Null-null components of the generalized Einstein tensor for Lovelock models

TL;DR

This paper derives explicit expressions for the null-null components of the generalized Einstein tensor in Lovelock gravity under spherical symmetry, aiding in theoretical analyses like Birkhoff's theorem and energy conditions.

Contribution

It provides new formulas for null-null components of the Einstein tensor in Lovelock models, facilitating advanced theoretical investigations.

Findings

Explicit expressions for null-null components derived

Application to Birkhoff-like theorem demonstrated

Relation between null energy and null convergence conditions established

Abstract

For spherical symmetry, we provide expressions for the radial null-null components of the generalized Einstein tensor $E_{ab}$ for Lovelock models for diagonal $E_{ab}$ in terms of the metric and of the radial null-null components of the Ricci tensor. We show they can be usefully employed for example in obtaining the Birkhoff-like theorem for Lovelock models, as well as in providing a relation between the null energy and null convergence conditions for the same models.