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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…
One of the main predictions of general relativity is the existence of black holes featuring a horizon beyond which nothing can escape. Gravitational waves from the remnants of compact binary coalescences have the potential to probe new…
We present solutions of DHOST theories describing a rotating black hole embedded in an expanding universe. The solution is constructed by conformal transformation of a stealth Kerr(-de Sitter) black hole. The conformal factor depends…
We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and…
Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original…
Physically admissible choice of the "essential" coordinates identified with components of the metric tensor and co-moving frame of reference reduced to the formulation of the stationary axisymmetric GR problem. Such nontraditional approach…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…
This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified…
In the context of $f(R)$ theories of gravity, we address the problem of finding static and spherically symmetric black hole solutions. Several aspects of constant curvature solutions with and without electric charge are discussed. We also…
Extended gravitational models have gained large attention in the last couple of decades. In this work, we examine the solution space of vacuum, static, and spherically symmetric spacetimes within $F(R)$ theories, introducing novel methods…
In this paper, we have introduced new viable solutions of Einstein-Maxwell field equations by incorporating the features of anisotropic matter distribution in the realm of General theory of Relativity ($GR$). For this procurement, we have…
A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several…
We use soliton methods in order to investigate the interior electrovacuum region of axisymmetric and stationary, electrically charged black holes with arbitrary surrounding matter in Einstein-Maxwell theory. These methods can be applied…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…
We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is…
We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses…
Through an illuminating thought experiment we demonstrate that the nonsingular "continued collapse" picture of a black hole is the only consistent and physical one. We provide a class exact solutions on the boundary of the space of physical…
Recent observations of the orbits of star clusters around Sgr $A^\star$, imaging of black holes and gravitational waveforms of merging compact objects require a detailed understanding of the general relativistic geodesic motion. We came up…