Gravitational footprints of black holes and their microstate geometries

Abstract

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.

Non-BPS floating branes and bubbling geometries

“…One can compare them with the non-extremal black hole with the same mass and charges as in [3]. Moreover, one can derive their multipole moments, probe them by light geodesics or compute their quasi-normal modes using technologies developed for similar geometries [52,[56][57][58][59][60][61]. One could also being interested in performing M2-brane probe computation in the smooth bubbling solutions in M-theory.…”

“…We further reduce to four dimensions after compactification along y 7 . One can simply use known results about the reduction of the STU model from five to four dimensions (see for instance [45,51,52]). Therefore, the reduced four-dimensional action is given by…”

“…We further reduce to four dimensions by compactifying along y 7 for solutions where y 7 corresponds to a compact direction. One could reapply the generic reduction rules summarized before, but, thanks to the identification (2.24), it is simpler to directly use known results about the reduction of the STU model from five to four dimensions [45,51,52].…”

More on the SW-QNM correspondence

“…The interest in accurate values of ω QN M is two-fold. On the one hand they dominate the Gravitational-Wave ring-down signal in binary mergers and may help discriminating BHs from fuzzballs or other Exotic Compact Objects [10][11][12][13][14]. On the other hand, due to the choice of boundary conditions, QNMs solve non self-adjoint spectral problems, such as Regge-Wheeler-Zerilli or Teukolsky equations [15][16][17], and form an over-complete set that play a crucial role in the study of BH perturbations.…”

AdS$_3$ holography for non-BPS geometries

“…It is natural to ask whether the picture sketched above can be generalised to describe semiclassical non-BPS states. A host of regular and horizonless non-supersymmetric geometries have been found by either generalising the bubbling BPS ansatz [13][14][15][16] or by exploiting the Weyl formalism [17,18] but, much like the bubbling geometries, these solutions do not currently have a known holographic dual. A first approach to the construction of non-supersymmetric microstates with a clear holographic interpretation is to consider non-BPS descendants of well understood BPS configurations as was done in [19] or, at the perturbative level, in [20].…”