Gravitational collapse is still poorly understood in the context of $f(R)$ theories of gravity, since the Oppenheimer-Snyder model is incompatible with their junction conditions. In this work, we will present a systematic approach to the problem. Starting with a thorough analysis of how the Oppenheimer-Snyder construction should be generalised to fit within metric $f(R)$ gravity, we shall subsequently proceed to explore the existence of novel exterior solutions compatible with physically viable interiors. Our formalism has allowed us to show that some paradigmatic vacuum metrics cannot represent spacetime outside a collapsing dust star in metric $f(R)$ gravity. Moreover, using the junction conditions, we have found a novel vacuole solution of a large class of $f(R)$ models, whose exterior spacetime is documented here for the first time in the literature as well. Finally, we also report the previously unnoticed fact that the Oppenheimer-Snyder model of gravitational collapse is incompatible with the Palatini formulation of $f(R)$ gravity.
We use 1-dimensional numerical simulations to study spherical collapse in the f(R) gravity models. We include the nonlinear coupling of the gravitational potential to the scalar field in the theory and use a relaxation scheme to follow the collapse. We find an unusual enhancement in density near the virial radius which may provide observable tests of gravity. We also use the estimated collapse time to calculate the critical overdensity $δ_c$ used in calculating the mass function and bias of halos. We find that analytical approximations previously used in the literature do not capture the compl…
Critical collapse in tensor-multi-scalar gravity theories is studied, and found that for any given target space all the theories conformally related belong to the same universal class. When only one scalar field is present, the universality is extended to include a class of non-linear gravity theories.
Model of gravitational collapse of anisotropic compact stars in a new theory of $ f(R) $ gravity has been developed. The author considers the modified gravity model of $ f(R) = ξR^4 $ to investigate a physically acceptable model of gravitational collapse of anisotropic compact stars. First, the author presents a brief review of the development of field equations of gravitational collapse in $ f(R) $ gravity for a particular interior metric for compact stars. Then analytical solutions for various physical quantities of collapsing anisotropic compact stars in $ ξR^4 $ gravity have been developed…
Numerical simulations are performed of the gravitational collapse of a scalar field with a λϕ^4 potential. Comparisons are made with the thin shell approximation.
Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions in cylindrically symmetric models of gravitational collapse to singularities. The models result from the matching of collapsing dust fluids interiors with gravitational wave exteriors, given by the Einstein-Rosen type solutions. For a given choice of a frame adapted to the symmetry of the matching hypersurface, we are able to compute the total gravitational …
It is shown that the gravitational field, as a physical field developing in the Minkowsky space, does not lead to unlimited gravitational collapse of massive bodies and, hence, excludes a possibility of the formation of the ``black holes''.
The present work investigates the gravitational collapse of a perfect fluid in $f(R)$ gravity models. For a general $f(R)$ theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
What happens to a massive star at the end of its life cycle is one of the most important and intriguing questions in theoretical physics. An unhindered gravitational collapse of such a sufficiently massive star can give rise to a spacetime singularity. This thesis discusses the phenomenon of such unhindered gravitational collapse and the causal structure of the singularity thus formed.
We investigate the end state of the gravitational collapse of an inhomogeneous dust cloud in higher dimensional space-time. The naked singularities are shown to be developing as the final outcome of non-marginally bound collapse. The naked singularities are found to be gravitationally strong in the sense of Tipler .
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) tha…
Two classes of metrics obtained from non-Riemannian gravitational collapse are presented.The first is the Taub planar symmetric exact solutions of Einstein-Cartan field equations of gravity describing torsion walls which are obtained from gravitational collapse of time dependent perturbation of Riemannian Taub symmetric solutions of General Relativity.The second is a modification of the Vilenkin Riemannian planar wall which is obtained from a non-Riemannian planar distribution of spinning matter.
Lecture given at the workshop "Mathematical aspects of theories of gravitation", Stefan Banach International Mathematical Centre, 7 March 1996. A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of the regularity of the ``critical spacetimes'' dominating these phenomena.
This paper deals with the dynamics of a shearfree charged radiating collapse in modified Gauss-Bonnet gravity. The field equations for shearfree spherical interior geometry of a charged dissipative star are formulated. To study the dynamical behavior of collapsing matter, we derive the dynamical as well as transport equations. We conclude that the gravitational force in modified Gauss-Bonnet gravity is much stronger as compared to general relativity which implies the increase in the rate of collapse. Finally, we study the effect of charge on the dynamics of collapse.
