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# Gravitational collapse of quantum matter

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## 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.
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... 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. ...
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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. ...
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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. ...
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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.
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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.
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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.
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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.
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