Four-dimensional supersymmetric black holes are static and so have all vanishing multipoles (except the mass monopole). Nevertheless, it is possible to define finite multipole ratios for these black holes, by taking the ratio of (finite) multipoles of supersymmetric multicentered geometries and then taking the black hole scaling limit of the multipole ratios within these geometries. An alternative way to calculate these multipole ratios is to deform the supersymmetric black hole slightly into a non-extremal, rotating black hole, calculate the multipole ratios of this altered black hole, and then take the supersymmetric limit of the ratios. Bena and Mayerson observed that for a class of microstate geometries, these two a priori completely different methods give spectacular agreement for the resulting supersymmetric black hole multipole ratios. They conjectured that this agreement is due to the smallness of the entropy parameter for these black holes. We correct this conjecture and give strong evidence supporting a more refined conjecture, which is that the agreement of multipole ratios as calculated with these two different methods is due to both the microstate geometry and its corresponding black hole having a property we call “large dipole”, which can be interpreted as their center of mass being far away from its apparent center.

France

Bogdan Ganchev

Belgium

Daniel Mayerson

On supersymmetric multipole ratios

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass M  n  and current S  n  multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles S 2n  ≠ 0 and M 2n+1 ≠ 0 that break equatorial symmetry, and the parity-preserving corrections that only modify S 2n+1 and M 2n . Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments.

Pablo Cano

Italy

Alejandro Ruipérez

Black hole multipoles in higher-derivative gravity

We study probe scalar correlation functions in a Solodukhin wormhole corresponding to the non-rotating BTZ black hole, as a toy model for microstate geometries thereof. Using real-time holography, we obtain the retarded scalar correlator in the wormhole geometry and quantitatively compare it to the result of the hybrid WKB method for the same correlator. We also calculate an off-diagonal correlator ∼ 〈HLLH ′〉 involving two different (heavy) wormhole states.

Vasil Dimitrov

Vincent Min

Real-time holography and hybrid WKB for BTZ wormholes

We construct a family of non-supersymmetric extremal black holes and their horizonless microstate geometries in four dimensions. The black holes can have finite angular momentum and an arbitrary charge-to-mass ratio, unlike their supersymmetric cousins. These features make them and their microstate geometries astrophysically relevant. Thus, they provide interesting prototypes to study deviations from Kerr solutions caused by new horizon-scale physics. In this paper, we compute the gravitational multipole structure of these solutions and compare them to Kerr black holes. The multipoles of the black hole differ significantly from Kerr as they depend non-trivially on the charge-to-mass ratio. The horizonless microstate geometries (that are comparable in size to a black hole) have a similar multipole structure as their corresponding black hole, with deviations to the black hole multipole values set by the scale of their microstructure.

United States

Ibrahima Bah

Iosif Bena

Pierre Heidmann

Yixuan Li

Gravitational footprints of black holes and their microstate geometries

We explain in detail how to calculate the gravitational mass and angular momentum multipoles of the most general non-extremal four-dimensional black hole with four magnetic and four electric charges. We also calculate these multipoles for generic supersymmetric four-dimensional microstate geometries and multi-center solutions. Both for Kerr black holes and BPS black holes many of these multipoles vanish. However, if one embeds these black holes in String Theory and slightly deforms them, one can calculate an infinite set of ratios of vanishing multipoles which remain finite as the deformation is taken away, and whose values are independent of the direction of deformation. For supersymmetric black holes, we can also compute these ratios by taking the scaling limit of multi-center solutions, and for certain black holes the ratios computed using the two methods agree spectacularly. For the Kerr black hole, these ratios pose strong constraints on the parameterization of possible deviations away from the Kerr geometry that should be tested by future gravitational wave interferometers.

Black holes lessons from multipole ratios

The most detailed constructions of microstate geometries, and particularly of superstrata, are done using   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = (1, 0) supergravity coupled to two anti-self-dual tensor multiplets in six dimensions. We show that an important sub-sector of this theory has a consistent truncation to a particular gauged supergravity in three dimensions. Our consistent truncation is closely related to those recently laid out by Samtleben and Sarıoğlu [1], which enables us to develop complete uplift formulae from the three-dimensional theory to six dimensions. We also find a new family of multi-mode superstrata, indexed by two arbitrary holomorphic functions of one complex variable, that live within our consistent truncation and use this family to provide extensive tests of our consistent truncation. We discuss some of the future applications of having an intrinsically three-dimensional formulation of a significant class of microstate geometries.

Robert Walker

Nicholas Warner

Microstate geometries from gauged supergravity in three dimensions

We obtain the largest families constructed to date of   <math> <mfrac> <mn>1</mn> <mn>8</mn> </mfrac> </math>  $$ \frac{1}{8} $$ -BPS solutions of type IIB supergravity. They have the same charges and mass as supersymmetric D1-D5-P black holes, but they cap off smoothly with no horizon. Their construction relies on the structure of superstratum states, but allows the momentum wave to have an arbitrary shape. Each family is based on an arbitrary holomorphic function of one variable. More broadly, we show that the most general solution is described by two arbitrary holomorphic functions of three variables. After exhibiting several new families of such “holomorphic superstrata,” we reformulate the BPS backgrounds and equations in holomorphic form and show how this simplifies their structure. The holomorphic formulation is thus both a fundamental part of superstrata as well as an effective tool for their construction. In addition, we demonstrate that holomorphy provides a powerful tool in establishing the smoothness of our solutions without constraining the underlying functions. We also exhibit new families of solutions in which the momentum waves of the superstrata are highly localized at infinity but diffuse and spread into the infra-red limit in the core of the superstratum. Our work also leads to some results that can be tested within the dual CFT.

Holomorphic waves of black hole microstructure

We find a family of complete non-linear Kaluza-Klein reduction ansätze from type IIB supergravity to Romans’ 6D F (4) gauged supergravity in the bosonic sector. The reduction is over a sphere S 2 and a Riemann surface Σ, and depends on a pair of arbitrary locally holomorphic functions  <math><msub><mi>A</mi><mo>±</mo></msub></math> $$ {\mathcal{A}}_{\pm } $$ on Σ. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped AdS 6 solutions of IIB supergravity that depend on these same functions  <math><msub><mi>A</mi><mo>±</mo></msub></math> $$ {\mathcal{A}}_{\pm } $$.

Junho Hong

James Liu

Gauged six-dimensional supergravity from warped IIB reductions

We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate algebraic bootstrap equations by demanding that only physical operators contribute to the OPE. We find that there are no perturbatively interacting CFTs with only fundamental scalars in d &gt; 6 dimensions (to at least second order in the perturbation). Our results can be seen as a modest step towards understanding the space of interacting CFTs in d &gt; 6 and are consistent with the intuition that no such CFTs exist.

John Golden

Mellin bootstrap for scalars in generic dimension

We analyze large logarithmic corrections to 4D black hole entropy and relate them to the Weyl anomaly. We use duality to show that counter-terms in EinsteinMaxwell theory can be expressed in terms of geometry alone, with no dependence on matter terms. We analyze the two known N $$ \mathcal{N} $$ = 2 supersymmetric invariants for various non-supersymmetric black holes and find that both reduce to the Euler invariant. The c -anomaly therefore vanishes in these theories and the coefficient of the large logarithms becomes topological. It is therefore independent of continuous black hole parameters, such as the mass, even far from extremality.