Noether charge astronomy

TL;DR

This paper demonstrates that surface gravity in dynamical spacetimes can be interpreted as a measurable Noether charge, enabling direct observational access to gravitational energy and mass distribution in astrophysical objects.

Contribution

It establishes a link between surface gravity and Noether charges in dynamical spacetimes, providing a method to measure gravitational energy directly from astronomical observations.

Findings

Surface gravity acts as a measurable Noether charge.

The gravitating energy can be derived from surface measurements.

Potential to map mass distribution in galaxies and clusters.

Abstract

Noether's theorem identifies fundamental conserved quantities, called Noether charges, from a Hamiltonian. To-date Noether charges remain largely elusive within theories of gravity: We do not know how to directly measure them, and their physical interpretation remains unsettled in general spacetimes. Here we show that the surface gravity as naturally defined for a family of observers in arbitrarily dynamical spacetimes is a directly measurable Noether charge. This Noether charge reduces to the accepted value on stationary horizons, and, when integrated over a closed surface, yields an energy with the characteristics of gravitating mass. Stokes' theorem then identifies the gravitating energy density as the time-component of a locally conserved Noether current in general spacetimes. Our conclusion, that this Noether charge is extractable from astronomical observations, holds the potential for determining the detailed distribution of the gravitating mass in galaxies, galaxy clusters and beyond.