Accurate Quasinormal Modes of the Five-Dimensional Schwarzschild-Tangherlini Black Holes

Abstract

The objective of this paper is to construct the accurate (say, to 11 decimal places) frequencies of the quasinormal modes of the 5-dimensional Schwarzschild-Tangherlini black hole using three major techniques: the Hill determinant method, the continued fractions method and the WKB-Padé method and to discuss the limitations of each. It is shown that for the massless scalar, gravitational tensor, gravitational vector and electromagnetic vector perturbations considered in this paper, the Hill determinant method and the method of continued fractions (both with the convergence acceleration) always give identical results, whereas the WKB-Padé method gives the results that are amazingly accurate in most cases. Notable exception are the gravitational vector perturbations ($j=2$ and $\ell =2$), for which the WKB-Padé approach apparently does not work. Here we have interesting situation in which the WKB-based methods (WKB-Padé and WKB-Borel-Le Roy) give the complex frequency that differs from the from the result obtained within the framework of the continued fraction method and the Hill determinant method. For the fundamental mode, deviation of the real part of frequency from the exact value is $0.5\%$ whereas the deviation of the imaginary part is $2.7\%.$ For $\ell \ge 3$ the accuracy of the WKB results is similar again to the accuracy obtained for other perturbations. The case of the gravitational scalar perturbations is briefly discussed.

References in corpus (23)

• Quasinormal modes of black holes and black branes
• Quasi-Normal Modes of Stars and Black Holes
• Quasinormal modes of black holes: from astrophysics to string theory
• Quasinormal behavior of the D-dimensional Schwarzshild black hole and higher order WKB approach
• Quasinormal modes of black holes. The improved semianalytic approach
• Master equations for perturbations of generalised static black holes with charge in higher dimensions
• Stability of Higher-Dimensional Schwarzschild Black Holes
• Advanced Methods in Black-Hole Perturbation Theory
• Gravitational instability in higher dimensions
• Gravitational quasinormal radiation of higher-dimensional black holes
• Quasinormal modes of Schwarzschild black holes in four and higher dimensions
• Quasinormal modes of black holes and Borel summation
• Gravitational energy loss in high energy particle collisions: ultrarelativistic plunge into a multidimensional black hole
• Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena
• Quasinormal modes of black holes. II. Padé summation of the higher-order WKB terms
• Black Hole Ringing, Quasinormal Modes, and Light Rings
• Asymptotic Quasinormal Frequencies of d-dimensional Schwarzschild Black Holes
• Scalar-gravitational perturbations and quasinormal modes in the five dimensional Schwarzschild black hole
• Quasinormal Modes of Charged Fields in Reissner-Nordstrom Backgrounds by Borel-Pade Summation of Bender-Wu Series
• Quasinormal modes of dirty black holes in the two-loop renormalizable effective gravity
• Black hole collision with a scalar particle in four, five and seven dimensional anti-de Sitter spacetimes: ringing and radiation
• Quasinormal modes of $p$-forms in spherical black holes
• New Results for Quasi Normal Modes of Gravitational Waves

Cited by in corpus (13)

• Black holes in Starobinsky-Bel-Robinson Gravity and the breakdown of quasinormal modes/null geodesics correspondence
• Quasinormal modes of black holes in f(T) gravity
• Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Euler-Heisenberg electrodynamics
• Quasinormal modes of the bumblebee black holes with a global monopole
• Gravitational perturbations of the Hayward spacetime and testing the correspondence between quasinormal modes and grey-body factors
• Grey-body factors of higher dimensional regular black holes in quasi-topological theories
• Analyzing the effect of higher dimensions on the black hole silhouette, deflection angles, and PINN approximated quasinormal modes
• Gravitational quasinormal modes of Dymnikova black holes
• Gravitational perturbations of Dymnikova black holes: grey-body factors and absorption cross-sections
• Critical masses and numerical computation of massive scalar quasinormal modes in Schwarzschild black holes
• Absorption and scattering of massless scalar waves by black holes in quasi-topological gravity
• Pseudospectrum and (in)stability of black hole total transmission modes
• Long-lived quasinormal modes in the Euler-Heisenberg electrodynamics