Related papers: Painleve-Gullstrand Coordinates for the Kerr Solut…
Black holes are among the most intriguing objects in nature. They are believed to be fully described by General Relativity (GR), and the astrophysical black holes are expected to belong to the Kerr family, obeying the no-hair theorems.…
We present a new proof of linear stability of the Schwarzschild solution to gravitational perturbations. Our approach employs the system of linearised gravity in the new geometric gauge of \cite{benomio_kerr}, specialised to the $|a|=0$…
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\delta K^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $\delta$ with the Finsler non-linear…
In this study, beginning with the 4D asymptotically flat Kerr black hole solution in the Boyer-Lindquist (BL) coordinate system, then by using the technique of frame-dragging and some coordinate transformation to incorporate the…
We reconsider the problem of a slowly rotating homogeneous star, or Schwarzschild star, when its compactness goes beyond the Buchdahl bound and approaches the gravastar limit $R\to 2M$. We compute surface and integral properties of such…
We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general…
A solution of Einstein's vacuum field equation is derived that describes a general boosted Kerr black hole relative to a Lorentz frame at future null infinity. The metric contains five independent parameters -- mass $m$, rotation $\omega$,…
Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the…
It is now widely accepted that the universe as we understand it is accelerating in expansion and fits the de Sitter model rather well. As such, a realistic assumption of black holes must place them on a de Sitter background and not…
We present a novel formulation of the Kerr spacetime solution, based on the Lema\^itre coordinates. Such an approach allows one to avoid the coordinate singularities of the Boyer-Lindquist metric, thus offering the possibility to explore in…
The astrophysical importance of the Kerr spacetime cannot be overstated. Of the currently known exact solutions to the Einstein field equations, the Kerr spacetime stands out in terms of its direct applicability to describing astronomical…
The complete solution of Einstein's gravitational equations with a vacuum-vacuum Kerr-Schild pencil of metrics $g_{ab}+V l_al_b$ is obtained. Our result generalizes the solution of the Kerr-Schild problem with a flat metric $g_{ab}$…
We extract elegant and concise analytic formulae for the mass and rotation parameters of the Kerr black hole as well as its distance from the Earth only in terms of directly measurable quantities of the accretion disk revolving in the black…
We consider stationary axisymmetric solutions of general relativity that asymptote to five dimensional Minkowski space. It is known that this system has a hidden SL(3,R) symmetry. We identify an SO(2,1) subgroup of this symmetry group that…
An exact and analytical solution of four dimensional vacuum General Relativity representing a system of two static black holes at equilibrium is presented. The metric is completely regular outside the event horizons, both from curvature and…
We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion -- the energy, the angular momentum, and the Carter constant -- and initial…
We give circularly symmetric solutions for null fluid collapse in 2+1-dimensional Einstein gravity with a cosmological constant. The fluid pressure $P$ and energy density $\rho$ are related by $P=k\rho$ $(k\le 1)$. The long time limit of…
A nonstatic Schwarzschild black hole interior solution in Painleve-Gullstrand coordinates is proposed in this paper, by means of a coordinate transformation that changes the spatial coordinate but the timelike one is preserved. The timelike…
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…
The Kerr-Newman black hole solution can be constructed straightforwardly as the unique solution to the boundary value problem of the Einstein-Maxwell equations corresponding to an asymptotically flat, stationary and axisymmetric…