Related papers: Bounds on M/R for static objects with a positive c…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
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…
We study static, spherically symmetric black hole solutions of the Einstein equations with a positive cosmological constant and a conformally coupled self interacting scalar field. Exact solutions for this model found by Mart{\'\i}nez,…
The non-relativistic self-gravitating gas in thermal equilibrium in the presence of a positive cosmological constant Lambda (dark energy) is investigated. The dark energy introduces a force pushing outward all particles with strength…
We give a conjecture on the lower bound of the ADM mass $M$ by using the null energy condition. The conjecture includes a Penrose-like inequality $3M\geq\kappa\mathcal{A}/(4\pi)+\sqrt{\mathcal{A}/4\pi}$ and the Penrose inequality $…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We are concerned with the large-time behavior of the radially symmetric solution for multidimensional Burgers equation on the exterior of a ball $\mathbb{B}_{r_0}(0)\subset \mathbb{R}^n$ for $n\geq 3$ and some positive constant $r_0>0$,…
We present simple, analytic solutions to the Einstein-Maxwell equation, which describe an arbitrary number of charged black holes in a spacetime with positive cosmological constant $\Lambda$. In the limit $\Lambda=0$, these solutions reduce…
We report about stability conditions for static, spherically symmetric objects that share the essential features of mass varying neutrinos in cosmological scenarios. Compact structures of particles with variable mass are held together…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
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…
Bounds for the area of general closed marginally trapped surfaces (MTSs) are presented. They do not require any stability condition, and are determined by a constant that depends on a particular component of the Einstein tensor on the…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the…
Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $\Lambda$. We assume that the spacetime has symmetries corresponding to the isometries…
The rigidity statement of the positive mass theorem asserts that an asymptotically flat initial data set for the Einstein equations with zero ADM mass, and satisfying the dominant energy condition, must arise from an embedding into…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
A perfect fluid, spatially flat cosmology in a $f(T)$ model, derived from a recently proposed general Born-Infeld type theory of gravity is studied. Four dimensional cosmological solutions are obtained assuming the equation of state…