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The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…
In the large dimension ($D$) limit, Einstein's equation reduces to an effective theory on the horizon surface, drastically simplifying the black hole analysis. Especially, the effective theory on the black brane has been successful in…
In the present work, we extend and generalize our previous work regarding the scale dependence applied to black holes in the presence of non-linear electrodynamics [1]. The starting point for this study is the Einstein-power-Maxwell theory…
Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. L\"u, A. Perkins, C. Pope, K. Stelle [Phys.Rev.Lett. 114 (2015), 171601]…
Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on…
The gauge-gravity duality can be used to relate connected multi-point graviton functions to connected multi-point correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we constructed in Part I a family…
I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a…
In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out…
We study a black hole solution for the generalized Einstein Hilbert action with scale dependent couplings G(r) and Lambda(r). The form of the couplings is not imposed, but rather deduced from the existence of a non trivial symmetrical…
Focusing on the special case of generalized Rastall theory, as a subclass of the non-minimal curvature-matter coupling theories in which the field equations are mathematically similar to the Einstein field equations in the presence of…
f(R) gravity is one of the simplest generalizations of general relativity, which may explain the accelerated cosmic expansion without introducing a cosmological constant. Transformed into the Einstein frame, a new scalar degree of freedom…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
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…
There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
Physical arguments related with the existence of black hole solutions having a non trapping interior are discussed. Massive scalar fields interacting with gravity are considered. Interior asymptotic solutions showing a scalar field…
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…
A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the…