Higher dimensional black holes and supersymmetry

Abstract

It has recently been shown that the uniqueness theorem for stationary black holes cannot be extended to five dimensions. However, uniqueness is an important assumption of the string theory black hole entropy calculations. This paper partially justifies this assumption by proving two uniqueness theorems for supersymmetric black holes in five dimensions. Some remarks concerning general properties of non-supersymmetric higher dimensional black holes are made. It is conjectured that there exist new families of stationary higher dimensional black hole solutions with fewer symmetries than any known solution.

SupersymmetricAdS5black holes

“…H = H ∩ Σ where Σ is a spacelike slice that intersects H). In the ungauged theory considered in [33] it was shown that these equations can be completely solved when H is compact and the near-horizon geometry can therefore be determined explicitly. This has also been done in the minimal six-dimensional ungauged supergravity [28].…”

“…Therefore it is not possible to identify which solutions have horizons just by looking at the solution in the form presented above. We shall instead adopt the approach introduced in [33]. This approach is equally valid for timelike or null solutions.…”

“…From the first expression we see that V is timelike or null (the possibility of V vanishing anywhere can be excluded using an argument in [33]). …”

“…In the ungauged theory, it is possible to exploit compactness of H to prove that h must be a Killing vector field on H [33]. In the gauged theory, it is natural to guess that if such a Killing vector field exists then it will be a linear combination of h and Z 1 .…”

“…For r > 0, if ∆ > 0 then V is timelike and hence G + is well-defined. Self-duality implies that G + can be written [33] …”