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Gravitational collapse of quantum matter
Abstract
We describe a class of exactly soluble models for gravitational collapse in
spherical symmetry obtained by patching dynamical spherically symmetric
exterior spacetimes with cosmological interior spacetimes. These are
generalizations of the Oppenheimer-Snyder type models to include classical and
quantum scalar fields as sources for the interior metric, and null fluids with
pressure as sources for the exterior metric. In addition to dynamical
exteriors, the models exhibit other novel features such as evaporating
horizons, and singularity avoidance without quantum gravity.
... A main purpose of this paper is to take the second approach and extend results of spherically symmetric gravitational collapse of null dust in [28] to that of a class of matter including cosmological constant. (See also [31][32][33] for earlier study of matter collapse.) Upon this extension a shell crossing singularity [13] becomes a non-trivial obstruction, which constrains the parameter space of consistent solutions. ...
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 at 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 free from shell crossing singularity. We finally show that adopting the definition presented in gr-qc/2005.13233 the total energy in this time-dependent system is invariant under the given time evolution.
... • The Hamiltonian formulation of gravitational collapse of a scalar field and its quantization was developed in [62]. The authors found an upper bound for the curvature as a kinematical consequence of the construction of the quantum operators. ...
In the last four decades different programs have been carried out aiming at understanding the final fate of gravitational collapse of massive bodies once some prescriptions for the behaviour of gravity in the strong field regime are provided. The general picture arising from most of these scenarios is that the classical singularity at the end of collapse is replaced by a bounce. The most striking consequence of the bounce is that the black hole horizon may live for only a finite time. The possible implications for astrophysics are important since, if these models capture the essence of the collapse of a massive star, an observable signature of quantum gravity may be hiding in astrophysical phenomena. One intriguing idea that is implied by these models is the possible existence of exotic compact objects, of high density and finite size, that may not be covered by an horizon. The present article outlines the main features of these collapse models and some of the most relevant open problems. The aim is to provide a comprehensive (as much as possible) overview of the current status of the field from the point of view of astrophysics. As a little extra, a new toy model for collapse leading to the formation of a quasi static compact object is presented.
... Therefore, we can deduce that at later stages of the collapse the failure of formation of trapped surfaces is accompanied by a negative pressure [57]. From the second part of equation (47) it is seen that the occurrence of negative pressure impliesṀ < 0. This can be interpreted as if the collapsing cloud may loose away some of its content causing the non-occurrence of trapped surfaces till the collapsing process ends [56,58], since there remains not enough mass at each stage of the collapse to get the light trapped. On the other hand, if n < −2 and w > − 1 3 (the Gray region in figure 1), which satisfies the condition for trapped surface formation, the pressure can be initially set to be positive and remains positive up to the final stages of the collapse. ...
We consider the gravitational collapse of a spherically symmetric homogeneous matter distribution consisting of a Weyssenhoff fluid in the presence of a negative cosmological constant. Our aim is to investigate the effects of torsion and spin averaged terms on the final outcome of the collapse. For a specific interior space-time setup, namely the homogeneous and isotropic FLRW metric, we obtain two classes of solutions to the field equations where depending on the relation between spin source parameters, (i) the collapse procedure culminates in a space-time singularity or (ii) it is replaced by a non-singular bounce. We show that, under certain conditions, for a specific subset of the former solutions, the formation of trapped surfaces is prevented and thus the resulted singularity could be naked. The curvature singularity that forms could be gravitationally strong in the sense of Tipler. Our numerical analysis for the latter solutions shows that the collapsing dynamical process experiences four phases, so that two of which occur at the pre-bounce and the other two at post-bounce regimes. We further observe that there can be found a minimum radius for the apparent horizon curve, such that the main outcome of which is that there exists an upper bound for the size of the collapsing body, below which no horizon forms throughout the whole scenario.
