Related papers: From Geometry to Numerics: interdisciplinary aspec…

Black holes have often provided profound insights into the nature of gravity and the structure of space-time. The study of the mathematical properties of black objects is a major research theme of contemporary theoretical physics. This…

Classical black holes and event horizons are highly non-local objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and…

This is an introduction into the problem of how to set up black hole initial-data for the matter-free field equations of General Relativity. The approach is semi-pedagogical and addresses a more general audience of astrophysicists and…

We present recent developments on numerical algorithms for computing photon and particle trajectories in the surrounding of compact objects. Strong gravity around neutron stars or black holes causes relativistic effects on the motion of…

Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…

There are two mathematical relativity frameworks generalizing the black hole theory: the theory of isolated horizons (IH) and the theory of near horizon geometries (NHG). We outline here and discuss the derivation of the NHG from the theory…

We present an overview of recent developments in the numerical solution of Horndeski gravity theories, which are the class of all scalar-tensor theories of gravity that have second order equations of motion. We review several methods that…

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 review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of…

Over the last few years enormous progress has been made in the numerical description of the inspiral and merger of binary black holes. A particular effort has gone into the modelling of the physical properties of the final black hole,…

This paper presents a quasi-local method of studying the physics of dynamical black holes in numerical simulations. This is done within the dynamical horizon framework, which extends the earlier work on isolated horizons to time-dependent…

Asymptotic symmetries of black hole spacetimes have received much attention as a possible origin of the Bekenstein-Hawking entropy in black hole thermodynamics. In general, it takes hard efforts to find appropriate asymptotic conditions on…

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the…

Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic…

I discuss black hole evaporation in two different coordinate systems and argue that the results of the two are compatible once one takes the holographic principle into account. de Sitter space is then discussed along similar lines. Finally…

We review and announce recent results on the asymptotic behavior of asymptotically Euclidean relativistic initial data sets and asymptotic foliations thereof. In particular, we discuss the geometrization of asymptotic flatness and of…

Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…

General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…

We present a broad review on black holes. We analyse some of the fundamental concepts in black hole theory, the observational and theoretical status of stellar and galactic black holes, and their appearance as quantum objects.

We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are…