On Universal Black Holes

Abstract

Recent results [1] on universal black holes in d dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to virtually any metric theory of gravity in vacuum.

Universal p-form black holes in generalized theories of gravity

“…In view of ( 13), the latter reduces to three "scalar" equations F(r ) = 0, G(r ) = 0 and L(r ) = 0. However, similarly as in [13], it is easy to see that the identity ∇ ν E μν = 0 implies that L(r ) = 0 holds automatically once F(r ) = 0 = G(r ) and ( 5) are satisfied. We are thus left with just three ODEs for the two metric functions A(r ) and B(r ) and for the scalar field ϕ(r ).…”

“…In particular, we will show that the metric ansatz studied in [13] -i.e., (1) with h being an IHS -can also be consistently employed to construct d-dimensional static vacuum black hole solutions in any theory (2), provided the gauge fields are suitably adapted to the geometry. 3 Apart from recovering in a unified way results previously obtained on a case-by-case basis for par- 1 The details (including the precise form of A(r ) and B(r )) and physical properties of the solutions will naturally depend on the specific theory one is interested in -see [13] and references therein for various examples. 2 The dual cases p = 1 and p = d −1 are special and lead to static black holes with non-Einstein (and thus non-IHS) horizons [24].…”

“…Using also the fact that (M n , h) is IHS (see the comments in Sect. 2 and [13] for a related discussion), it follows that any symmetric 2-tensor E constructed from tensor products, sums and contractions from ∇ (k) R, ∇ (l) F and ∇ (m) ϕ (k, l, m ≥ 0) must be of the form…”

“…This dramatically enlarges the space of vacuum black hole solutions and permitted horizon geometries for generalized theories of gravity, well beyond the usual case of horizons of constant curvature. We dubbed these spacetime universal black holes [13] to stress the theoryindependence of this result. 1 Black holes with non-trivial gauge fields play an important role in supergravity and string theories (see, e.g., [1] and references therein).…”

“…Nevertheless, we have recently proved [13] (see also [14] for a short summary) that there does exist a special family of Einstein metrics h -the isotropy-irreducible homogeneous spaces (IHS) [15][16][17][18][19] (see Sect. 2 for a definition) -which is virtually immune to all possible tensorial constraints placed by any vacuum theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor R and its covariant derivatives of arbitrary order.…”