Related papers: Consistency between dynamical and thermodynamical …
The conformal Einstein equations for a tracefree (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de…
We investigate the field equations in the Einstein-aether theory for static spherically symmetric spacetimes and a perfect fluid source and subsequently with the addition of a scalar field (with an exponential self-interacting potential).…
We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the Third Law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
A rigorous thermodynamic analysis has been done at the apparent horizon of a spatially flat Friedmann-Lemaitre-Robertson-Walker universe for the gravitationally induced particle creation scenario with constant specific entropy and an…
We present a rigorous proof establishing the mathematical equivalence between two independent criteria for the marginal stability of multi-fluid relativistic stars: the dynamical criterion based on the vanishing of the fundamental radial…
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
We summarize a recent work on the title subject, skipping the detailed calculations but introducing the basic points with enough detail. The theory considered is formulated in a preferred reference frame in a four-dimensional spacetime…
In this paper we utilize symmetries in order to exhibit exact solutions to Einstein's equation of a perfect fluid on a static manifold all of whose spatial factor belongs to the conformal class of a Riemannian space of constant curvature.
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…
We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system…
A model approach to the description of static stars filled with a charged Pascal perfect fluid within the framework of general relativity is investigated. The metric is written in Bondi's radiation coordinates. The gravitational equations…
We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy…
As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear…
We subject to scrutiny the physical consistency of adopting the perfect-gas thermodynamic model within self-gravitation circumstances by studying the fluid statics of a self-gravitating isothermal sphere with the van der Waals'…
We examine the consistency of the thermodynamics of irrotational and non-isentropic perfect fluids complying with matter conservation by looking at the integrability conditions of the Gibbs-Duhem relation. We show that the latter is always…
For stationary, barotropic fluids in Newtonian gravity we give simple criteria on the equation of state and the "law of motion" which guarantee finite or infinite extent of the fluid region (providing a priori estimates for the…
A re-investigation of the gravothermal catastrophe is presented. By means of a linear perturbation analysis, we study the dynamical stability of a spherical self-gravitating isothermal fluid of finite volume and find that the conditions for…