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Abstract
We consider the inverse problem of determining all extreme black hole solutions to the Einstein equations with a prescribed nearhorizon geometry. We investigate this problem by considering infinitesimal deformations of the nearhorizon geometry along transverse null geodesics. We show that, up to a gauge transformation, the linearised Einstein equations reduce to an elliptic PDE for the extrinsic curvature of a crosssection of the horizon. We deduce that for a given nearhorizon geometry there exists a finite dimensional moduli space of infinitesimal transverse deformations. We then establish a uniqueness theorem for transverse deformations of the extreme Kerr horizon. In particular, we prove that the only smooth axisymmetric transverse deformation of the nearhorizon geometry of the extreme Kerr black hole, such that crosssections of the horizon are marginally trapped surfaces, corresponds to that of the extreme Kerr black hole. Furthermore, we determine all smooth and biaxisymmetric transverse deformations of the nearhorizon geometry of the fivedimensional extreme MyersPerry black hole with equal angular momenta. We find a three parameter family of solutions such that crosssections of the horizon are marginally trapped, which is more general than the known black hole solutions. We discuss the possibility that they correspond to new five dimensional vacuum black holes.
Original language  English 

Article number  075015 
Number of pages  34 
Journal  Classical and quantum gravity 
Volume  33 
Issue number  7 
DOIs  
Publication status  Published  11 Mar 2016 
Keywords
 grqc
 hepth
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 1 Finished

Particle Theory at the Higgs Centre
FigueroaO'Farrill, J., Lucietti, J. & Simon Soler, J.
1/10/14 → 30/09/18
Project: Research