Smarr's formula for black holes with non-linear electrodynamics

Details Smarr's formula for black holes with non-linear electrodynamics Smarr's formula for black holes with non-linear electrodynamics

2004-05-21

arxiv.org/abs/gr-qc/0405116v1

Gen.Rel.Grav.37:643-650,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 3 figures.Contribution to the Festscrift of Prof. A. Garcia

Scientific paper

10.1007/s10714-005-0051-x

It is known that for nonlinear electrodynamics the First Law of Black Hole Mechanics holds, however the Smarr's formula for the total mass does not. In this contribution we discuss the point and determine the corresponding expressions for the Bardeen black hole solution that represents a nonlinear magnetic monopole. The same is done for the regular black hole solution derived by Ayon-Beato and Garcia, showing that in the case that variations of the electric charge are involved, the Smarr's formula does not longer is valid.

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