Note on the First Law with p-form potentials

Abstract

The conserved charges for $p$-form gauge fields coupled to gravity are defined using Lagrangian methods. Our expression for the surface charges is compared with an earlier expression derived using covariant phase space methods. Additional properties of the surfaces charges are discussed. The proof of the first law for gauge fields that are regular when pulled-back on the future horizon is detailed and is shown to be valid on the bifurcation surface as well. The formalism is applied to black rings with dipole charges and is also used to provide a definition of energy in plane wave backgrounds.

13 pages, revtex, additional comments, published version

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• Gauge Invariant Derivation of Zeroth and First Laws of Black Hole Thermodynamics
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• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
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• Conserved charge of a gravity theory with $p$-form gauge fields and its property under Kaluza-Klein reduction
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• Three dimensional black strings: instabilities and asymptotic charges
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