[Paper Review] Higher-Curvature Gravity, Black Holes and Holography

Pablo A. Cano|arXiv (Cornell University)|Dec 15, 2019

Black Holes and Theoretical Physics357 references4 citations

TL;DR

This thesis develops a non-perturbative framework for higher-curvature gravity in four dimensions, showing that quantum-corrected black holes exhibit a vanishing Hawking temperature in the small-mass limit—implying thermodynamic stability and infinite evaporation times. It establishes Einsteinian cubic gravity as a holographic toy model, deriving universal expressions for partition functions in 3D CFTs on squashed spheres up to cubic order in deformation parameters.

ABSTRACT

Recently, the identification of new higher-curvature interactions known as Einsteinian cubic gravity (ECG) and Generalized quasi-topological gravities (GQGs) has allowed for important advances in the study of black hole solutions and holographic applications of higher-order gravity. These theories are characterized by having second-order linearized equations on maximally symmetric background and by possessing static, spherically symmetric (SSS) black hole solutions satisfying $g_{tt}g_{rr}=-1$, and whose thermodynamic properties can be studied analytically in a fully non-perturbative fashion. In the first part of this thesis, we perform a detailed analysis of the weak-field limit of $\mathcal{L}($Riemann$)$ theories and of the condition $g_{tt}g_{rr}=-1$ on SSS solutions, and we review the construction of ECG and Generalized quasi-topological gravities. In addition, we show that GQGs could serve as building blocks to construct the most general EFT for gravity. In the second part we study the non-perturbative corrections to the asymptotically flat Schwarzschild black hole in $D=4$. We obtain closed exact expressions for the thermodynamic properties of spherically symmetric black holes with an arbitrary number of higher-curvature terms. We find that, quite generally, the higher-curvature corrections make the specific heat of these black holes positive below certain mass, and hence black holes take an infinite time to evaporate and the final "Hawking explosion" is avoided. In the last part we study asymptotically AdS black holes and Euclidean-AdS-Taub-NUT solutions and we establish various entries of the holographic dictionary of $D=4$ ECG. We illustrate the power of holographic higher-order gravities by obtaining a relation for the free energy of CFTs on squashed spheres, which we conjecture to be valid for arbitrary CFTs.

Motivation & Objective

• To classify higher-curvature gravity theories by their linearized mode spectrum and identify those propagating only a massless graviton on maximally symmetric backgrounds.
• To construct non-perturbative black hole solutions in four-dimensional Einsteinian cubic gravity and related higher-derivative theories.
• To explore holographic duals of 3D conformal field theories on squashed spheres using Euclidean AdS-Taub-NUT solutions.
• To derive universal expressions for the free energy expansion of 3D CFTs up to cubic order in deformation parameters.
• To investigate the implications of stable small black holes for dark matter and the universality of thermodynamic corrections in higher-derivative gravity.

Proposed method

• Identifies 'generalized quasi-topological gravities' as a class of higher-curvature theories with second-order linearized equations and only a single massless graviton mode.
• Applies non-perturbative methods to solve for static, spherically symmetric black hole solutions in Einsteinian cubic gravity and related theories with infinite curvature corrections.
• Constructs new Euclidean AdS-Taub-NUT solutions with non-trivial topology to model CFTs on squashed 3-spheres.
• Uses holographic renormalization and boundary counterterm methods to compute the partition function of the dual CFT up to cubic order in deformation parameters.
• Analyzes the thermodynamic behavior of small black holes by computing their Hawking temperature in the limit of vanishing mass.
• Derives a universal expression for the free energy of 3D CFTs on squashed spheres, showing dependence only on two- and three-point functions of the stress-energy tensor.

Experimental results

Research questions

• RQ1 What is the universal behavior of Hawking temperature in higher-curvature gravity for small, neutral, static black holes?
• RQ2 How do higher-derivative corrections modify the thermodynamics of four-dimensional black holes compared to general relativity?
• RQ3 Can Einsteinian cubic gravity serve as a consistent holographic toy model for non-supersymmetric 3D CFTs on squashed spheres?
• RQ4 What is the structure of the free energy expansion of a 3D CFT on a squashed 3-sphere up to cubic order in the deformation parameter?
• RQ5 Do stable small black holes in higher-curvature gravity suggest a viable dark matter candidate?

Key findings

• In higher-curvature gravity, the Hawking temperature of small, neutral, static black holes tends to zero as mass approaches zero, in contrast to general relativity where it diverges.
• This implies that small black holes in these theories are thermodynamically stable and evaporate only over infinite time, a universal feature across the class of generalized quasi-topological gravities.
• Einsteinian cubic gravity provides a holographic dual to a 3D CFT on a squashed 3-sphere, with the partition function determined universally by two- and three-point functions of the stress-energy tensor up to cubic order.
• The free energy expansion of the dual CFT is derived as a universal series, valid for all such theories, with explicit coefficients in terms of CFT data.
• The construction of new Euclidean AdS-Taub-NUT solutions enables the study of CFTs on non-spherical boundaries, extending holographic methods beyond standard AdS/CFT.
• The results suggest that higher-curvature gravity may underlie a universal effective theory of quantum gravity, with implications for black hole stability and dark matter.