Related papers: A general maximum entropy principle for self-gravi…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the…
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
We argued previously that the well-known equation for hydrostatic equilibrium in a static spherically symmetric spacetime supported by an isotropic perfect fluid should be called the Oppenheimer-Volkoff (OV) equation, rather than the…
A relativistic self-gravitating equilibrium system with spherical symmetry as well as with steady energy flow is investigated perturbatively around the hydrostatic limit, where the radial component of the fluid velocity field $u^\mu$ is…
We argue that an arbitrary general relativistic static anisotropic fluid sphere, (static and spherically symmetric but with transverse pressure not equal to radial pressure), can nevertheless be successfully mimicked by suitable linear…
The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
It was recently conjectured that the ratio of the shear viscosity to entropy density, $ \eta/ s$, for any fluid always exceeds $\hbar/(4 \pi k_B)$. This conjecture was motivated by quantum field theoretic results obtained via the AdS/CFT…
A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…
We explore gravitating relativistic spheres composed of an anisotropic, barotropic uid. We assume a bi-polytropic equation of state which has a linear and a power-law terms. The generalized Tolman-Oppenheimer-Volkoff (TOV) equation which…
We investigate the stability criterions for perfect fluid in $f(R)$ theories which is an important generalization of general relativity. Firstly, using Wald's general variation principle, we recast Seifert's work and obtain the dynamical…
This work is concerned with the finiteness problem for static, spherically symmetric perfect fluids in both Newtonian Gravity and General Relativity. We derive criteria on the barotropic equation of state guaranteeing that the corresponding…
The Euler equations governing a relativistic perfect fluid are put into symmetric hyperbolic form with dependent variables the fluid's specific entropy plus a generalized velocity vector equal to the fluid's unit relativistic velocity…
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a…
The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in addition to regular ones. Here, we prove the following theorem. For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure…
We derive the analog of the Tolman - Oppenheimer - Volkoff equation in conformal Killing gravity in a static spherically symmetric spacetime, sourced by anisotropic fluid matter. It differs from the original equation by new dark terms…
In a recent manuscript published in the Arxives (arXiv:1610.03049v1), it is claimed that it should be more appropriate to refer to the equation of hydrostatic equilibrium in a static spherically symmetric spacetime, supported by an…
The accelerated expansion of the universe can be interpreted as a quest for satisfying holographic equipartition. It can be expressed by a simple law, $\Delta V = \Delta t\left(N_{surf}- N_{bulk}\right)$ which leads to the standard…
We consider perfect fluid bodies ("stars") in general relativity that are axisymmetric, asymptotically flat, and that admit a maximal hypersurface. We show that configurations that extremize the total entropy at fixed ADM mass, ADM angular…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…