Warping effects in strongly perturbed metrics

TL;DR

This paper presents an exact solution for the leading order Einstein equations under strong perturbations, revealing an exponential warp factor affecting the 4-velocity in a spherically symmetric Schwarzschild metric.

Contribution

It provides a novel exact solution for strongly perturbed Einstein equations, demonstrating the warp effect on 4-velocity in spherical symmetry.

Findings

Warp factor always exceeds one

Exact solution for the leading order Einstein equations

Numerical examples illustrating the warp effect

Abstract

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translates into a gradient expansion that, at the leading order, can recover the BKL solution in general relativity. We solve exactly the leading order Einstein equations in a spherical symmetric case, assuming a Schwarzschild metric under the effect of a time-dependent perturbation, and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.