Counterterm Method in Lovelock Theory and Horizonless Solutions in Dimensionally Continued Gravity

TL;DR

This paper extends the counterterm method to Lovelock gravity, derives horizonless brane solutions with conic singularities, and computes their conserved quantities, enhancing understanding of such spacetimes in higher curvature theories.

Contribution

It generalizes the quasilocal stress tensor and counterterm approach to Lovelock gravity and constructs horizonless solutions with no curvature singularities.

Findings

Solutions have no curvature singularities or horizons.

These spacetimes are asymptotically AdS with two fundamental constants.

Conserved quantities are successfully computed using the extended counterterm method.

Abstract

In this paper we, first, generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of Lovelock gravity, by introducing the tensorial form of surface terms that make the action well-defined. We also introduce the boundary counterterm that removes the divergences of the action and the conserved quantities of the solutions of Lovelock gravity with flat boundary at constant $t$ and $r$. Second, we obtain the metric of spacetimes generated by brane sources in dimensionally continued gravity through the use of Hamiltonian formalism, and show that these solutions have no curvature singularity and no horizons, but have conic singularity. We show that these asymptotically AdS spacetimes which contain two fundamental constants are complete. Finally we compute the conserved quantities of these solutions through the use of the counterterm method introduced in the first part of the paper.