Evidence for the existence of a novel class of supersymmetric black holes with AdS$_5\times$S$^5$ asymptotics

TL;DR

The paper addresses the problem of realizing supersymmetric black holes with AdS5×S5 asymptotics and understanding their entropy in the AdS/CFT context. It introduces a two-parameter family of rotating, charged hairy black holes in a five-dimensional N=8 gauged supergravity truncation that includes a charged scalar and uplifts to type IIB, with SUSY limits approaching the bound $M=2J+3Q$. The main findings show that these hairy black holes exist arbitrarily close to the BPS limit for all charges, possess finite curvature invariants, and exhibit tidal divergences at extremality consistent with a weak pp-type singularity, while the first law holds numerically to high precision. These results expand the landscape of AdS5 black holes relevant for holography and pave the way for ten-dimensional uplift, microscopic entropy counting, and potential stringy corrections, providing a concrete platform to test holographic dualities beyond the original Gutowski-Reall solution.

Abstract

We construct a new class of charged, rotating hairy black holes in a consistent truncation of $\mathcal{N} = 8$ supergravity, which retains one charged scalar field and a U$(1)$ gauge field. These hairy solutions can be uplifted to solutions of type IIB supergravity with AdS$_5\times$S$^5$ asymptotics. We find rotating hairy black holes with finite entropy arbitrarily close to the supersymmetric bound - the resulting supersymmetric solution is a one-parameter extension of the Gutowski-Reall solution. These solutions have finite curvature invariants (including at extremality), but in the extremal limit exhibit diverging tidal forces in the near horizon region. Nevertheless, we argue that these limiting supersymmetric black holes can be consistently studied within the supergravity approximation.

Figures (3)

• Figure 1: Extrapolated zero temperature entropy of the hairy black holes with constant $j = 0.02$ (orange disks), $j = 0.05$ (red squares) and $j = 0.08$ (black diamonds) against the central scalar field $\varepsilon_H$. The variation in the entropy as we lower the temperature further gives error less than 0.1$\%$.
• Figure 2: Left: The measure of tidal forces, as felt by a unit energy particle infalling along a radial geodesic, $T_{ab}\dot{X}^a\dot{X}^b$ at the hairy black hole horizon against the temperature. The quantity shown is for a black hole family with fixed $j = 0.05$ and $\varepsilon_H = 1$, and the plot is in a log-log scale. Right: The log-log plot of the Tipler integral, for hairy black hole family with constant angular momentum $j=0.05$ and horizon scalar $\varepsilon_H=1$. The integral was computed using the $R^t_{\,\,\psi t\psi}$ component found in a PPON frame. Different components have similar qualitative behaviour.
• Figure 3: Left: Convergence of the energy for a few coldest $J=0.05$, $\varepsilon_H=1$ hairy black holes considered in the paper, with $T=0.00052$ (black rhombi), $T=0.00031$ (blue squares) and $T=0.00016$ (gray triangles). Here we plot the fractional error $\Delta$ against the grid size $n$. Right: Low temperature ($T= 10^{-2}\pm 10^{-3}$) hairy black hole energy convergence for a few different horizon scalar values $\varepsilon_H$. Black rhombi are for $\varepsilon_H=1$, blue squares for $\varepsilon_H=8.5$, and gray triangles for $\varepsilon_H=14.5$. Here we show the fractional error against the grid size in a log scale.