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

Understand

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.