Turning black-holes and D-branes inside out their photon-spheres

Abstract

Very much as extremal Reissner-Nordstöm BHs, D3-branes and their intersecting bound-states in lower dimensions enjoy a remarkable symmetry under conformal inversions that exchange the horizon with infinity and keep the photon-sphere fixed. We explore the implications of this symmetry for the dynamics of massless and massive BPS particles. In particular we find a remarkable identity between the scattering angle of a probe impinging from infinity and the in-spiraling angle of a probe with the very same energy and angular momentum falling into the horizon from inside the photon-sphere. We argue for the identity of the radial actions and Shapiro time-delays for the two processes, when a cutoff regulator or an AdS ambient is adopted. We spell out the detailed conditions for the inversion symmetry to hold in the case of large BPS BHs in four dimensions. We address conformal inversions for other BHs and Dp-branes with photon-spheres in various dimensions with flat or AdS asymptotics. We briefly discuss the fate of the symmetry at the quantum level as well as for non spherically symmetric BHs and branes and sketch potential implications for the holographic correspondence.

A new method for exact results on Quasinormal Modes of Black Holes

“…We have to numerically input l in the TBA with the boundary condition at θ → −∞: ε±,±(θ) ≃ 4P θ ≃ 4(l + 1/2)θ, also following from the asymptotic of the ODE (25) (the precision improves by adding also the constant at the subleading order). This TBA is a generalization of those found in [29,31] for the Perturbed Hairpin IM and the N f = 2 gauge theory with equal masses m 1 = m 2 respectively, although we shall pay particular attention to the change of variables from gravity or gauge to integrability: this results in n l TBA Leaver WKB 0 1 0.86814 − 0.36917i 0.86893 − 0.37286i 0.89642 − 0.36596i 0 2 1.4755 − 0.36411i 1.4778 − 0.3682i 1.4940 − 0.36596i 0 3 2.0767 − 0.36178i 2.0801 − 0.3671i 2.0916 − 0.36596i 0 4 2.6758 − 0.36007i 2.6803 − 0.3666i 2.6893 − 0.36596i (33), (through (34) with n ′ = 0) and WKB approximation (Σ1 = 0.1, Σ2 = 0.2, Σ3 = 0.3, Σ4 = 1). Since Σ1 = Σ3 the Leaver method seems not applicable (N.A.…”

“…also [13,29]), that would generalize the alternative quantization condition ( 21) only if M 1 = M 2 . Moreover (38) is just the symmetry that exchange infinity (y → +∞) and the (analogue) horizon (y → −∞), leaving the photon sphere (y = 0) fixed as in [33] (thanks to identifications of certain scattering angles with the SW period). In this respect, under (38)…”

Irregular Liouville correlators and connection formulae for Heun functions

“…In our viewpoint this intriguing correspondence could be further clarified in CFT terms, as started in [13], and other massive gravitational sources can be studied along the same lines by making use of the results of this paper. For related topics, see also [53,54,55,56,57,58].…”

Turning rotating D-branes and BHs inside out their photon-halo

“…CT transformations are known to exchange the event horizon with null infinity [6][7][8][9][10][11][12][13]. Quite remarkably, we have found that the fixed loci of the (generalised) CT transformations are precisely the photon-spheres [5], thus opening new paths to explore physical implications for QNMs and other observables such as deflection angles and time delays, coded in the so-called radial action, and ultimately on a bulk-to-boundary relation proposed in [14,15].…”

“…In [5] we have shown that D3-branes and their bound-states in lower dimensions admit a symmetry under conformal inversions that generalise the Couch-Torrence (CT) transformations known to leave the metric of extremal Reissner-Nordström BHs invariant up to a Weyl rescaling [6]. CT transformations are known to exchange the event horizon with null infinity [6][7][8][9][10][11][12][13].…”