The first law of heterotic stringy black hole mechanics at zeroth order in α′ - INSPIRE

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The first law of heterotic stringy black hole mechanics at zeroth order in α′

Dec 24, 2020

45 pages

Published in:

JHEP 07 (2021) 007

Published: Jul 5, 2021

e-Print:

2012.13323 [hep-th]

DOI:

10.1007/JHEP07(2021)007

Report number:

IFT-UAM/CSIC-20-181

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Abstract: (Springer)

We prove the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in α′, using Wald’s formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law. We study explicitly a non-extremal, charged, black ring solution of pure

\mathcal{N}

= 1, d = 5 supergravity embedded in the Heterotic Superstring effective field theory.This work is a first step towards the derivation of the first law at first order in α′ where, more complicated, non-Abelian, Lorentz (“gravitational”) and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.

Note:

A complete example in which the momentum maps of a non-extremal, charged, black ring are computed, has been added to the paper. 45 pages

Black Holes in String Theory
Classical Theories of Gravity
Differential and Algebraic Geometry
black hole: mechanics
invariance: gauge
black hole: entropy
Chern-Simons term: abelian
black hole: string
charge: conservation law
superstring: heterotic

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