Related papers: Numerical evolutions of the linearised conformal E…

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…

We establish the linear instability of the semiclassical Einstein-Klein-Gordon system linearised about the Minkowski vacuum spacetime. The proof relies on formulating a forcing problem for both metric and state perturbations within the…

We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial…

We prove the global stability of the Minkowski space viewed as the trivial solution of the Einstein-Vlasov system. To estimate the Vlasov field, we use the vector field and modified vector field techniques developed in [FJS15; FJS17]. In…

One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…

We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of space-times.

A unified general approach is presented for construction of solutions of the characteristic initial value problems for various integrable hyperbolic reductions of Einstein's equations for space-times with two commuting isometries in General…

We develop an exact functional method applied to the bosonic string on a shperical world sheet, in graviton and dilaton backgrounds, consistent with conformal invariance. In this method, quantum fluctuations are controled by the amplitude…

The linearized field equations for causal fermion systems in Minkowski space are analyzed systematically using methods of functional analysis and Fourier analysis. Taking into account a direction-dependent local phase freedom, we find a…

This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and $f(R,T)$-modifications. The constructions are possible in terms of…

Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the…

The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, high-order nonlinearities correspond to a…

The Einstein evolution equations have been written in a number of symmetric hyperbolic forms when the gauge fields--the densitized lapse and the shift--are taken to be fixed functions of the coordinates. Extended systems of evolution…

We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…

A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…

Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…

A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. These resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the…

Einstein field equations with a cosmological constant are approximated to the second order in the perturbation to a flat background metric. The final result is a set of Einstein-Maxwell-Proca equations for gravity in the weak field regime.…

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…