of both interior and exterior regions. The dynamical equations are formulated through Misner–Sharp formalism that give the collapse rate for both general and constant curvature terms. Finally, we formulate a relationship between correction terms, Weyl scalar and matter variables. For constant value of f (𝒢 , T) , it is found that the metric is conformally flat if and only if energy density of the collapsing system is homogeneous while the positive correction terms decrease the collapse rate. [ABSTRACT FROM AUTHOR]

The realistic models of neutron stars are considered for simple R + α R 2 gravity and equivalent Brance–Dicke theory with dilaton field in Einsein frame. For negative values of α we have no acceptable results from astrophysical viewpoint: the resulting solution for spherical stars doesn't coincide with Schwarzschild solution on spatial infinity. The mass of star from viewpoint of distant observer tends to very large values. For α > 0 it is possible to obtain solutions with required asymptotics and well-defined star mass. The mass confined by stellar surface decreases with increasing of α but we have some contribution to mass from gravitational sphere appearing outside the star. The resulting effect is increasing of gravitational mass from viewpoint of distant observer. But another interpretation take place in a case of equivalent Brance–Dicke theory with massless dilaton field in Einstein frame. The mass of star increases due to contribution of dilaton field inside the star. We also considered the possible constraints on R 2 gravity from GW 170817 data. According to results of Bauswein et al. the lower limit on threshold mass is 2. 7 4 − 0. 0 1 + 0. 0 4 M ⊙ . This allows to exclude some equations of state (EoS) for dense matter. But in R 2 gravity the threshold mass increases for given EoS with increasing of α. In principle it can helps in future discriminate between General Relativity and square gravity (of course one need to know EoS with more accuracy rather than now). [ABSTRACT FROM AUTHOR]

In this paper, all possible orbits of test particles are investigated by using the phase plane method in regular Hayward black hole space–time. Our results show that the time-like orbits are divided into four types: unstable circular orbits, separates stable orbits, stable hyperbolic orbits, and elliptical orbits in regular Hayward black hole space–time. We find that the orbital properties vary with the change of ℓ (a convenient encoding of the central energy density 3/8πℓ2). If ℓ = 1/3 and b < 3.453 21, the test particles moving toward the black hole will definitely plunge into the black hole. In addition, it is obtained that the innermost stable circular orbit happens at rmin = 5.930 55 for b = 3.453 21. [ABSTRACT FROM AUTHOR]

We use perturbation theory in the strong-field regime to study the inspiral-to-plunge transition of a test particle into a Kerr black hole. We found a smooth transition, without burst, and with lower energy and angular momentum radiated in gravitational waves with respect to previous treatments in the literature. Besides their theoretical interest, our results are relevant for the waveform templates of binary black hole mergers used for gravitational waves detection which are constructed on the basis of a inspiral-to-plunge transition with a high energetic burst. [ABSTRACT FROM AUTHOR]

The Induced Gravitational Collapse (IGC) paradigm points to a binary origin for the longduration gamma-ray burst (GRBs) associated with supernovae (SN). In this one, a carbon-oxygen core (COcore) explodes in a Type Ib/c SN in presence of a close neutron star (NS) companion. The SN triggers a hypercritical accretion into the NS and depending on the initial binary parameters, two outcomes are possible givimg place to two family of long GRBs: binary-driven hypernova (BdHNe), where the NS reaches its critical mass, and collapses to a black hole (BH), emitting a GRB; and x-ray flashes (XRFs) where the hypercritical accretion onto the NS is not sufficient to induce its gravitational collapse. We perform 3-dimensional (3D) numerical simulations of the IGC paradigm with the smoothed particle hydrodynamics (SPH) technique. We determine whether the star gravitational collapse is possible and assess if the binary holds gravitationally bound or it becomes unbound by the SN explosion. [ABSTRACT FROM AUTHOR]

We make use of a perturbative scheme to implement an equation of state guided, gravitational collapse of a compact stellar object. General relativity is used in which a spherically symmetric spacetime in Schwarzschild coordinates is assumed with an appropriate energy–momentum tensor allowing for heat-flux. For the dissipative collapse, the Vaidya metric is used for the exterior with the required matching to the interior metric. An initial static configuration is firstly set up and then a linear equation of state is used to assist in closing the system of equations for the perturbative part. The resulting model is physically viable and the effect of shearing stresses are examined in terms of the luminosity. We see that shearing augments the luminosity and duration of the collapse process. Further improvements in the modelling process are believed possible by using more sophisticated gravitational potentials and equations of state. [ABSTRACT FROM AUTHOR]

We consider the 'kinematics' of space-like congruences and apply them to a family of selfgravitating magnetic forcelines. Our aim is to investigate the convergence and the possible focusing of these lines, as well as their rotation and shear deformation. In so doing, we introduce a covariant 1+2 splitting of the 3-D space, parallel and orthogonal to the direction of the field lines. The convergence, or not, of the latter is monitored by a specific version of the Raychaudhuri equation, obtained after propagating the spatial divergence of the unit magnetic vector along its own direction. The resulting expression shows that, although the convergence of the magnetic forcelines is affected by the gravitational pull of all the other sources, it is unaffected by the field's own gravity, irrespective of how strong the latter is. This rather counterintuitive result is entirely due to the magnetic tension, namely to the negative pressure the field exerts parallel to its lines of force. In particular, the magnetic tension always cancels out the field's energy-density input to the Raychaudhuri equation, leaving the latter free of any direct magnetic-energy contribution. Similarly, the rotation and the shear deformation of the aforementioned forcelines are also unaffected by the magnetic input to the total gravitational energy. In a sense, the magnetic lines do not seem to 'feel' their own gravitational field no matter how strong the latter may be. [ABSTRACT FROM AUTHOR]

