Related papers: Sharp bounds on $2m/r$ of general spherically symm…
The Schwarzschild-deSitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a $Lamda$-dominant world…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
We generalise results of Ford and Roman which place lower bounds -- known as quantum inequalities -- on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results…
This paper is mainly concerned with the free boundary problem for an approximate model (for example, arising from the study of sonoluminescence) of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid,…
The equations determining the energy density $\rho$ of a gas of photons in thermodynamic equilibrium with a spherical mass $M$ at a non-zero temperature $T_s>0$ is derived from Einstein's equations. It is found that for large $r$, $\rho…
Self-gravitating horizonless ultra-compact objects that possess light rings have attracted the attention of physicists and mathematicians in recent years. In the present compact paper we raise the following physically interesting question:…
We derive spherically symmetric solutions of the classical \lambda-R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 + 1 decomposition of the…
The paper deals with a nontrivial density result for $C^m(\overline{\Omega})$ functions, with $m\in{\mathbb N}\cup\{\infty\}$, in the space $$W^{k,\ell,p}(\Omega;\Gamma)= \left\{u\in W^{k,p}(\Omega): u_{|\Gamma}\in…
We obtain a new exact solution to the field equations in the EGB modified theory of gravity for a 5-dimensional spherically symmetric static distribution. By using a transformation, the study is reduced to the analysis of a single second…
We establish an optimal \emph{Widder theory} for a weighted porous medium equation with rough and inhomogeneous density that may be singular at a point and tends to zero at spatial infinity. Specifically, for this equation, we identify a…
In this paper, we consider the radially symmetric compressible Navier-Stokes equations with swirl in two-dimensional disks, where the shear viscosity coefficient \(\mu = \text{const}> 0\), and the bulk one \(\lambda = \rho^\beta(\beta>0)\).…
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic…
The monopole solution of the Einstein vacuum field equations (Schwarzschild`s solution) in Weyl coordinates involves a metric function that can be interpreted as the gravitational potential of a bar of length $2m$ with constant linear…
In this work we study static perfect fluid stars in 2+1 dimensions with an exterior BTZ spacetime. We found the general expression for the metric coefficients as a function of the density and pressure of the fluid. We found the conditions…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density \r{ho}(x) on an infinite graph which supports the Sobolev inequality. For nonnegative solutions when p > 2, we prove the precise rate of…
We present novel neutral and uncharged solutions that describe the cluster of Einstein in the teleparallel equivalent of general relativity (TEGR). To this end, we use a tetrad field with non-diagonal spherical symmetry which gives the…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…
In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context.…