Research activities

Research Interests

My research is mainly focused on classical and quantum aspects of gravity. A non-exhaustive list of topics includes:

  • General Relativity and black hole physics
  • Gravity/CFT correspondence
  • Symmetries and asymptotic symmetries of spacetimes
  • Classical/semiclassical/quantum resonant scattering and S-matrix in various physical settings, and especially in the context of gravity
  • Gauge theories of gravity
  • The role of 2-spinors in the description of spacetime, matter and gravity

List of publications

My list of publications is available on INSPIRE-hep, ORCID

Selected works

  • B. Raffaelli (2022), Hidden conformal symmetry on the black hole photon sphere
    We consider a class of static and spherically symmetric black hole geometries endowed with a photon sphere. On the one hand, we show that close to the photon sphere, a massless scalar field theory exhibits a simple dynamical $SL(2, \mathbb{R})$ algebraic structure which allows to recover the discrete spectrum of the weakly damped quasinormal frequencies in the eikonal approximation, and the associated quasinormal modes from the algebra representations. On the other hand, we consider the non-radial motion of a free-falling test particle, in the equatorial plane, from spatial infinity to the black hole. In the ultrarelativistic limit, we show that the photon sphere acts as an effective Rindler horizon for the geodesic motion of the test particle in the $(t, r)-$plane, with an associated Unruh temperature $T_c = \Lambda_c/2πk_B$, where $\Lambda_c$ is the Lyapunov exponent that characterizes the unstable circular motions of massless particles on the photon sphere. The photon sphere then appears as a location where the thermal bound on chaos for quantum systems with a large number of degrees of freedom, in the form conjectured a few years ago by Maldacena et al., is saturated. The study developed in this paper could hopefully shed a new light on the gravity/CFT correspondence, particularly in asymptotically flat spacetimes, in which the photon sphere may also be considered as a holographic screen.

  • Y. Decanini, A. Folacci, B. Raffaelli (2010), Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
    We consider a wide class of static spherically symmetric black holes of arbitrary dimension with a photon sphere (a hypersurface on which a massless particle can orbit the black hole on unstable circular null geodesics). This class includes various spacetimes of physical interest such as Schwarzschild, Schwarzschild-Tangherlini, and Reissner-Nordström black holes, the canonical acoustic black hole, or the Schwarzschild–de Sitter black hole. For this class of black holes, we provide general analytical expressions for the Regge poles of the S-matrix associated with a massless scalar field theory. This is achieved by using third-order WKB approximations to solve the associated radial wave equation. These results permit us to obtain analytically the nonlinear dispersion relation and the damping of the “surface waves” lying close to the photon sphere as well as, from Bohr-Sommerfeld–type resonance conditions, formulas beyond the leading-order terms for the complex frequencies corresponding to the weakly damped quasinormal modes.

PhD thesis (in French)

Semiclassical analysis of resonant and absorption phenomena by black holes
This work uses and develops the Complex Angular Momentum (CAM) theory in the context of resonant scattering of massless (and massive) scalar fields by static and spherically symmetric black holes, endowed with a photon sphere. CAM theory allows to have simple and quite intuitive physical interpretations of resonance and absorption phenomena. One of the key tools of CAM theory in the context of resonant scattering is the Sommerfeld-Watson transform, which brings the Regge poles (poles of the related S-matrix in the complex angular momenum plane) at the center of the black hole resonances description. In a few words, it is shown that each Regge pole is associated with the propagation of a surface wave on the black hole photon sphere. In particular, a resonance, i.e. a quasinormal mode (or, more precisely here, a “ Regge mode ”), is understood as a Breit-Wigner resonance produced by constructive interferences between different components of the associated surface wave , each component corresponding to a different number of circumvolutions of the wave around the photon sphere. Amongst other results, an explicit expression of the Regge poles, beyond the eikonal WKB order, for a massless (and massive) scalar field theory in a static and spherically symmetric black hole geometry as well as a reconstruction of the quasinormal frequency spectrum (still beyond eikonal WKB order) from the Regge pole spectrum are obtained.