Explicit black hole thermodynamics in natural variables

We initiate a systematic study of supersymmetric backgrounds in 4d 𝒩 = 2 Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the action in terms of nuts and bolts, we consider the two maximally symmetric vacua ℝ4 and ℍ4 (Euclidean AdS4) and their unique supersymmetric deformations with (anti-) self-dual Maxwell tensors corresponding to a single nut at the center. These are the Omega background of Nekrasov-Okounkov, Ωℝ4, and its generalization with a cosmological constant of Martelli-Passias-Sparks, denoted Ωℍ4 (also known as the gravity dual of the U(1) × U(1) squashed sphere). We write down the BPS configurations in the superconformal formalism in the presence of vector multiplets and derive the corresponding off- and on-shell actions. Our results provide a rigorous proof for important parts of the conjecture in [1] and its holographic corollary in [2], which we discuss in detail along with extensions such as the addition of hypermultiplets and the presence of conical defects.

Section: List Of Open Questionsmentioning

confidence: 99%

Maximally symmetric nuts in 4d 𝒩 = 2 higher derivative supergravity

Hristov

2023

Black hole thermodynamics in natural variables: quadrophenia

Hristov

2024

It was recently observed in [1] for thermal Kerr-Newman black holes in 4d flat space that one can rewrite the conventional thermodynamics on the inner and outer horizons in terms of left- and right-moving variables with a remarkable simplification of the corresponding expressions. With the goal of illustrating the wide applicability of these newly proposed natural variables, we extend the original observation in four independent directions that can be further superimposed on each other. These four generalizations can be thought of as different deformations of the original 4d Einstein-Maxwell theory, all within the framework of supergravity: higher derivative (HD) corrections in minimal 4d supergravity; additional scalar and vector couplings in matter-coupled 4d supergravity; higher dimensions, in particular 5d minimal supergravity; and a cosmological constant in 4d minimal gauged supergravity with Anti-de Sitter (AdS) vacuum. Each of these generalizations offers a different lesson about the novel thermodynamics, and we pay special attention to the respective BPS limits that can be understood from fixed point formulae, demonstrating the power of the natural variables to capture the full phase space.

Explicit black hole thermodynamics in natural variables

Hristov

2023

We consider the general thermal asymptotically flat Kerr-Newman black holes in 4d Einstein-Maxwell theory. Even though their thermodynamics has been understood for decades, the Gibbs free energy and on-shell action are only known implicitly as functions of the standard chemical potentials. Using the so-called left and right moving (or holomorphic and anti-holomorphic) variables related to the chemical potentials on both the outer and the inner horizons, we are able to present explicit and very simple expressions for all quantities. We discuss various limits in the parameter space, remarkably finding a smooth BPS limit allowing direct access to the extremal surface. In the BPS limit the anti-holomorphic part of the on-shell action vanishes identically, leading automatically to the holomorphic expression expected microscopically. This gives us confidence that the newly defined thermal partition function in terms of these variables is the natural candidate for a full microscopic description.