The first law of black brane mechanics

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  • 26 July 2001
Abstract
We obtain ADM and Komar surface integrals for the energy density, tension and angular momentum density of stationary $p$-brane solutions of Einstein's equations. We use them to derive a Smarr-type formula for the energy density and hence a first law of black brane mechanics. The intensive variable conjugate to the worlspace p-volume is an `effective' tension that equals the ADM tension for uncharged branes, but vanishes for isotropic boost-invariant charged branes.

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