Related papers: Generating potentials via difference equations
The explicit expression of ergotropy (a.k.a. available energy) of a classical system is known for the case when the system phase space density is continuous and with no plateaus. Here we provide the general expression of ergotropy that…
An isotropic metric for a black hole and a better vacuum condition \nabla^2 V_G =0 are presented which yield distinct terms for the energy densities of ordinary matter and gravitational fields in the Einstein tensor (G^44 =-g^2 (2\nabla^2…
We propose a novel mathematical method to construct an exact polytropic sphere in self-gravitating hydrostatic equilibrium, improving the non-linear Poisson equation. The central boundary condition for the present equation requires a ratio…
The general solution of Einstein's gravity equation in $D$ dimensions for an anisotropic and spherically symmetric matter distribution is calculated in a bulk with position dependent cosmological constant. Results for $n$ concentric…
The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…
In this paper, the gravitational field equations for static spherically symmetric perfect fluid models with a polytropic equation of state, $p=k\rho^{1+1/n}$, are recast into two complementary 3-dimensional {\it regular} systems of ordinary…
We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic…
In "Classical Electrodynamics" (Jackson) a theorem is proved on the average of an electrostatic or magnetostatic field over a spherical volume. The proof of the theorem is based on an expansion in spherical harmonics and it is useful for…
This paper constructs three different anisotropic extensions of the existing isotropic solution to the modified field equations through the gravitational decoupling in $f(\mathbb{R},\mathbb{T})$ theory. For this, we take a static sphere…
In this work, an exact solution of Einstein's field equations in isotropic coordinates for anisotropic matter distribution is obtained by considering a particular metric choice of metric potential $g_{rr}$. To check the feasibility of the…
We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type…
The paper considers a set of equations describing the static isotropic gravity field of a macroscopic body within the framework of the theory of gravity with a constraint. A general approximate solution of these equations is obtained. The…
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters---the…
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
In static and spherically symmetric spacetime, we solve the Einstein Maxwell equations. The effective gravitational potential and the electric field for charged anisotropic fluid are defined in terms of two free parameters. For such…
We investigate theories in which gravity arises as a consequence of entropy. We distinguish between two approaches to this idea: holographic gravity, in which Einstein's equation arises from keeping entropy stationary in equilibrium under…
We develop the mathematics needed to treat the interaction of geometry and stress at any isotropic spacetime singularity. This enables us to handle the Einstein equations at the initial singularity and characterize allowed general…
We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically…
A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the…
We investigate the spacetime of anisotropic stars admitting conformal motion. The Einstein field equations are solved using different ansatz of the surface tension. In this investigation, we study two cases in details with the anisotropy…