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

Journal Article · Sat May 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.104039· OSTI ID:21409751

Decanini, Yves; Folacci, Antoine; Raffaelli, Bernard ^[1]

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1. UMR CNRS 6134 SPE, Equipe Physique Theorique, Universite de Corse, Faculte des Sciences, BP 52, 20250 Corte (France)

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-Nordstroem 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.

• OSTI ID: 21409751
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 81; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
APPROXIMATIONS
BLACK HOLES
BOSONS
CALCULATION METHODS
DE SITTER GROUP
DE SITTER SPACE
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELEMENTARY PARTICLES
EQUATIONS
GEODESICS
LIE GROUPS
MASSLESS PARTICLES
MATHEMATICAL SPACE
MATRICES
NONLINEAR PROBLEMS
ORBITS
PARTIAL DIFFERENTIAL EQUATIONS
PHOTONS
REGGE POLES
RESONANCE
S MATRIX
SCALAR FIELDS
SPACE
SPACE-TIME
SYMMETRY
SYMMETRY GROUPS
WAVE EQUATIONS
WAVE PROPAGATION
WKB APPROXIMATION