Absolute conservation law for black holes

TL;DR

This paper establishes a universal conservation law in 2D gravity theories linking the mass aspect function with matter fields, applicable across various gauges and related to ADM and Bondi masses, with potential for broad applications.

Contribution

It derives a general conservation law in 2D gravity theories using a first order formulation, clarifying its relation to ADM and Bondi masses and enabling straightforward generalizations.

Findings

Conservation law connects mass aspect and matter fields at all times and radii.

Relation of conserved quantity to ADM and Bondi mass is clarified.

Framework allows easy gauge fixing and potential applications to higher dimensions and AdS spacetimes.

Abstract

In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as determining the initial value together with the initial values for the matter field. We discuss this for spherically reduced Einstein-gravity in a diagonal metric and in a Bondi-Sachs metric using the first order formulation of spherically reduced gravity, which allows easy and direct fixations of any type of gauge. The relation of our conserved quantity to the ADM and Bondi mass is investigated. Further possible applications (ideal fluid, black holes in higher dimensions or AdS spacetimes etc.) are straightforward generalizations.