The First Law of Isolated Horizons via Noether Theorem

Details The First Law of Isolated Horizons via Noether Theorem The First Law of Isolated Horizons via Noether Theorem

2001-10-24

arxiv.org/abs/gr-qc/0110104v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

29 pages

Scientific paper

A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to Einstein-Maxwell theory. The electromagnetic field is analysed in the geometric framework of natural bundles. Einstein-Maxwell theory turns then out to be natural rather than gauge-natural. As a consequence of this assumption a correction term \a la Regge-Teitelboim is needed to define the variation of energy, also for the pure electromagnetic part of the Einstein-Maxwell Lagrangian. Integrability conditions for the variational equation which defines the variation of energy are analysed in relation with boundary conditions on physical data. As an application the first law of thermodynamics for rigidly rotating horizons is obtained.

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