Generalised mass variation formula for a stationary axisymmetric star or black hole with surrounding accretion disc

TL;DR

This paper develops a general relativistic mass-energy variation formula for stationary axisymmetric systems, applicable to self-gravitating fluids like stars or black holes with accretion discs, considering complex matter states.

Contribution

It introduces a new mass-energy variation formula tailored for axisymmetric, self-gravitating fluids with multiple constituents in stationary equilibrium.

Findings

Derived a relativistic mass variation formula for axisymmetric systems.

Applicable to systems with multiconstituent fluids or superfluids.

Enhances understanding of mass-energy relations in astrophysical objects.

Abstract

The general relativistic mass-energy variation formula for axisymmetric equilibrium states of a selfgravitating system is developed in the particular case for which the relevant matter consists of a perfectly conducting multiconstituent fluid (or superfluid) with stationary circular or convective motion.