End State Of Gravitational Collapse Research Articles

An approach to stability analyses in general relativity via symplectic geometry

We begin with a review of the statements of non-linear, linear and mode stability of autonomous dynamical systems in classical mechanics, using symplectic geometry. We then discuss what the Arnowitt–Deser–Misner (ADM) phase space and the ADM Hamiltonian of general relativity are, what constitutes a dynamical system, and subsequently present a nascent attempt to draw a formal analogy between the notions of stability in these two theories. We wish to note that we have not discussed here the construction of the reduced phase space by forming the quotient space of the constrained phase space with the gauge orbits. Our approach here is pedagogical and geometric, and the motivation is to unify and simplify a formal understanding of the statements regarding the stability of stationary solutions of general relativity. That is, typically the governing equations of motion of a Hamiltonian dynamical system are simply the flow equations of the associated symplectic Hamiltonian vector field, defined on phase space, and the non-linear stability analysis of its critical points have simply to do with the divergence of its flow there. Further, the linear stability of a critical point is related to the properties of the tangent flow of the Hamiltonian vector field. In the second half of this work, we posit that a study of the genericity of a particular black hole or naked singularity spacetime forming as an endstate of gravitational collapse is equivalent to an inquiry of how sensitive the orbits of the symplectic Hamiltonian vector field of general relativity are to changes in initial data. We demonstrate this by conducting a restricted non-linear stability analysis of the formation of a Schwarzschild black hole, working in the usual initial value formulation of general relativity.

Charged perfect fluid gravitational collapse in f(R, T) gravity

We explore the problem of charged perfect fluid spherically symmetric gravitational collapse in f(R, T) gravity (R is Ricci scalar and T is the trace of energy–momentum tensor). We have taken the interior boundary of a star as spherically symmetric metric filled with the charged perfect fluid. In order to study charged perfect fluid collapse, we have investigated the exact solutions of the Maxwell–Einstein field equations solutions using the most simplified form for f(R, T) model f(R, T) = R + 2[Formula: see text]T, where [Formula: see text] is model parameter. This study involves the effects of charge as well as coupling parameter on collapse of a star. We studied the nature of trapped surfaces, apparent horizon and singularity structure in detail. It has been found that singularity is formed earlier than the apparent horizons, so the end state of gravitational collapse in this case is black hole.

Gravitational collapse of baryonic and dark matter

A massive star undergoes a continual gravitational collapse when the pressures inside the collapsing star become insufficient to balance the pull of gravity. The Physics of gravitational collapse of stars is well studied. Using general relativistic techniques, one can show that the final fate of such a catastrophic collapse can be a black hole or a naked singularity, depending on the initial conditions of gravitational collapse. While stars are made of baryonic matter whose collapse is well studied, there is good indirect evidence that another type of matter, known as dark matter, plays an important role in the formation of large-scale structures in the universe, such as galaxies. It is estimated that some 85% of the total matter in the universe is dark matter. Since the particle constituent of dark matter is not known yet, the gravitational collapse of dark matter is less explored. Here, we consider first some basic properties of baryonic matter and dark matter collapse. Then, we discuss the final fate of gravitational collapse for different types of matter fields and the nature of the singularity which can be formed as an endstate of gravitational collapse. We then present a general relativistic technique to form equilibrium configurations, and argue that this can be thought of as a general relativistic analog of the standard virialization process. We suggest a modification, where the top-hat collapse model of primordial dark-matter halo formation is modified using the general relativistic technique of equilibrium. We also explain why this type of collapse process is more likely to happen in the dark-matter fields.

Conditions for the naked singularity formation in generalized Vaidya spacetime

The gravitational collapse of generalised Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v,r). Here we give conditions for the mass function which corresponds to the equation of the state P = αρ where α ∈ (0, ⅓] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong. Also we provide the metric which is the analogue of Vaidya metric in case of rotation.

Naked singularity formation in generalized Vaidya space-time

The gravitational collapse in generalized Vaidya space-time is considered. It is known that the end state of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v, r). Here we give conditions for the mass function which correspond to the equation of the state P = αρ. where α ∈ (0, 1/3], and according to these conditions we obtain either a black hole or a naked singularity as the end state of gravitational collapse. We also give the conditions for the mass function under which the singularity is gravitationally strong. We present simple examples showing when the result of gravitational collapse is a naked singularity and when this singularity is strong.

Gravitational collapse of Vaidya spacetime

The gravitational collapse of generalized Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function [Formula: see text]. Here we give conditions for the mass function which corresponds to the equation of the state [Formula: see text] where [Formula: see text] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong.

Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities

We formulate a generic Newtonian like analogous potential for static spherically symmetric general relativistic (GR) spacetime, and subsequently derived proper Newtonian like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordstr\"{o}m (RN) spacetimes, both exhibiting naked singularities. The derived potentials found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behavior with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in AGNs or in XRBs in the presence of naked singularities and thereby exploring any noticeable differences in their observational features from those in the presence of BHs to ascertain outstanding debatable issues relating to gravity - whether the end state of gravitational collapse in our physical Universe renders black hole (BH) or naked singularity.

