Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies

Abstract

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

v2: One reference corrected, typos fixed. v3: We now discuss the meaning of superluminal dispersion relations for the "surface waves" lying on the photon sphere. v4: Version to appear in Phys. Rev. D.

References in corpus (4)

• The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Complex angular momentum in black hole physics and quasinormal modes
• Quasinormal modes of the BTZ black hole are generated by surface waves supported by its boundary at infinity

Cited by in corpus (2)

• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit