Constraining strongly-warped extra dimensions with rotating black holes

TL;DR

The paper shows that rotating black holes constrain ultra-light spin-2 fields arising from warped extra dimensions, exploiting the strong spin-2 superradiant instability to bound the KK spectrum. Using the Dias et al. results for Kerr BHs with spin-2 perturbations, the authors map constraints on boson masses to the warping parameters of the Randall–Sundrum two-brane model, obtaining a bound approximately $kr_c \lesssim 28.5$ when the 5d curvature is sub-Planckian. They further relate these RS constraints to string-theory inspired warped throats, notably Klebanov–Strassler, via simple parameter correspondences, which translate BH data into bounds on flux quanta $M,K$, the string coupling $g_s$, and the tip warp factor $e^{2A_{tip}}$. A key result is that the full KK tower does not strengthen the exclusion beyond the union of individual mode exclusions, but it extends the reach to smaller black-hole masses. Overall, BH superradiance provides a gravity-only probe of warped extra dimensions and their role in string compactifications and de Sitter uplifts, complementary to fifth-force and collider constraints.

Abstract

Massive bosonic fields can trigger superradiant instabilities in rotating astrophysical black holes leading to gaps in their mass-spin distribution. For spin-2 fields, the instability timescale is orders of magnitude shorter than for any other superradiant mode, thereby yielding much stronger constraints. We consider a tower of ultra-light spin-2 fields arising from a warped compactification of a single extra dimension and translate superradiant constraints on their masses into constraints on the warping. As a concrete scenario we consider the 2-brane Randall-Sundrum model and find constraints on the size of the extra dimension and the curvature of $AdS_5$. We discuss the implications of these bounds for strongly warped throats and D-brane uplifts commonly used in attempts to realise metastable de Sitter vacua in string theory.

Figures (6)

• Figure 1: Pictorial representation of our 2-brane setup with a Standard Model brane and a dark brane at the boundaries of a warped interval of size $\pi r_c$. The warping localises the KK modes on the dark brane, while the graviton zero mode is homogeneous over the compact space. This localisation results in exponentially suppressed couplings (Fig. \ref{['fig:RS-wavefunctions']}) on the SM brane. We want to consider a 4d Kerr black hole, which could correspond to a 5d rotating black string stretching between the branes.
• Figure 2: Kaluza-Klein mode wavefunctions for the Randall-Sundrum model (\ref{['eq:KK-wavefunctions']}) normalised with respect to the graviton zero mode (for $kr_c=12$). The massive mode $(n>0)$ wavefunctions are localised and exponentially enhanced at $y=\pi$, and exponentially suppressed at $y=0$ .
• Figure 3: Experimental constraints on the parameters $\alpha$ (coupling strength) and $\lambda$ (range) of a Yukawa-type interaction, with the shaded area indicating the excluded region of parameter space at 95% confidence level. Figure adapted from Murata:2014nraCembranos:2017vgi. See Murata:2014nraCembranos:2017vgi for details and further references. We also include the region of parameter space excluded by superradiant instabilities triggered by massive spin-2 modes with masses in the range $m_b\in(10^{-23},10^{-11})$ eV, from Dias:2023ynv.
• Figure 4: BH spin-mass diagram with regions excluded by the superradiant instability of Kerr BHs against massive spin-2 fields (dominant $m=1$ mode). Figure reproduced from the results of Dias:2023ynv through the polynomial fits (\ref{['eq:fits']}) (for $\alpha<0.8$), with spin-2 masses translated to corresponding values of $kr_c$, with $k = M_{\rm Pl}$ for illustration.
• Figure 5: Constraints on the RS parameter space assuming BH spin measurements in the full range $M_{\rm BH}\in(1,10^{10})M_\odot$. Each excluded mass $m_b$ rules out a line in the $(k,kr_c)$ plane; the shaded region between the solid lines corresponds to spin-2 masses in the range $m_b\in(10^{-23},10^{-11})$ eV. In the case of a Kaluza-Klein spin-2 tower, even if the lightest mode falls outside this region for being too light, some of the higher modes will be within this range.