An Oppenheimer-Snyder (OS)-type collapse is considered for a Dvali-Gabadadze-Porrati (DGP) brane, whereas a Gauss-Bonnet (GB) term is provided for the bulk. We study the combined effect of the DGP induced gravity plus the GB curvature, regarding any modification of the general relativistic OS dynamics. Our paper has a twofold objective. On the one hand, we investigate the nature of singularities that may arise at the collapse end state. It is shown that all dynamical scenarios for the contracting brane would end in one of the following cases, depending on conditions imposed: either a central shell-focusing singularity or what we designate as a “sudden collapse singularity.” On the other hand, we also study the deviations of the exterior spacetime from the standard Schwarzschild geometry, which emerges in our modified OS scenario. Our purpose is to investigate whether a black hole always forms regarding this brane world model. We find situations where a naked singularity emerges instead.
The Hawking–Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner–Nordström situation. For a distant observer the horizon crossing occurs in an infinite time and the pulsations of the black hole quantum “beating heart” are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.
Based on a previously found general class of quantum improved exact solutions
composed of non-interacting (dust) particles, we model the gravitational collapse of
stars. As the modeled star collapses a closed apparent 3-horizon is generated due to
the consideration of quantum e�ects. The e�ect of the subsequent emission of Hawking
radiation related to this horizon is taken into consideration. Our computations lead us
to argue that a total evaporation could be reached. The inferred global picture of the
spacetime corresponding to gravitational collapse is devoid of both event horizons and
shell-focusing singularities. As a consequence, there is no information paradox and no
need of �rewalls.
We study the collapse process of a massive star whose matter content is a
Weyssenhoff fluid and show that the spin of matter, in the context of a
negative pressure, acts against the pull of gravity. Such a mechanism and
decelerates the collapse dynamics to finally replace the spacetime singularity
by a bounce after which an expanding phase starts. We analyze the solutions in
the large and small scale factor regimes and show that the scale factor never
vanishes but reaches a minimum in the later one. Depending on the model
parameters, there can be found a minimum value for the boundary of the
collapsing star or correspondingly a threshold value for the mass content below
which the formation of a dynamical horizon can be avoided. Our results are
supported by a thorough numerical analysis.
We study a semiclassical description of the spherically symmetric
gravitational collapse with a massless scalar field. An effective scenario
provided by holonomy corrections from loop quantum gravity is applied to the
homogeneous interior spacetime. The classical singularity that arises at the
final stage of our collapsing system, is resolved and replaced by a bounce. Our
main purpose is to investigate the evolution of trapped surfaces during this
semiclassical collapse. We find that there exists a small threshold mass for
the collapsing cloud in order for horizons to form. By employing suitable
matching conditions at the boundary shell, quantum gravity effects are carried
out to the exterior region, leading to an effective Vaidya geometry. In
addition, the effective mass loss emerging in this model predicts an outward
energy flux from the collapse interior.
We consider a spherically symmetric gravitational collapse with a tachyon
field coupled with a barotropic fluid, as matter source. The tachyonic
potential is assumed to be of an inverse square form. By employing the holonomy
correction imported from loop quantum gravity, we study the dynamics of the
collapse within a semiclassical description. We find that the classical black
hole and naked singularities, appearing in the corresponding standard general
relativistic collapse, are avoided by quantum gravity induced effects.
The purpose of this paper is to extend the analysis presented in Goswami et al. [ Phys. Rev. Lett. 96 031302 (2006)] by means of investigating how a specific type of loop (quantum) effect can alter the outcome of gravitational collapse. To be more concrete, a particular class of spherically symmetric spacetime is considered with a tachyon field ϕ and a barotropic fluid constituting the matter content; the tachyon potential V(ϕ) is assumed to be of the form ϕ-2. Within inverse triad corrections, we then obtain, for a semiclassical description, several classes of analytical as well as numerical solutions. Moreover, we identify a subset whose behavior corresponds to an outward flux of energy, thus avoiding either a naked singularity or a black hole formation.
We consider a polymer quantization of a free massless scalar field in a homogenous and isotropic classical cosmological spacetime. This quantization method assumes that field translations are fundamentally discrete, and is related to but distinct from that used in loop quantum gravity. The semiclassical Friedmann equation yields a universe that is nonsingular and nonbouncing, without quantum gravity. The model has an early nearly de Sitter inflationary phase with sufficient expansion to resolve the horizon and entropy problems, and a built-in mechanism for a graceful exit from inflation.
We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with the help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress energy preventing the formation of a singularity.
