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We explore the fate of matter falling into a macroscopic Schwarzschild black hole for the simplified case of a radially collapsing thin spherical shell for which the back reaction of the geometry can be neglected. We treat the internal dynamics of the infalling matter in the framework of viscous relativistic hydrodynamics and calculate how the internal temperature of the collapsing matter evolves as it falls toward the Schwarzschild singularity. We find that viscous hydrodynamics fails when either, the dissipative radial pressure exceeds the thermal pressure and the total radial pressure becomes negative, or the time scale of variation of the tidal forces acting on the collapsing matter becomes shorter than the characteristic hydrodynamic response time.
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We perform numerical simulations of the gravitational collapse of a k-essence scalar field. When the field is sufficiently strongly gravitating, a black hole forms. However, the black hole has two horizons: a light horizon (the ordinary black hole horizon) and a sound horizon that traps k-essence. In certain cases the k-essence signals can travel faster than light and the sound horizon is inside the light horizon. Under those circumstances, k-essence signals can escape from the black hole. Eventually, the two horizons merge and the k-essence signals can no longer escape.
We discuss a proposal on how gravitational collapse of a NEC (Null Energy Condition) violating spherically symmetric fluid distribution can avoid the formation of a zero proper volume singularity and eventually lead to a Lorentzian wormhole geometry. Our idea is illustrated using a time-evolving wormhole spacetime in which, we show how a collapsing sphere may never reach a zero proper volume end-state. The nature of geodesic congruences in such spacetimes is considered and analyzed. Our construction is inspired from a recently proposed static wormhole geometry, the multi-parameter Simpson-Visser line element, which is known to unite wormholes and black holes (regular and singular) in a single framework.
We present results from a numerical study of spherical gravitational collapse in shift symmetric Einstein dilaton Gauss-Bonnet (EdGB) gravity. This modified gravity theory has a single coupling parameter that when zero reduces to general relativity (GR) minimally coupled to a massless scalar field. We first show results from the weak EdGB coupling limit, where we obtain solutions that smoothly approach those of the Einstein-Klein-Gordon system of GR. Here, in the strong field case, though our code does not utilize horizon penetrating coordinates, we nevertheless find tentative evidence that approaching black hole formation the EdGB modifications cause the growth of scalar field hair, consistent with known static black hole solutions in EdGB gravity. For the strong EdGB coupling regime, in a companion paper we first showed results that even in the weak field (i.e. far from black hole formation), the EdGB equations are of mixed type: evolution of the initially hyperbolic system of partial differential equations lead to formation of a region where their character changes to elliptic. Here, we present more details about this regime. In particular, we show that an effective energy density based on the Misner-Sharp mass is negative near these elliptic regions, and similarly the null convergence condition is violated then.
We numerically study spherical gravitational collapse in shift symmetric Einstein dilaton Gauss Bonnet (EdGB) gravity. We find evidence that there are open sets of initial data for which the character of the system of equations changes from hyperbolic to elliptic type in a compact region of the spacetime. In these cases evolution of the system, treated as a hyperbolic initial boundary value problem, leads to the equations of motion becoming ill-posed when the elliptic region forms. No singularities or discontinuities are encountered on the corresponding effective Cauchy horizon. Therefore it is conceivable that a well-posed formulation of EdGB gravity (at least within spherical symmetry) may be possible if the equations are appropriately treated as mixed-type.
This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuiks black hole mass scaling law.
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