Authors : Chun-Hung Chen (IF, NU), Hing-Tong Cho (TKU,), Anna Chrysostomou (UJ), and Alan S. Cornell (UJ)
Motivation and background
The black hole quasinormal modes (QNMs) were realized as a set of specific frequencies for the perturbation of the black hole spacetimes with various kinds of fields. As an example that the phenomenons of the ring-down behavior of the gravitational wave were understood by the linear combination of spin-2 QNMs in Kerr spacetime. The experiment results in the current stage hint us that the theory of black hole perturbation theory includes confidence to be detectable, therefore, further applications of this theory are of interest for helping us to study some unknown physics.
The higher overtone of QNMs or the QNMs within the large “n” limit were known as the asymptotic quasinormal frequency (aQNF). The expression aQNF garnered specific interest for its speculated link to a quantum theory of gravity, initiated by Hod S. in 1998. The numerical results presented that the real part of aQNF converge to “~ln 3” for the Schwarzschild black hole under Planck units as the fundamental variable to the scaling of a “quantum Schwarzschild black hole” area. The application of different analytical methods in the later years confirmed this “ln 3” result for 4D and higher-dimensional Schwarzschild black holes. On the basis of statistical arguments and the established relationships between BH entropy and surface area, Hod also derived a minimum equidistant spacing of “ΔS = ln 3” for the Bekenstein–Hawking entropy spectrum.
Though Hod’s conjecture gained traction for several years, a possible link to a quantum theory of gravity was quickly proven tenuous when the “ln 3” results did not emerge for the 4D Reissner–Nordström black hole. Therefore, a further iteration of Hod’s conjecture by Maggiore caste black hole perturbations as a collection of damped harmonic oscillations, with the real frequency defined as the square-root of the square of real part plus the square of imaginary part and a subsequent result of “ΔS = 2π” for the Bekenstein–Hawking entropy spectrum in 2008. The results were done in the Schwarzschild black holes, and the researchers continue to work on this with various methods in various kinds of spacetimes. These investigations motivate the present work, where we study the aQNF by exploiting the more flexible methodology used by Natário and Schiappa, the monodromy technique, to extend the results of reference to higher-dimensional Schwarzschild, Schwarzschild (A)dS, and Reissner–Nordström spacetimes for the spin-{0,1/2, 1, 3/2, 2} perturbations.
Key results
– We computed the aQNFs of spin s ∈ {0, 1/2, 1, 3/2, 2}, where all half-integer aQNFs reflect new results. To know the details one needs to check our paper.
– For Schwarzschild, non-extremal Reissner–Nordström, and Schwarzschild dS BH spacetimes, the Dirac aQNFs emerged consistently as a purely imaginary solution proportional to the surface gravity of the horizon.
– The aQNFs associated with spin-3/2 perturbations and spin-2 perturbations are coincidentally partially consistent in the extremal/ non-extremal Reissner–Nordström black hole, the justification for these observed behaviors is not obvious and warrants further investigation.
Journal : https://doi.org/10.1088/1361-6382/ac4955