We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution. [ABSTRACT FROM AUTHOR]

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two-fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered. [ABSTRACT FROM AUTHOR]

We implement a spatially fixed mesh refinement under spherical symmetry for the characteristic formulation of General Relativity. The Courant-Friedrich-Levy condition lets us deploy an adaptive resolution in (retarded-like) time, even for the nonlinear regime. As test cases, we replicate the main features of the gravitational critical behavior and the spacetime structure at null infinity using the Bondi mass and the News function. Additionally, we obtain the global energy conservation for an extreme situation, i.e. in the threshold of the black hole formation. In principle, the calibrated code can be used in conjunction with an ADM 3+1 code to confirm the critical behavior recently reported in the gravitational collapse of a massless scalar field in an asymptotic anti-de Sitter spacetime. For the scenarios studied, the fixed mesh refinement offers improved runtime and results comparable to code without mesh refinement. [ABSTRACT FROM AUTHOR]

The Schwarzschild interior solution, or 'Schwarzschild star', which describes a spherically symmetric homogeneous mass with a constant energy density, shows a divergence in pressure when the radius of the star reaches the Schwarzschild--Buchdahl bound. Recently, Mazur and Mottola showed that this divergence is integrable through the Komar formula, inducing non-isotropic transverse stresses on a surface of some radius R0. When this radius approaches the Schwarzschild radius Rs = 2 M, the interior solution becomes one of negative pressure evoking a de Sitter space--time. This gravitational condensate star, or gravastar, is an alternative solution to the idea of a black hole as the ultimate state of gravitational collapse. Using Hartle's model to calculate equilibrium configurations of slowly rotating masses, we report results of surface and integral properties for a Schwarzschild star in the very little studied region Rs < R < (9/8)Rs. We found that in the gravastar limit, the angular velocity of the fluid relative to the local inertial frame tends to zero, indicating rigid rotation. Remarkably, the normalized moment of inertia I/MR² and the mass quadrupole moment Q approach the corresponding values for the Kerr metric to second order in Ω. These results provide a solution to the problem of the source of a slowly rotating Kerr black hole. [ABSTRACT FROM AUTHOR]

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose's singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity. [ABSTRACT FROM AUTHOR]

This article argues that a consistent description is possible for gravitationally collapsed bodies, in which collapse stops before the object reaches its gravitational radius, the density reaching a maximum close to the surface and then decreasing towards the centre. The way towards such a description was indicated in the classic Oppenheimer-Snyder (OS) 1939 analysis of a dust star. The title of that article implied support for a black-hole solution, but the present article shows that the final OS density distribution accords with gravastar and other shell models. The parallel Oppenheimer-Volkoff (OV) study of 1939 used the equation of state for a neutron gas, but could consider only stationary solutions of the field equations. Recently we found that the OV equation of state permits solutions with minimal rather than maximal central density, and here we find a similar topology for the OS dust collapsar; a uniform dust-ball which starts with large radius, and correspondingly small density, and collapses to a shell at the gravitational radius with density decreasing monotonically towards the centre. Though no longer considered central in black-hole theory, the OS dust model gave the first exact, time-dependent solution of the field equations. Regarded as a limiting case of OV, it indicates the possibility of neutron stars of unlimited mass with a similar shell topology. Progress in observational astronomy will distinguish this class of collapsars from black holes. [ABSTRACT FROM AUTHOR]

The concept of dark energy can be a candidate for preventing the gravitational collapse of compact objects to singularities. According to the usefulness of gravity's rainbow in UV completion of general relativity (by providing a new description of spacetime), it can be an excellent option to study the behavior of compact objects near phase transition regions. In this work, we obtain a modified Tolman-Openheimer-Volkof (TOV) equation for anisotropic dark energy as a fluid by solving the field equations in gravity's rainbow. Next, to compare the results with general relativity, we use a generalized Tolman-Matese-Whitman mass function to determine the physical quantities such as energy density, radial pressure, transverse pressure, gravity profile, and anisotropy factor of the dark energy star. We evaluate the junction condition and investigate the dynamical stability of dark energy star thin shell in gravity's rainbow. We also study the energy conditions for the interior region of this star. We show that the coefficients of gravity's rainbow can significantly affect this non-singular compact object and modify the model near the phase transition region. [ABSTRACT FROM AUTHOR]

The conditions for naked singularity formation are considered for a radiating metric of Boulware–Deser type within an electromagnetic field in second order Lovelock (or Einstein–Gauss–Bonnet) gravity. The spacetime metric remains real only up to certain maximum charge contribution. This differs from general relativity. Beyond a certain maximal charge, there exists no real and physical spacetime since the metric becomes complex. We establish that, under certain parameters and for specific values of the mass function and charge contribution, this branch singularity is indeed a naked singularity. This is in contrast to the neutral case where the spacetime metric is always real for a positive mass function, and further, a weak, initially naked singularity always occurs before it becomes covered by an event horizon for all future time. We highlight that both neutral and charged collapse under gravity in Einstein–Gauss–Bonnet gravity differ significantly to their general relativistic counterparts. • Naked singularity formation with charge in second order Lovelock gravity. • Beyond a certain maximal charge there is no physical spacetime. • Mass function and charge are related to formation of singularities. • Collapse in Einstein–Gauss–Bonnet theory differs from general relativity. [ABSTRACT FROM AUTHOR]