$n+1$-dimensional Bertotti-Robinson solutions in gravity coupled with nonlinear electrodynamics

TL;DR

This paper derives conformally flat Bertotti-Robinson solutions in higher-dimensional gravity coupled with nonlinear electrodynamics, identifying specific power-law conditions and addressing the special case of four dimensions separately.

Contribution

It extends Bertotti-Robinson solutions to $n+1$ dimensions with nonlinear electrodynamics, providing explicit conditions and solutions for various dimensions.

Findings

Conformally flat solutions exist in all dimensions except four.

Specific power-law conditions for the Lagrangian are identified.

The four-dimensional case is treated separately due to its unique properties.

Abstract

We consider the pure electric type power-law Lagrangian in nonlinear electrodynamics theory of dimensions $n+1$. Conformally flat form of Bertotti-Robinson type spacetimes are obtained in all these dimensions with the specific power $s=-\frac{1}{n-4},$which naturally excludes $n=4.$ This particular dimension is considered separately which is not of power-law form.