First law of black hole mechanics in Einstein-Maxwell and Einstein-Yang-Mills theories
Sijie Gao
TL;DR
This paper derives the first law of black hole mechanics for Einstein-Maxwell and Einstein-Yang-Mills theories by comparing nearby stationary black hole solutions, extending classical results to these gauge field theories.
Contribution
It provides a derivation of the first law of black hole mechanics within Einstein-Maxwell and Einstein-Yang-Mills frameworks, highlighting their similarities and differences.
Findings
First law derived for Einstein-Maxwell black holes
First law derived for Einstein-Yang-Mills black holes
Method based on comparing infinitesimally nearby stationary solutions
Abstract
The first law of black hole mechanics is derived from the Einstein-Maxwell (EM) Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills (EYM) theory is also derived.
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