The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime

Abstract

We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in alpha prime using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in alpha prime that can be reliably used in a comparison with the microscopic ones. Such a formula was still lacking in the literature. In the proof we use momentum maps to define covariant variations and Lie derivatives and \textit{restricted generalized zeroth laws} which state the closedness of certain differential forms on the bifurcation sphere and imply the constancy of the associated potentials on it. We study the relation between our entropy formula and other formulae that have been used in the literature.

arXiv comment35 pages, no figures

References in corpus (29)

• Microscopic Origin of the Bekenstein-Hawking Entropy
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Black Hole Entropy in the presence of Chern-Simons Terms
• Boundary charges in gauge theories: using Stokes theorem in the bulk
• Global Extensions of Spacetimes Describing Asymptotic Final States of Black Holes
• Black hole entropy and Lorentz-diffeomorphism Noether charge
• The Role of Dipole Charges in Black Hole Thermodynamics
• The First Law of Black Hole Mechanics for Fields with Internal Gauge Freedom
• A Non--Supersymmetric Dyonic Extreme Reissner--Nordström Black Hole
• On the supersymmetries of anti de Sitter vacua
• Solution Phase Space and Conserved Charges: A General Formulation for Charges Associated with Exact Symmetries
• A Note on Lie-Lorentz Derivatives
• Note on the First Law with p-form potentials
• ${\alpha }^{\prime }$-corrected black holes in String Theory
• T duality and Wald entropy formula in the Heterotic Superstring effective action at first order in ${\alpha }^{\prime }$
• Beyond the near-horizon limit: Stringy corrections to Heterotic Black Holes
• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime
• Surface Charges for Gravity and Electromagnetism in the First Order Formalism
• Exact charges from heterotic black holes
• T-duality equivalences beyond string theory
• Surface Charges Toolkit for Gravity
• On the dualization of scalars into (d-2)-forms in supergravity. Momentum maps, R-symmetry and gauged supergravity
• First law of black hole mechanics with fermions
• Covariant Noether Charge for Higher Dimensional Chern-Simons Terms
• On the supersymmetric solutions of the Heterotic Superstring effective action
• General theory of Lie derivatives for Lorentz tensors

Cited by in corpus (21)

• Corrections to AdS${}_5$ Black Hole Thermodynamics from Higher-Derivative Supergravity
• Love numbers and magnetic susceptibility of charged black holes
• String gravity in $D=4$
• O(n,n) invariance and Wald entropy formula in the Heterotic Superstring effective action at first order in alpha'
• Komar integrals for theories of higher order in the curvature and black-hole chemistry
• The first law of heterotic stringy black hole mechanics at zeroth order in alpha prime
• Magnetic charges and Wald entropy
• On scalar charges and black-hole thermodynamics
• Black hole chemistry, the cosmological constant and the embedding tensor
• Boundary terms and conserved charges in higher-derivative gauged supergravity
• Thermodynamics of accelerating AdS${}_4$ black holes from the covariant phase space
• Komar integral and Smarr formula for axion-dilaton black holes versus S duality
• Improved Wald formalism and First Law of Dyonic Black Strings with Mixed Chern-Simons Terms
• Non-extremal, ${\alpha }^{\prime }$-corrected black holes in 5-dimensional Heterotic Superstring Theory
• Black hole superpotential as a unifying entropy function and BPS thermodynamics
• Higher derivative couplings of hypermultiplets
• Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
• Higher-derivative Heterotic Kerr-Sen Black Holes
• A note on the Noether-Wald and generalized Komar charges
• Starobinsky-Bel-Robinson gravity
• Non-supersymmetric black holes with ${\alpha }^{\prime }$ corrections