Einstein-Born-Infeld on Taub-NUT Spacetime in 2k+2 Dimensions

TL;DR

This paper numerically constructs Taub-NUT solutions in Einstein-Born-Infeld gravity across 4, 6, and 8 dimensions, revealing dimension-dependent existence of NUT solutions.

Contribution

It provides the first numerical analysis of Taub-NUT solutions in Einstein-Born-Infeld gravity in multiple dimensions, extending previous Einstein-Maxwell results.

Findings

NUT solution exists only in 8 dimensions for specific parameters

Numerical solutions obtained via Runge-Kutta method

Data fitting confirms the absence of Nut solutions in 4 and 6 dimensions

Abstract

We wish to construct solutions of Taub-NUT spacetime in Einstein-Born-Infeld gravity in even dimensions. Since Born-Infeld theory is a nonlinear electrodynamics theory, in leads to nonlinear differential equations. However a proper analytical solution was not obtain, we try to solve it numerically (by the Runge-Kotta method) with initial conditions coinciding with those of our previous work in Einstein-Maxwell gravity. We solve equations for 4, 6 and 8 dimensions and do data fitting by the least-squares method. For N=l=b=1, the metric turns to the NUT solution only in 8 dimensions, but in 4 and 6 dimensions the spacetime does not have any Nut solution.