Magnetized configurations with black holes and Kaluza-Klein bubbles: Smarr-like relations and first law

Abstract

We present a general class of exact solutions in Einstein-Maxwell-dilaton gravity describing configurations of black holes and Kaluza-Klein bubbles magnetized along the compact dimension. Smarr-like relations for the mass and the tension are found. We also derive the mass and tension first law for the configurations under consideration using the Noether current approach. The solutions we consider are explicit examples showing that in Kaluza-Klein spacetimes the interval (rod) structure and the charges (which are zero by construction for the solutions here), are insufficient to classify the solutions and additional data is necessary, namely the magnetic flux(es).

arXiv comment13 pages

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• Magnetized Black Hole on Taub-Nut Instanton
• Sequences of dipole black rings and Kaluza-Klein bubbles
• Charged black holes on a Kaluza-Klein bubble
• Rotating black ring on Kaluza-Klein bubbles
• A Uniqueness theorem for black holes with Kaluza-Klein asymptotic in 5D Einstein-Maxwell gravity
• Charged rotating dilaton black holes with Kaluza-Klein asymptotics
• New forms and thermodynamics of the neutral rotating squashed black hole in five-dimensional vacuum Einstein gravity theory
• Initial data for a black string and a Kaluza-Klein bubble: Space-dependent compactification radius