Is the gravitational action additive?

TL;DR

This paper investigates the non-additivity of gravitational action in certain spacetime configurations and proposes a generalized form of additivity that applies broadly, with implications for quantum gravity superposition.

Contribution

It introduces a general prescription for action change under boundary identifications and defines a concept of generalized additivity applicable to arbitrary spacetime compositions.

Findings

Gravitational action is not always additive in standard sense

A new prescription for action change under boundary identifications

Generalized additivity holds for arbitrary spacetime compositions

Abstract

The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss possible implications for the superposition law of quantum gravity. We present a definition of `generalized additivity' which does hold for arbitrary spacetime composition.