Related papers: Numerical solutions to Einstein's equations in a s…
In the framework of non-riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein-Hilbert action when torsion degrees of freedom are taken into account. By…
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework…
We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for…
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of…
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…
Relativistic numerical cosmology is most often based either on the exact solutions of the Einstein equations, or perturbation theory, or weak-field limit, or the BSSN formalism. The Silent Universe provides an alternative approach to…
Since the development of Relativity theory, a variety of solutions have been found around Einstein field equations, depending on the time-space. For instance, we can find the axially symmetric space which describes a rotanting black hole.…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
The standard numerical tools for studying non-linear collapse of matter are Newtonian $N$-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{\mu \nu}T^{\mu \nu})$ type. To prove this statement, exact and approximate solutions are…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
We present a new N-body code, gevolution, for the evolution of large scale structure in the Universe. Our code is based on a weak field expansion of General Relativity and calculates all six metric degrees of freedom in Poisson gauge.…
We investigate the interplay between quantum theory and gravity by exploring gravitational lensing and Einstein ring images in a weak gravitational field induced by a mass source in spatial quantum superposition. We analyze a quantum…
The constructive gravity programme applied to electrodynamics with vacuum birefringence yields the---up to unknown gravitational constants---unique compatible gravity theory for the underlying non-metric geometry. Starting from a…
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such…
This article deals with a nonrelativistic cosmological model based on Galilean covariance, formulated within a five-dimensional Galilean manifold. Within this framework, we construct an isotropic and homogeneous metric analogous to the…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
In the framework of Lagrangian perturbation theory in general relativity we discuss the possibility to split the Einstein equations, written in terms of spatial Cartan coframes within a 3+1 foliation of spacetime, into gravitoelectric and…
We present formulations of effective potentials suitable for approximating general relativistic effects in Newtonian simulations of core-collapse supernovae. Assuming a spherically symmetric spacetime and a stress-energy tensor that…