Smooth Gowdy-symmetric generalised Taub–NUT solutions in Einstein–Maxwell theory

Abstract

We introduce a new class of inhomogeneous cosmological models as solutions to the Einstein-Maxwell equations in electrovacuum. The new models can be considered to be nonlinear perturbations, through an electromagnetic field, of the previously studied 'smooth Gowdy-symmetric generalised Taub-NUT solutions' in vacuum. Utilising methods from soliton theory, we analyse the effects of the Maxwell field on global properties of the solutions. In particular, we show existence of regular Cauchy horizons, and we investigate special singular cases in which curvature singularities form.

A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes

“…Theoretical advances can be found in [1,4,5,7,9,13,23], including the derivation of expansions for solutions in the vicinity of a cosmological singularity. Of course, in most cases the solutions are not known in a close form (with the exception of, for instance, [6,[17][18][19]) and therefore we must appeal to numerical approximation in order to analyze the qualitative properties of solutions. Since the solutions of interest blow-up on the singularity t = 0, it it necessary to develop an adapted methodology in order to reach reliable conclusions on, for instance, the stability of solutions with respect to their initial data.…”

On the balance problem for two rotating and charged black holes

“…According to (10), the function λ simplifies to λ = ±1 on the two Riemannian sheets. As a consequence, the LP (11) and ( 12) also becomes particularly simple and reduces to an ODE. The general solution can easily be derived.…”

“…These considerations crucially rely on the fact that the Einstein-Maxwell equations in electrovacuum for axisymmetric and stationary spacetimes can be reformulated in terms of a linear matrix problem, as a consequence of which methods from soliton theory are applicable. Note that closely related techniques also work in the context of Gowdy-symmetric cosmological models (which have two spacelike Killing vectors rather than a spacelike and a timelike Killing vector) [4,10,11,13]. Yet another type of application is the investigation of the interior region of axisymmetric and stationary black holes [2,12].…”