We compute the gravitational multipole moments and ratios of moments of nonextremal and of supersymmetric black holes in four dimensions, as well as of horizonless microstate geometries of the latter. For supersymmetric and for Kerr black holes many of these multipole moments vanish, and their dimensionless ratios are ill defined. We present two methods to compute these dimensionless ratios, which for certain supersymmetric black holes agree surprisingly well. We also compute these dimensionless ratios for the Kerr solution. Our methods allow us to calculate an infinite number of hitherto unknown parameters of Kerr black holes, giving us a new window into their physics.

We present the string dual to SU(N _c ) \( \mathcal{N} = 4 \) SYM, coupled to N _f massless fundamental flavors, at finite temperature and baryon density. The solution is determined by two dimensionless parameters, both depending on the ’t Hooft coupling λ _h at the scale set by the temperature T: ϵ _h ∼ λ _h N _f /N _c , weighting the backreaction of the flavor fields and \( \tilde{\delta } \sim {{{\lambda_h^{{{{ - 1}} \left/ {2} \right.}}{n_b}}} \left/ {{\left( {{N_f}{T^3}} \right)}} \right.} \), where n _b is the baryon density. For small values of these two parameters the solution is given analytically up to second order. We study the thermodynamics of the system in the canonical and grand-canonical ensembles. We then analyze the energy loss of partons moving through the plasma, computing the jet quenching parameter and studying its dependence on the baryon density. Finally, we analyze certain “optical” properties of the plasma. The whole setup is generalized to non abelian strongly coupled plasmas engineered on D3-D7 systems with D3-branes placed at the tip of a generic singular Calabi-Yau cone. In all the cases, fundamental matter fields are introduced by means of homogeneously smeared D7-branes and the flavor symmetry group is thus a product of abelian factors.

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.

We obtain the largest families constructed to date of $$ \frac{1}{8} $$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.

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.

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 $$ {\mathcal{A}}_{\pm } $$ A ± 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 $$ {\mathcal{A}}_{\pm } $$ A ± .