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

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.

9 pages; some references, and comments on the connection of the results here with the null energy and null convergence conditions, added

References in corpus (4)

• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Dynamical black holes with symmetry in Einstein-Gauss-Bonnet gravity
• Jebsen-Birkhoff theorem and its stability in f(R) gravity
• Entropy bounds and field equations