This article presents a comprehensive overview of numerical hydrodynamics and magneto-
hydrodynamics (MHD) in general relativity. Some significant additions have been …

The present status of the quasi-local mass, energy-momentum and angular-momentum
constructions in general relativity is reviewed. First, the general ideas, concepts, and …

Clarity, readability, and rigor combine in the third edition of this widely used textbook to
provide the first step into general relativity for advanced undergraduates with a minimal …

Equations arising in general relativity are usually too complicated to be solved analytically
and one must rely on numerical methods to solve sets of coupled partial differential …

Event and apparent horizons are key diagnostics for the presence and properties of black
holes. In this article I review numerical algorithms and codes for finding event and apparent …

This book treats the classical problem of gravitational physics within Einstein's theory of
general relativity. It presents basic principles and equations needed to describe rotating fluid …

We propose a new concept, the transversely trapping surface (TTS), as an extension of the
static photon surface characterizing the strong gravity region of a static/stationary spacetime …

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 …

High-accuracy binary black hole simulations are presented for black holes with spins anti-
aligned with the orbital angular momentum. The particular case studied represents an equal …

In the realm of astrophysics, black holes exist within nonvacuum cosmological backgrounds,
making it crucial to investigate how these backgrounds influence the properties of black …