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The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code…
We study the linear perturbations about a nonrotating black hole solution of Horndeski's theory, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial infinity and near the horizon) directly from…
We develop a modified CCZ4 formulation of the Einstein equations in $d+1$ spacetime dimensions for general relativity plus a Gauss-Bonnet term, as well as for the most general parity-invariant scalar-tensor theory of gravity up to four…
We obtain a new exact black-hole solution in Einstein-Gauss-Bonnet gravity with a cosmological constant which bears a specific relation to the Gauss-Bonnet coupling constant. The spacetime is a product of the usual 4-dimensional manifold…
In this study, we investigate a nonlinear mechanism driving the formation of scalarized rotating black holes within a scalar-Gauss-Bonnet gravity framework that includes an additional squared Gauss-Bonnet term. With the specific coupling…
Einstein-dilaton-Gauss-Bonnet gravity is a theoretically well-motivated alternative theory of gravity emerging as a low-energy 4-dimensional model from heterotic string theory. Its rotating black hole solutions are known numerically and can…
From time to time, different observations suggest that Einstein's theory of general relativity (GR) may not be the ultimate theory of gravity. Various researchers have suggested that the $f(R)$ theory of gravity is the best alternative to…
We integrate the third and a half post-Newtonian equations of motion for a fully generic binary black hole system, allowing both for non-circular orbits, and for one or both of the black holes to spin, in any orientation. Using the second…
In this thesis, we use numerical relativity to investigate gravitational waves from binary black holes in extensions of GR. We first study spherically symmetric gravitational collapse in cubic Horndeski theories of gravity. By varying the…
We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of…
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…
This book chapter gives an introductory review of a numerical framework for finding static and stationary vacuum black hole solutions. Such methods may be applied to explore the exotic space of higher dimensional black holes that are…
We present a calculation of the conservative two-body Hamiltonian of a compact binary system including a spinning black hole. We include up-to third order corrections in Newton's constant $G$, all orders in velocity, and linear and…
We systematically study the field equations of $f(\mathbb Q)$ gravity for spherically symmetric and stationary metric-affine spacetimes. Such spacetimes are described by a metric as well as a flat and torsionless affine connection. In the…
Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary.…
Gravitational waves from spin-precessing binaries exhibit amplitude oscillations that provide an invaluable method to extract the spins of the inspiraling compact objects. The spin-spin and spin-orbit interactions that cause this effect are…
We study linear perturbations around a static and spherically symmetric black hole solution in spatially covariant gravity with just two tensorial degrees of freedom. In this theory, gravity modification is characterized by a single…
The ability to test general relativity in extreme gravity regimes using gravitational wave observations from current ground-based or future space-based detectors motivates the mathematical study of the symmetries of black holes in modified…
We study the instability of Schwarzschild black holes and the appearance of scalarized solutions in Einstein-scalar-Gauss-Bonnet gravity performing a time-domain analysis in a perturbative scheme. First we consider a quadratic coupling…
We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of…