The first law and Wald entropy formula of heterotic stringy black holes at first order in α'

Black-hole thermodynamics is probably one of the most active fields of research in The- oretical Physics. It interconnects seemingly disparate areas of Physics such as Gravity, Quantum Field Theory, and Information Theory, providing deep insights in all of them.

While initially valid only for General Relativity, Wald and collaborators developed a new approach to demonstrate the first law of black hole mechanics in general diffeomorphism- invariant theories, beyond General Relativity. As a by-product, this approach lead to the identification of an expression that plays the role of entropy (Wald entropy) in the first law in theories beyond General Relativity. However, the first laws and the entropy formulas derived in the literature with this formalism (the Iyer-Wald prescription) present severe shortcomings in certain string theories, such as missing work terms in the first laws and lack of gauge invariance of the entropy formula.

This thesis will be broken down into 2 parts. After providing a brief introduction to black hole thermodynamics and Iyer-Wald formula and its shortcomings, we will begin introducing a technique to calculate the entropy in a gauge invariant way.

In Part I, we test our ideas on the d-dimensional Reissner-Nordström-Tangherlini black hole in the context of the Einstein-Maxwell theory. This simplified test case allows us clearly demonstrate the techniques and its power.

After, we shall illustrate this gauge covariant formula in a non trivial case: the action of the heterotic string at first order in $\alpha'$.  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 α' that can be reliably used in a comparison with the microscopic ones.

pie de foto: 

Zach Elgood