Related papers: Hydrodynamic Simulations in 3+1 General Relativity
We perform fully relativistic calculations of binary neutron stars in corotating, circular orbit. While Newtonian gravity allows for a strict equilibrium, a relativistic binary system emits gravitational radiation, causing the system to…
Some of the most interesting scenarios that can be studied in astrophysics, contain fluids and plasma moving under the influence of strong gravitational fields. To study these problems it is required to implement numerical algorithms robust…
Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…
We present tests and results of a new axisymmetric, fully general relativistic code capable of solving the coupled Einstein-matter system for a perfect fluid matter field. Our implementation is based on the Bondi metric, by which the…
A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity…
We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian…
We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein's equations for the gravitational field, and…
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM…
We investigate the possibility to approximate relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic…
We introduce a computational framework which avoids solving explicitly hydrodynamic equations and is suitable to study the pre-merger evolution of black hole-neutron star binary systems. The essence of the method consists of constructing a…
We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A recent paper by Lucas-Serrano et al. indicates that a high-resolution central (HRC) scheme is robust enough to yield accurate hydrodynamical simulations of special relativistic flows in the presence of ultrarelativistic speeds and strong…
Recent observations of compact binary systems have provided evidence for black holes with masses below standard expectations. When paired with neutron stars (NSs), such low-mass black holes (BHs) have the potential to be detected by future…
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…
We propose a novel numerical method for solving multi-dimensional, special relativistic Boltzmann equations for neutrinos coupled to hydrodynamics equations. It is meant to be applied to simulations of core-collapse supernovae. We handle…
Motivated by a recent paper by the Potsdam numerical relativity group, we have constructed a new numerical code for hydrodynamic simulation of axisymmetric systems in full general relativity. In this code, we solve the Einstein field…
We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions…
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented.…
We develop a hydrodynamic representation of the Klein-Gordon-Maxwell-Einstein equations. These equations combine quantum mechanics, electromagnetism, and general relativity. We consider the case of an arbitrary curved spacetime, the case of…