Related papers: A Simple, Direct Finite Differencing of the Einste…
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…
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…
A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized wave equation alone, for an arbitrary gauge using standard general relativity. In any harmonic gauge, the form…
We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow…
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to the Einstein's linearized field equations. We show that only the Ricci squared quadratic invariant contributes to…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
We study how the changes of coordinates between the class of harmonic coordinates affect the analitycal solutions of Einstein's equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the…
Through averaging the Einstein equations over transverse gravitational perturbations it is obtained a closed system of two ordinary differential equations describing macroscopic cosmological evolution of the isotropic space-flat Universe…
In axial symmetry, there is a gauge for Einstein equations such that the total mass of the spacetime can be written as a conserved, positive definite, integral on the spacelike slices. This property is expected to play an important role in…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
We study the evolution equations for gravitational waves, which are derived using the full metric to raise and lower indices. This method ensures full consistency between the Ricci tensor and all gauge restrictions and requirements, and…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
The existence of gravitational radiation is a natural prediction of any relativistic description of the gravitational interaction. In this chapter, we focus on gravitational waves, as predicted by Einstein's general theory of relativity.…
We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor…
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…
We develop a method for constructing of the basic functions with witch to expand small perturbations of space-time in General Relativity. The method allows to obtain the tensor harmonics for perturbations of the background space-time…
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…