Gravitational collapse of a class of spherically symmetric stars are investigated. We quantise the geometries describing the gravitational collapse by a deformation quantisation procedure. This gives rise to noncommutative spacetimes with gravitational collapse.
General relativity as well as Newtonian gravity admits self-similar solutions due to its scale-invariance. This is a review on these self-similar solutions and their relevance to gravitational collapse. In particular, our attention is mainly paid on the crucial role of self-similar solutions in the critical behavior and attraction in gravitational collapse.
It is argued in the literature that gravity is an emergent phenomenon and is a statistical tendency for a gravitational system to attain the maximal entropy state which maintains the holographic principle. In this paper, we show that gravitational collapse is due to the same mechanism as the expansion of the universe that the departure of the surface degrees of freedom and the bulk degrees of freedom in a region of space drives the evolution of a gravitational system. We also argue that the ordinary thermal radiation can be taken as a signal for the existence of some kind of "confined" bulk de…
Preliminary version No.~2 of the lecture notes for the talk ``Quantum theory of gravitational collapse'' given at the 271. WE-Heraeus-Seminar ``Aspects of Quantum Gravity'' at Bad Honnef, 25 February--1 March 2002
In this paper, we study the dynamics of shearfree dissipative gravitational collapse in modified Gauss-Bonnet theory of gravity - so called f(G) gravity. The field equations of f(G) gravity are applied to shearfree spherical interior geometry of the dissipative star. We formulate the dynamical as well as transport equations and then couple them to investigate the process of collapse. We conclude that the gravitational force in this theory is much stronger as compared to general relativity which indicates increase in the rate of collapse. Further, the relation between the Weyl tensor and matter…
Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatori…
A sufficient condition for the validity of Cosmic Censorship in spherical gravitational collapse is formulated and proved. The condition relies on an attractive mathematical property of the apparent horizon, which holds if ''minimal'' requirements of physical reasonableness are satisfied by the matter model.
It is shown that the theoretical arguments for the unavoidable collapse of massive stars, which are valid within standard general relativity, are not valid in extended gravity. In particular a calculation is reported of neutron stars within a theory obtained from an Einstein-Hilbert action involving a function of $R^{2}-1/2R_{μν}R^{μν}$ added to the Ricci scalar $R$. The calculation suggests that within that theory there are stable neutron stars with arbitrarily high baryon number.
In this paper, we investigate the nature of the singularity in the spherically symmetrical, shear-free, gravitational collapse of a star with heat flux using a separable metric [cqg1]. For any non-singular, regular, radial density profile for a star described by this metric, eq. (2.1), the singularity of the gravitational collapse is not naked locally. Our results here unequivocally support the Strong Cosmic Censorship Hypothesis.
We construct an exact solution for the spherical gravitational collapse in a single coordinate patch. To describe the dynamics of collapse, we use a generalized form of the Painlevé-Gullstrand coordinates in the Schwarzschild spacetime. The time coordinate of the form is the proper time of a free-falling observer so that we can describe the collapsing star not only outside but also inside the event horizon in a single coordinate patch. We show the both solutions corresponding to the gravitational collapse from infinity and from a finite radius.
In this paper, the role of anisotropy and inhomogeneity has been studied in quasi-spherical gravitational collapse. Also the role of initial data has been investigated in characterizing the final state of collapse. Finally, a linear transformation on the initial data set has been presented and its impact has been discussed.
This note discusses possible quantum effects in the context of homogeneous flat FLRW and inhomogeneous LTB gravitational spherical collapse, which lead to bounce solutions.
We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We discuss the nature of the singularity formed by analyzing the outgoing radial null geodesics. We examine the formation of trapped surfaces during the collapse.
We examine the problem of the gravitational collapse using higher dimensional Husain spacetime for the null fluid. The equations of state chosen to solve the field equations contain linear, quadratic and arbitrary powers of the radial parameter. The resulting mass evolution is discussed for each case.
It is shown that the Diósi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of space-time, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of space-time may result in rapider collapse of the superposition of energy eigenstates than required by the Diósi-Penrose criterion.
