More on the SW-QNM correspondence

We exploit the recently proposed correspondence between gravitational perturbations and quantum Seiberg-Witten curves to compute the spectrum of quasi-normal modes of asymptotically flat Kerr Newman black holes and establish detailed gauge/gravity dictionaries for a large class of black holes, D-branes and fuzzballs in diverse dimensions. QNM frequencies obtained from the quantum periods of SU(2) $$ \mathcal{N} $$ N = 2 SYM with Nf = 3 flavours are compared against numerical results, WKB (eikonal) approximation and geodetic motion showing remarkable agreement. Starting from the master example relating quasi-normal modes of Kerr-Newman black holes in AdS4 to SU(2) gauge theory with Nf = 4, we illustrate the procedure for some simple toy-models that allow analytic solutions. We also argue that the AGT version of the gauge/gravity correspondence may give precious hints as to the physical/geometric origin of the quasi-normal modes/Seiberg-Witten connection and further elucidate interesting properties (such as tidal Love numbers and grey-body factors) that can help discriminating black holes from fuzzballs.

Exploration of a singular fluid spacetime

We investigate the properties of a special class of singular solutions for a self-gravitating perfect fluid in general relativity: the singular isothermal sphere. For arbitrary constant equation-of-state parameter $$w=p/\rho $$ w = p / ρ , there exist static, spherically-symmetric solutions with density profile $$\propto 1/r^2$$ ∝ 1 / r 2 , with the constant of proportionality fixed to be a special function of w. Like black holes, singular isothermal spheres possess a fixed mass-to-radius ratio independent of size, but no horizon cloaking the curvature singularity at $$r=0$$ r = 0 . For $$w=1$$ w = 1 , these solutions can be constructed from a homogeneous dilaton background, where the metric spontaneously breaks spatial homogeneity. We study the perturbative structure of these solutions, finding the radial modes and tidal Love numbers, and also find interesting properties in the geodesic structure of this geometry. Finally, connections are discussed between these geometries and dark matter profiles, the double copy, and holographic entropy, as well as how the swampland distance conjecture can obscure the naked singularity.

Viscoelastic Love numbers and long period geophysical effects

Summary Long term deformations strongly depend on the Earth model and its rheological parameters, and in particular its viscosity. We give the general theory and the numerical scheme to compute them for any spherically non rotating isotropic Earth model with linear rheology, either elastic or viscoelastic. Although the Laplace transform is classically used to compute viscoelastic deformation, we choose here instead, to implement the integration with the Fourier transform in order to take advantage of the Fast Fourier Transform algorithm and avoid some of the Laplace transform mathematical difficulties. We describe the methodology to calculate deformations induced by several geophysical signals regardless of whether they are periodic or not, especially by choosing an adapted time sampling for the Fourier transform. As examples, we investigate the sensitivity of the displacements due to long period solid Earth tides, Glacial Isostatic Adjustment (GIA), and present-day ice melting, to anelastic parameters of the mantle. We find that the effects of anelasticity are important for long period deformation and relatively low values of viscosities for both Maxwell and Burgers models. We show that slight modifications in the rheological models could significantly change the amplitude of deformation but also affect the spatial and temporal pattern of the signal to a lesser extent. Especially, we highlight the importance of the mantle anelasticity in the low degrees deformation due to present-day ice melting and encourage its inclusion in future models.

Tidal deformation of quantum black holes

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical black holes (BHs). Here we show, using standard time-independent quantum perturbation theory, that for a quantum BH, generically, the Love numbers are nonvanishing and negative. We calculate the quadrupolar electric quantum Love number of slowly rotating BHs and show that it depends most strongly on the first excited level of the quantum BH. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favourable circumstances, its magnitude is large enough to imprint an observable signature on the gravitational waves emitted during the inspiral. Phase of two moderately spinning BHs.