(Un)attractor black holes in higher derivative AdS gravity

TL;DR

This work addresses the problem of characterizing charged AdS black holes in five-dimensional gravity with higher-derivative Gauss-Bonnet corrections and neutral scalars non-minimally coupled to gauge fields. The authors develop boundary counterterms within holographic renormalization and compare the resulting boundary stress tensor with Wald's Noether-charge entropy, while also employing the entropy-function formalism to analyze extremal configurations; they supplement analytic results with numerical extremal solutions. Key contributions include explicit counterterms for both GB branches, exact non-extremal GB-AdS black holes, comprehensive thermodynamics in grand canonical and canonical ensembles, and a detailed attractor analysis for extremal black holes with and without scalar hair, showing that the near-horizon AdS_2 × S^3 structure persists with α' corrections. The results clarify how higher-derivative corrections modify entropy and horizon data, reveal unattractor behavior for massless scalars, and demonstrate that the attractor mechanism persists in the presence of massive scalars under BF-bound constraints, providing insights into holographic RG flows in string-corrected AdS contexts.

Abstract

We investigate five-dimensional static (non-)extremal black hole solutions in higher derivative Anti-de Sitter gravity theories with neutral scalars non-minimally coupled to gauge fields. We explicitly identify the boundary counterterms to regularize the gravitational action and the stress tensor. We illustrate these results by applying the method of holographic renormalization to computing thermodynamical properties in several concrete examples. We also construct numerical extremal black hole solutions and discuss the attractor mechanism by using the entropy function formalism.

Figures (4)

• Figure 1: The profiles of the functions $m(r)$, $\sigma(r)$ and $\phi(r)$ are shown for typical $k=1$ non-extremal black holes with with $r_h=1,q_1=0.3,q_2=0.5,\Lambda=-6$, $\alpha'=0.1$ and two values of the scalar field on the event horizon
• Figure 2: The relevant parameters are ploted as a function of the even horizon radius for $k=1$ non-extremal black holes with $\Lambda=-0.001$, $\alpha'=0.01$, $q_1=0.3$, $q_2=0.5$, $\alpha_1=-\alpha_2=2$.
• Figure 3: The attractor behaviour is shown for $k=1$ extremal black holes with $\Lambda=-1$, $\alpha'=0.1$, $q_1=4$, $q_2=0.5$, $\alpha_1=-\alpha_2=1/2$.
• Figure 4: The profiles of the functions $m(r)$, $\sigma(r)$ and $\phi(r)$ are shown for a typical $\alpha'=0.2$, black hole with $k=1$, $\alpha_1=-\alpha_2=1/2,\phi_1=1,q_1=7.1,q_2=1.15$. For comparison, we included also the profiles of the corresponding solution in Einstein gravity ($\alpha'=0).$