The present work deals with dynamics of gravitational collapse with cylindrical symmetry as developed by Misner and Sharp. The interior collapsing anisotropic cylindrical perfect fluid is matched to an exterior vacuum cylindrically symmetric space-time due to Einstein--Rosen using the Darmois matching conditions. It is found that the radial pressure of the anisotropic perfect fluid is non-zero on the boundary surface and is related to the components of shear viscosity. As a result, there is formation of gravitational waves outside the collapsing matter.
A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.
The present works deals with gravitational collapse of cylindrical viscous heat conducting anisotropic fluid following the work of Misner and Sharp. Using Darmois matching conditions, the dynamical equations are derived and the effect of charge and dissipative quantities over the cylindrical collapse are analyzed. Finally, using the Miller-Israel-Steward causal thermodynamic theory, the transport equation for heat flux are derived and its influence on collapsing system has been studied.
Generalizing the results of Joshi and Dwivedi in Commun.Math.Phys. 146, p.333 (1992), it is pointed out that strong curvature naked singularities could occur in the self-similar gravitational collapse of any form of matter satisfying the weak energy condition for the positivity of mass-energy density.
We study the gravitational collapse in ($n+2$)-D quasi-spherical Szekeres space-time (which possess no killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate `$r$' as the initial value for the scale factor $R$, we consider a power function of $r$ as the initial scale for the radius $R$. We examine the influence of initial data on the formation of singularity in gravitational collapse.
We derive the matching conditions between FLRW and generalised Vaidya spacetimes with spherical, planar or hyperbolic symmetry, across timelike hypersurfaces. We then construct new models of gravitational collapse of FLRW spacetimes with a negative cosmological constant having electromagnetic radiation in the exterior. The final state of the collapse are asymptotically AdS black holes with spherical, toroidal or higher genus topologies. We analyse the collapse dynamics including trapped surface formation, for various examples.
We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects predict a threshold scale below which no horizon can form as the collapse evolves towards the bounce.
We study the effect of charge on gravitational collapse of inhomogeneous dust cloud in the Einstein, Gauss-Bonnet and Lovelock gravity. Dynamics of the collapsing shell is analyzed. The conditions for the occurrence of bounce during collapse are given. We also show that shell crossing occurs inevitably if the shell near the center is weakly charged.
A distinguishable physical property between a naked singularity and a black-hole, formed during a gravitational collapse has important implications for both experimental and theoretical relativity. We examine the energy radiated during the spherically symmetric Gravitational collapse in this context within the framework of general relativity. It is shown that total energy radiated(Mass Loss) during the collapse ending in a naked singularity scenario cannot be more than the case when a collapse scenario ends in a black-hole. In cases of interest(for example stars having same mass, size, and int…
Numerical simulations are performed of a test scalar field in a spacetime undergoing gravitational collapse. The behavior of the scalar field near the singularity is examined and implications for generic singularities are discussed. In particular, our example is the first confirmation of the BKL conjecture for an asymptotically flat spacetime.
Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation…
We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar Type II critical behavior at the threshold of black hole formation.
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 upon 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 im…
We estimate the stochastic gravitational-wave background arising from all stellar core-collapse events in the universe based on the gravitational-wave signal predictions of recent numerical simulations. We focus on waveforms from slowly or non-rotating stars and include rapidly rotating, highly massive progenitors as extreme case limits. Our most realistic estimates are more than one hundred times below the sensitivity of third-generation terrestrial gravitational-wave detectors and likely weaker than cosmological contributions to the stochastic gravitational-wave background.
We study the fate of gravitational collapse in presence of a cosmological constant. The junctions conditions between static and non-static space-times are deduced. Three apparent horizon are formed, but only two have physical significance, one of them being the black hole horizon and the other the cosmological horizon. The cosmological constant term slows down the collapse of matter, limiting also the size of the black hole.
The spherical gravitational collapse of a compact packet consisting of perfect fluid is studied. The spacetime outside the fluid packet is described by the out-going Vaidya radiation fluid. It is found that when the collapse has continuous self-similarity the formation of black holes always starts with zero mass, and when the collapse has no self-similarity, the formation of black holes always starts with a finite non-zero mass. The packet is usually accompanied by a thin matter shell. The effects of the shell on the collapse are also studied.
