The Gravitational Action in Asymptotically AdS and Flat Spacetimes

TL;DR

This paper investigates how to regularize the gravitational action in asymptotically AdS and flat spacetimes by using local counterterms, providing efficient methods for both cases to handle divergences.

Contribution

It introduces a systematic counterterm prescription for both asymptotically AdS and flat spacetimes, improving the finiteness of gravitational actions.

Findings

Counterterms effectively remove divergences in AdS and flat spacetimes.

An iterative method for AdS counterterms is developed.

A new approach for flat space counterterms is proposed.

Abstract

The divergences of the gravitational action are analyzed for spacetimes that are asymptotically anti-de Sitter and asymptotically flat. The gravitational action is rendered finite using a local counterterm prescription, and the relation of this method to the traditional reference spacetime is discussed. For AdS, an iterative procedure is devised that determines the counterterms efficiently. For asymptotically flat space, we use a different method to derive counterterms which are sufficient to remove divergences in most cases.