More on the conformal mapping of quasi-local masses: The Hawking-Hayward case

TL;DR

This paper reexamines the conformal transformation properties of the Hawking-Hayward quasi-local mass, showing it aligns with expected behavior when expressed through field equations, and explores implications in scalar-tensor theories.

Contribution

It demonstrates that the Hawking-Hayward mass exhibits the correct conformal factor when related to matter content, clarifying previous discrepancies and analyzing scalar-tensor theories.

Findings

Hawking-Hayward mass aligns with expected conformal behavior when expressed via field equations.

The equivalence with Misner-Sharp mass is confirmed in spherically symmetric spacetimes.

Conformal invariance in scalar-tensor theories is also examined.

Abstract

The conformal transformation of the Hawking-Hayward quasi-local mass is reexamined. It has been found recently that the conformal transformation of the latter exhibits the 'wrong' conformal factor compared to the way usual masses transform under conformal transformations of spacetime. We show, in analogy with what was found recently for the Misner-Sharp mass, that unlike the purely geometric definition of the Hawking-Hayward mass, the latter exhibits the 'right' conformal factor whenever expressed in terms of its material content via the field equations. The case of conformally invariant scalar-tensor theories of gravity is also examined. The equivalence between the Misner-Sharp mass and the Hawking-Hayward mass for spherically symmetric spacetimes manifests itself by giving identical peculiar behaviors under conformal transformations.