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Register a new userCausal thermodynamics of a gravitational collapse model for an anisotropic fluid with dissipative flows
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This paper presents a hydrodynamic and thermodynamic treatment of a radiant star model that undergoes a dissipative gravitational collapse, from a certain initial configuration until it becomes a black hole. The collapsing star consists of a locally anisotropic non-perfect fluid, where we explore the consequences of including viscous pressures, both shear and bulk viscosities, as well as radial heat flow. We analyze the temporal evolution of the heat flux, mass function, luminosity perceived by an observer at infinity and the effective surface temperature. It is shown that this simple exact model, satisfying all the energy conditions throughout the interior region of the star and during all the collapse process, provides a physically reasonable behavior for the temperature profile in the context of the extended irreversible thermodynamics.
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Interested in the collapse of a radiating star, we study the temporal evolution of a fluid with heat flux and bulk viscosity, including anisotropic pressure. As a starting point, we adopt an initial configuration that satisfies the regularities conditions as well as the energy conditions to a certain range of the mass-radius ratio for the star, defining acceptable models. For this set of models, we verify that the energy conditions remain satisfied until the black hole formation. Astrophysical relevant quantities, such as the luminosity perceived by an observer at infinity, the time of event horizon formation and the loss of mass during the collapse are presented.
We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure which is explicitly time dependent of the fluid is zero and that the fluid moves along time-like geodesics. The energy conditions, geometrical and physical properties of the solutions are studied. The energy conditions are all satisfied at the beginning of the collapse but when the system approaches the singularity the energy conditions are violated, allowing for the appearance of an attractive phantom energy. We have found that, depending on the self-similar parameter $alpha$ and the geometrical radius, they may represent a naked singularity. We speculate that the apparent horizon disappears due to the emergence of exotic energy at the end of the collapse, or due to the characteristics of null acceleration systems as shown by recent work.
This investigation is devoted to the solutions of Einsteins field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial pressure vanishes, we show that there exists a solution of the equations that represents the gravitational collapse of an anisotropic fluid, and this collapse will eventually form a black hole, even when it is constituted by the phantom energy.
We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when $rho+3p_1>0$ and $rho+p_1+2p_2< 0$, where the second violates the strong energy condition.
We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.
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