In general relativity black holes can be formed from regular initial data that do not contain a black hole already. The space of regular initial data for general relativity therefore splits naturally into two halves: data that form a black hole in the evolution and data that do not. The spacetimes that are evolved from initial data near the black hole threshold have many properties that are mathematically analogous to a critical phase transition in statistical mechanics.Solutions near the black hole threshold go through an intermediate attractor, called the critical solution. The critical solution is either time-independent (static) or scale-independent (self-similar). In the latter case, the final black hole mass scales as along any 1-parameter family of data with a regular parameter p such that is the black hole threshold in that family. The critical solution and the critical exponent γ are universal near the black hole threshold for a given type of matter.We show how the essence of these phenomena can be understood using dynamical systems theory and dimensional analysis. We then review separately the analogy with critical phase transitions in statistical mechanics, and aspects specific to general relativity, such as spacetime singularities. We examine the evidence that critical phenomena in gravitational collapse are generic, and give an overview of their rich phenomenology.
We study free scalar field theory on flat spacetime using a background
independent (polymer) quantization procedure. Specifically we compute the
propagator using a method that takes the energy spectrum and position matrix
elements of the harmonic oscillator as inputs. We obtain closed form results in
the infrared and ultraviolet regimes that give Lorentz invariance violating
dispersion relations, and show suppression of propagation at sufficiently high
energy.
The energy tensor for a mixture of matter and outflowing radiation is derived, and a set of equations following from Einstein's field equations are written down whose solutions would represent nonstatic radiating spherical distributions. A few explicit analytical solutions are obtained, which describe a distribution of matter and outflowing radiation for $r$\le${}a(t)$, an ever-expanding zone of pure radiation for $a(t)$\le${}r$\le${}b(t)$ and empty space beyond $r=b(t)$. Since $\frac{\mathrm{db}(t)}{\mathrm{dt}}$ is almost equal to 1 and $\frac{\mathrm{da}(t)}{\mathrm{dt}}$ is negative, the solutions obtained represent contracting distributions, but the contraction is not gravitational because $\frac{m}{r}$ is a constant on the boundary $r=a(t)$, $m$ being the mass. The contraction is a purely relativistic effect, the corresponding newtonian distributions being equilibrium distributions. It is hoped that the scheme developed here will be useful in working out solutions which would help in a clear understanding of the initial or the final stages of stellar evolution.
When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.
In Vaidya's metric for a radiating sphere, ds2=-(1-2mr-1)du2-2dudr+r2dΩ2, where m(u) is a nonincreasing function of the retarded time u=t-r, we verify that -dmdu is the total power output as given by the Landau-Lifshitz stress-energy pseudotensor, and relate it through red-shift and Doppler-shift factors to the apparent luminosity L for an observer moving radially in this gravitational field. We argue that the hypersurface r=2m(u) cannot be realized physically, but see that a hypersurface r=2m() at u=(which is not adequately represented in presently available coordinate systems) shows the total red-shift characteristic of the Schwarzschild "singularity." The geodesic equations are written out to display a gravitational "induction field" -GLc3r associated with a changing mass in the Newtonian -Gmr2 field.
We apply techniques recently introduced in quantum cosmology to the Schwarzschild metric inside the horizon and near the black hole singularity at r=0. In particular, we use the quantization introduced by Husain and Winkler, which is suggested by Loop Quantum Gravity and is based on an alternative to the Schrödinger representation introduced by Halvorson. Using this quantization procedure, we show that the black hole singularity disappears and spacetime can be dynamically extended beyond the classical singularity.
In order to study gravitational collapse we introduce a class of stellar models which neither stabilize nor bounce. In these models all the energy conditions are fulfilled, however the collapsing stars radiate away their matter avoiding the formation of singularities. We discuss the viability of such a collapse and its implications in the resolution of the singularity issue. We also examine the possibility of living in a singularity-free locally open or flat FLRW universe satisfying all the energy conditions.
The authors give the necessary conditions for the matching of a general Robertson-Walker geometry to general spherically symmetric radiating metric. They also found the conditions for the matching of a Vaidya metric (1951) to a general Robertson-Walker metric. The possible applications of the results to the stellar collapse and to the study of local inhomogeneities in a cosmological context are considered. An alternative interpretation of the energy-momentum tensor of the Robertson-Walker part of spacetime is given in such a way that the physical processes can be better understood.