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We introduce the notion of thermal entropy density, and first obtain the thermal entropy density of any arbitrary spacetime without firstly assuming a temperature or a horizon. The results indicate that gravity possesses thermal effects or…
We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of…
Does relativistic gravity provide arguments against the existence of a preferred frame? Our answer is negative. We define a viable theory of gravity with preferred frame. In this theory, the EEP holds exactly, and the Einstein equations of…
Starting from Enskog equation of hard spheres of mass m and diameter D under the gravity g, we first derive the exact equation of motion for the equilibrium density profile at a temperature T and examine its solutions via the gradient…
We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…
We investigate gravitational collapse of thick shell of fluid in the isotropic homogeneous universe without radiation described by the Einstein gravity with cosmological constant. We construct analytic solutions of this kind interpolating…
In Newtonian theory, gravity inside a constant density static sphere is independent of spacetime dimension. Interestingly this general result is also carried over to Einsteinian as well as higher order Einstein-Gauss-Bonnet (Lovelock)…
We present a general and unified formulation which can handle the classical evolution and quantum generation processes of the cosmological gravitational wave in a broad class of generalized gravity theories. Applications are made in several…
We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical…
We consider Horava gravity coupled to Maxwell and higher derivative magnetic terms. We construct static spherically symmetric black hole solutions in the low-energy approximation. We calculate the horizon locations and temperatures in the…
We demonstrate how the Einstein's equations for the $D$-dimensional spherical gravity can be written in the covariant vector-like form. These equations reveal easily the causal structure of curved spherically symmetric manifolds and may…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the…
Gravitation might make a preferred frame appear, and with it a clear space/time separation--the latter being, a priori, needed by quantum mechanics (QM) in curved space-time. Several models of gravitation with an ether are discussed: they…
We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to…
We present a particular solution to the Einstein field equations that could arise as a magnetic monopole in the strong field limit of the Born-Infeld electrodynamics. We solve its geodesics exactly and show that they can mimic the…
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for…
We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation…
The Bekenstein-Hawking entropy suggests that thermodynamics is an intrinsic ingredient of gravity. Here, we explore the idea that requirements of thermodynamic consistency could determine the gravitational entropy in other set-ups. We…
We study the stationary state of a rough granular sphere immersed in a thermal bath composed of point particles. When the center of mass of the sphere is fixed the stationary angular velocity distribution is shown to be Gaussian with an…