Lemaitre–Tolman–Bondi dust cloud collapse in Brans–Dicke gravity

This paper investigates the phenomenon of gravitational collapse of Lemaitre–Tolman–Bondi (LTB) model in the presence of Brans–Dicke (BD) scalar field with nonzero potential field. We find a class of solutions by taking perfect fluid as well as scalar field and check the validity of weak energy conditions. It turns out that two different types of singularities are formed in the presence of scalar field. We conclude that the end state of gravitational collapse turns out to be a black hole (BH) contrary to general relativity (GR).

Kαiron line profile from accretion disks around regular and singular exotic compact objects

The nature of the super-massive black hole candidates in galactic nuclei can be tested by analyzing the profile of the K$\alpha$ iron line observed in their X-ray spectrum. In this paper, we consider the possibility that the spacetime in the immediate vicinity of these objects may be described by some non vacuum exact solutions of Einstein's equations resulting as the end-state of gravitational collapse. The vacuum far away portion of the spacetime is described by the Schwarzschild metric, while the interior part may be either regular or have a naked singularity at the center. The iron line generated around this class of objects has specific features, which can be used to distinguish such objects from Kerr black holes. In particular, their iron line cannot have the characteristic low-energy tail of the line generated from accretion disks around fast-rotating Kerr black holes. We can thus conclude that the super-massive black hole candidates whose spin parameter has been estimated to be close to 1 assuming the Kerr background cannot be this kind of objects.

Can strong gravitational lensing distinguish naked singularities from black holes?

In this paper we study gravitational lensing in the strong field limit from the perspective of cosmic censorship, to investigate whether or not naked singularities, if at all they exist in nature, can be distinguished from black holes. We study the gravitational lensing in the strong field regime in the JMN spacetime, a spherically symmetric geometry that contains a naked singularity and which matches smoothly with Schwarzschild metric beyond a finite radius. This metric is a toy model which was shown recently to be the end state of gravitational collapse. In the presence of the photon sphere gravitational lensing signature of this spacetime is identical to that of Schwarzschild black hole with infinitely many relativistic images and Einstein rings, all of them located beyond a certain critical angle from optic axis and the inner relativistic images all clumped together. However, in the absence of the photon sphere, which is the case for a wide range of parameter values in this spacetime, we show that we get finitely many relativistic images and Einstein rings spaced reasonably apart from one another, some of which can be formed inside the critical angle for the corresponding Schwarzschild black hole. This study suggests that the observation of relativistic images and rings might, in principle, allow us to unravel the existence of the naked singularity in the absence of the photon sphere. The results obtained here are in contrast with the earlier investigation on JNW naked singularities radial caustic was always present in the absence of photon sphere, while it is absent in JMN geometry. We also point out the practical difficulties that might be encountered in the observation of the relativistic images and suggest that new dedicated experiments and techniques must be developed in future for this purpose.

Classical and quantum gravitational collapse ind-dimensional AdS spacetime: Classical solutions

We study the collapse of a spherically symmetric dust distribution in $d$-dimensional AdS spacetime. We investigate the role of dimensionality, and the presence of a negative cosmological constant, in determining the formation of trapped surfaces and the end state of gravitational collapse. We obtain the self-similar solution for the case of zero cosmological constant, and show that one cannot construct a self-similar solution when a cosmological constant is included.

Black Hole Mass Threshold from Nonsingular Quantum Gravitational Collapse

Quantum gravity is expected to remove the classical singularity that arises as the end state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous scalar field. We show that nonperturbative semiclassical effects of loop quantum gravity cause a bounce and remove the black hole singularity. Furthermore, we find a critical threshold scale below which no horizon forms: quantum gravity may exclude very small astrophysical black holes.

What role do pressures play in determining the final end state of gravitational collapse?

We examine here in what way pressures affect the final fate of a continual gravitational collapse. It is shown that the presence of a non-vanishing pressure gradient in the collapsing cloud can determine directly the epoch of formation of trapped surfaces and the apparent horizon, thus changing the causal structure in the vicinity of a singularity.

COSMIC CENSORSHIP: A CURRENT PERSPECTIVE

End state of gravitational collapse and the related cosmic censorship conjecture continue to be amongst the most important open problems in gravitation physics today. My purpose here is to bring out several aspects related to gravitational collapse and censorship, which may help towards a better understanding of the issues involved. Possible physical constraints on gravitational collapse scenarios are considered. It is concluded that the best hope for censorship lies in analyzing the genericity and stability properties of the currently known classes of collapse models which lead to the formation of naked singularities, rather than black holes, as the final state of collapse and which develop from a regular initial data.

Naked singularities in higher dimensional Vaidya space-times

We investigate the end state of gravitational collapse of null fluid in higher dimensional space-times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. The naked singularity spectrum in collapsing Vaidya region (4D) gets covered with increase in dimensions and hence higher dimensions favor black hole in comparison to naked singularity. The Cosmic Censorship Conjecture will be fully respected for a space of infinite dimension.