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Non-extreme black holes of five-dimensional $$N=2$$ AdS supergravity. (English) Zbl 0949.83072
Summary: We consider static black holes of $$D=5$$, $$N=2$$ gauged supergravity with general spatial curvature $$k$$ and show that the modifications due to the gauging as well as $$k$$ enter only the non-extremality function. Therefore, one can promote any (known) black hole solution of ungauged supergravity with $$k=+1$$ to a solution of gauged supergravity with an arbitrary $$k$$. As an example we discuss a solution for the STU model of gauged supergravity which is incidentally also a solution of $$D=5$$, $$N=4$$ and $$N=8$$ gauged supergravity. This solution is specified by three charges, the asymptotic negative cosmological constant (minimum of the potential) and a non-extremality parameter. While its BPS-saturated limit has a naked singularity, we find a lower bound on the non-extremality parameter (or equivalently on the ADM mass) for which the non-extreme solutions are regular. When this bound is saturated the extreme (non-supersymmetric) solution has zero Hawking temperature and finite entropy. Analogous qualitative features are expected to emerge for black hole solutions in $$D=4$$ gauged supergravity as well.

##### MSC:
 83E50 Supergravity 83C57 Black holes 83C75 Space-time singularities, cosmic censorship, etc. 80A10 Classical and relativistic thermodynamics
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