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2015

Transverse deformations of extreme horizons

Li, Carmen, Lucietti, James

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We consider the inverse problem of determining all extreme black hole solutions to the Einstein equations with a prescribed near-horizon geometry.

We investigate this problem by considering infinitesimal deformations of the near-horizon 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 cross-section of the horizon.
We deduce that for a given near-horizon geometry there exists a finite dimensional moduli space of infinitesimal transverse deformations.

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