2008/10/31 by Jan Perz, Paul Smyth, Thomas Van Riet +1 · 2 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/03/150
published as JHEP 0903:150,2009 · 27 pages, v2: small changes, referencing and misprints corrected, v3: text updated and a reference added to match the JHEP version
openalex publication_date 2009/03/31 · arxiv created 2009/06/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive a general form of first-order flow equations for extremal and non-extremal, static, spherically symmetric black holes in theories with massless scalars and vectors coupled to gravity. By rewriting the action as a sum of squares a la Bogomol'nyi, we identify the function governing the first-order gradient flow, the `generalised superpotential', which reduces to the `fake superpotential' for non-supersymmetric extremal black holes and to the central charge for supersymmetric black holes. For theories whose scalar manifold is a symmetric space after a timelike dimensional reduction, we present the condition for the existence of a generalised superpotential. We provide examples to illustrate the formalism in four and five spacetime dimensions.