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Numerical relativity is finally coming of age with the development of massively parallel computers. 3D problems, which were completely intractable several years ago due to limited computer power, can now be performed with grid sizes of…
Though the main applications of computer simulations in relativity are to astrophysical systems such as black holes and neutron stars, nonetheless there are important applications of numerical methods to the investigation of general…
Physics in curved spacetime describes a multitude of phenomena, ranging from astrophysics to high energy physics. The last few years have witnessed further progress on several fronts, including the accurate numerical evolution of the…
We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless…
Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of…
Numerical relativity has seen incredible progress in the last years, and is being applied with success to a variety of physical phenomena, from gravitational-wave research and relativistic astrophysics to cosmology and high-energy physics.…
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…
This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of…
There has never been a more exciting time in the overlapping areas of nuclear physics, particle physics and relativistic astrophysics than today. Orbiting observatories such as the Hubble Space Telescope, Rossi X-ray Timing Explorer (RXTE),…
Upcoming gravitational wave-experiments promise a window for discovering new physics in astronomy. Detection sensitivity of the broadband laser interferometric detectors LIGO/VIRGO may be enhanced by matched filtering with accurate…
The first attempts at solving a binary black hole spacetime date back to the 1960s, with the pioneering works of Hahn and Lindquist. In spite of all the computational advances and enormous efforts by several groups, the first stable,…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…
This set of notes was designed to accompany two hours of lectures and practical exercises at the New Horizons for Psi workshop in Lisbon in July 2024 entitled "Studying fundamental fields with numerical relativity". Numerical relativity is…
Advances in our understanding of the origin, evolution and structure of the universe have long been driven by cosmological perturbation theory, model building and effective field theory. In this review, we introduce numerical relativity as…
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,…
We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in three major areas of BH physics: (i) BHs as…
The evolution of black-hole binaries in vacuum spacetimes constitutes the two-body problem in general relativity. The solution of this problem in the framework of the Einstein field equations is a substantially more complex exercise than…
Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of…
Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the…
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…