The First Law of Isolated Horizons via Noether Theorem
Abstract
A general recipe proposed elsewhere to define, via Noether theorem, the variation of energy for a natural field theory is applied to EinsteinMaxwell theory. The electromagnetic field is analysed in the geometric framework of natural bundles. EinsteinMaxwell theory turns then out to be natural rather than gaugenatural. As a consequence of this assumption a correction term \a la ReggeTeitelboim is needed to define the variation of energy, also for the pure electromagnetic part of the EinsteinMaxwell 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:grqc/0110104
 Bibcode:
 2001gr.qc....10104A
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 29 pages