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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
A new class of vacuum black holes for the most general gravity theory leading
to second order field equations in the metric in even dimensions is presented.
These space-times are locally AdS in the asymptotic region, and are
characterized by a continuous parameter that does not enter in the conserve
charges, nor it can be reabsorbed by a coordinate transformation: it is
therefore a purely gravitational hair. The black holes are constructed as a
warped product of a two-dimensional space-time, which resembles the r-t plane
of the BTZ black hole, times a warp factor multiplying the metric of a
D-2-dimensional Euclidean base manifold, which is restricted by a scalar
equation. It is shown that all the Noether charges vanish. Furthermore, this is
consistent with the Euclidean action approach: even though the black hole has a
finite temperature, both the entropy and the mass vanish. Interesting examples
of base manifolds are given in eight dimensions which are products of Thurston
geometries, giving then a nontrivial topology to the black hole horizon. The
possibility of introducing a torsional hair for these solutions is also
discussed.