We investigate here gravitational collapse of a perfect fluid with a linear isentropic equation of state $p = k ρ$. A class of collapse models is given which is a family of solutions to Einstein equations and the final fate of collapse is analyzed in terms of the formation of black holes and naked singularities. The collapse evolves from a regular initial data and the positivity of energy conditions and other physical regularity conditions are satisfied. As we provided here an explicit class, this gives useful insights into the endstates of collapse with a physically reasonable and relevant eq…
This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar field equations is derived, after a small amount of numerical work with ordinary differential equations. The universal scaling and echoing behavior discovered by Choptuik in spherically symmetrical gravitational collapse appear in a somewhat different form. Properties of the endstate of the collapse are derived: The collapse leaves behind an irregular outgoi…
We show that the interior of a charged, spinning black hole formed from a general axially symmetric gravitational collapse is unstable to inflation of both its mass and angular momentum parameters. Although our results are formulated in the context of $(2+1)$-dimensional black holes, we argue that they are applicable to $(3+1)$ dimensions.
We demonstrate that evolutions of three-dimensional, strongly non-linear gravitational waves can be followed in numerical relativity, hence allowing many interesting studies of both fundamental and observational consequences. We study the evolution of time-symmetric, axisymmetric {\it and} non-axisymmetric Brill waves, including waves so strong that they collapse to form black holes under their own self-gravity. The critical amplitude for black hole formation is determined. The gravitational waves emitted in the black hole formation process are compared to those emitted in the head-on collisio…
We derive a theoretical model of mass and angular momentum scaling in type-II critical collapse with rotation. We focus on the case where the critical solution has precisely one, spherically symmetric, unstable mode. We demonstrate excellent agreement with numerical results for critical collapse of a rotating radiation fluid, which falls into this case.
We conduct numerical simulations in Painlevé-Gullstrand coordinates of a variety of K-essence-type scalar fields under spherically symmetric gravitational collapse. We write down generic conditions on the K-essence lagrangian that can be used to determine whether superluminality and Cauchy breakdown are possible. Consistent with these conditions, for specific choices of K-essence-type fields we verify the presence of superluminality during collapse, while for other type we do not. We also demonstrate that certain choices of K-essence scalar fields present issues under gravitational collapse in…
We study the gravitational collapse of a dust dark matter star in a $Λ$-background. We consider two distinct cases: First we do not have a dark matter and dark energy coupling; second, we consider that $Λ$ decay in dark particles. The approach adopted assumes a modified matter expansion rate and we have formation of a black hole, since that, we have the formation of an apparent horizon. A brief comparison of the process of the matter condensation using the gravitational collapse approach and the linear scalar perturbation theory is considered.
We revisit the gravitational collapse of spherically symmetric Lemaître - Tolman - Bondi (LTB) dust models. A sufficient condition for global visibility of singularity is given. This condition also allows us to extend the condition of local visibility to mass functions which are not Taylor expandable near the centre.
The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.
Based on a recent proposal for the gravitational entropy of free gravitational fields, we investigate the thermodynamic properties of black hole formation through gravitational collapse in the framework of the semitetrad 1+1+2 covariant formalism. In the simplest case of an Oppenheimer-Snyder-Datt collapse we prove that the change in gravitational entropy outside a collapsing body is related to the variation of the surface area of the body itself, even before the formation of horizons. As a result, we are able to relate the Bekenstein-Hawking entropy of the black hole endstate to the variation…
We give a very short proof that the vacuum Einstein equations in 4+1 dimensions have no cohomogeneity-two Bianchi IX continuously self-similar solutions.
We establish the formalism in the nonsymmetric gravitational theory (NGT) for stellar equilibrium and gravitational collapse. We study the collapse of a pressureless, spherically symmetric dust cloud. By assuming that the interior solution is smoothly matched at the surface of the star to the quasi-static, spherically symmetric vacuum solution, we find that the star does not collapse to a black hole. It is anticipated that the final collapsed object will reach a state of equilibrium, and will emit thermal, gravitational and other forms of radiation, although the radiation may be emitted only i…
This article reviews classical and quantum aspects of critical phenomena in gravitational collapse. We pay special attention to the origin of the scaling law for black hole mass, and to phase transitions in which black hole formation turns on at finite mass. We present some new results for perfect fluids with pressure proportional to density.
A simple self gravitating system --- a thin spherical shell of charged pressureless matter --- is naively quantized as a test case of quantum gravitational collapse. The model is interpreted in terms of an inner product on the positive energy states. An S-matrix is constructed describing scattering between negatively and positively infinite radius.
