Extremal black holes in D=4 GaussBonnet gravity
Abstract
We show that fourdimensional EinsteinMaxwelldilatonGaussBonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the ReissnerNordström type AdS_{2}×S^{2}. Such black holes exist for the dilaton coupling constant within the interval 0≤a^{2}<a_{cr}^{2}. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they cannot be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined a_{cr}≃0.488219703. For each value of the dilaton coupling a within this interval and for a fixed value of the GaussBonnet coupling α we have a family of black holes parametrized by their electric charge. The relation between the mass, the electric charge, and the dilaton charge at both ends of the allowed interval of a is reminiscent of the Bogomol’nyiPrasadSommerfield condition for dilaton black holes in the EinsteinMaxwelldilaton theory. The entropy of the dilatonGaussBonnet extremal black holes is twice the BekensteinHawking entropy.
 Publication:

Physical Review D
 Pub Date:
 April 2007
 DOI:
 10.1103/PhysRevD.75.084030
 arXiv:
 arXiv:hepth/0701004
 Bibcode:
 2007PhRvD..75h4030C
 Keywords:

 04.20.Jb;
 04.65.+e;
 98.80.k;
 Exact solutions;
 Supergravity;
 Cosmology;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 New material and references added, errors corrected including higher decimals in a_cr, figures improved