Related papers: Comment on ''The space-time line element for stati…
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a…
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…
We analyse two static spacetimes, recently generated from a Schwarzschild--Bertotti--Robinson electrovacuum seed through distinct symmetry transformations. The electromagnetic field of the transformed solutions can be set to zero and both…
Validating the results of [A.M. Abrahams and C.R. Evans, Phys. Rev. Lett. 70, 2980] poses a numerical challenge and has been inspiring a lot of research. We join these efforts and present our first steps to achieve this goal: we discuss a…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
We show how to parameterise solutions of the general relativistic vector constraint equation on Einstein manifolds by unconstrained potentials. We provide a similar construction for the trace-free part of tensors satisfying the linearised…
We present a time dependent isotropic fluid solution around a Schwarzschild black hole. We offer the solutions and discuss the effects on the field equations and the horizon. We derive the energy density, pressure and the equation of state…
In this paper, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz…
We derive here the metric for Einstein's static universe (ESU) directly from Einstein equation, i.e., by considering both $G_{ik}$ and $T_{ik}$. We find that in order that the fluid pressure and acceleration are {\em uniform} and finite…
In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and an equation…
This work presents a novel methodology for deriving stationary and axially symmetric solutions to Einstein field equations using the 1+3 tetrad formalism. This approach reformulates the Einstein equations into first order scalar equations,…
In this work, we extend for the first time the spherically symmetric Schwarzschild and Schwarzschild-De Sitter solutions with a Finsler-Randers-type perturbation which is generated by a covector $A_\gamma$. This gives a locally anisotropic…
An approximate solution to Einstein's equations representing two widely-separated non-rotating black holes in a circular orbit is constructed by matching a post-Newtonian metric to two perturbed Schwarzschild metrics. The spacetime metric…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance for the simulation of slowly rotating stars. Solving the Einstein field equations, we added terms of second order in the quadrupole moment…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
The literature features many instances of spacetimes containing two black holes held apart by a thin distribution of matter on the axis joining the holes. For all such spacetimes, the Einstein field equations are integrated with an…
Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity…
It is proved in the manuscript that as long as the proper coordinate transformation is introduced,, the equations of geodetic lines described in curved space-time can be transformed into the dynamic equations in flat space-time, that is to…