The first law of soliton and black hole mechanics in five dimensions

Abstract

We derive a mass formula and a mass variation law for asymptotically flat, stationary spacetimes, invariant under two commuting rotational symmetries, in a general five dimensional theory of gravity coupled to an arbitrary set of Maxwell fields and uncharged scalar fields. If the spacetime is everywhere regular, these mass formulas reduce to a sum of magnetic flux terms defined on its non-trivial 2-cycles. If there is a black hole, we obtain a mass variation law more general than previously obtained, which also has contributions from the 2-cycles exterior to the black hole. This can be interpreted as the first law of black hole mechanics in a background soliton containing bubbles.

13 pages. v2: minor changes, references added, published version

References in corpus (4)

• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• A Uniqueness theorem for 5-dimensional Einstein-Maxwell black holes
• Note on the First Law with p-form potentials
• Magnetized configurations with black holes and Kaluza-Klein bubbles: Smarr-like relations and first law

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