Conformal mapping of the Misner-Sharp mass from gravitational collapse

TL;DR

This paper investigates how the Misner-Sharp mass transforms under conformal mappings, revealing differences between geometric and original definitions, and reconciling these in gravitational collapse and scalar-tensor theories.

Contribution

It clarifies the conformal behavior of the Misner-Sharp mass in gravitational collapse and scalar-tensor theories, resolving discrepancies between geometric and original definitions.

Findings

Geometric Misner-Sharp mass differs from the original conception under conformal transformations.

In gravitational collapse, the usual conformal transformation of mass is recovered.

Scalar-tensor theories are also analyzed for conformal properties of the mass.

Abstract

The conformal transformation of the Misner-Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner-Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar-tensor theories of gravity is also examined.