Authors : Chun-Hung Chen (IF, NU), Hing-Tong Cho (TKU), Anna Chrysostomou (UJ), Alan S. Cornell (UJ)
Motivation and background
An isolated black hole (BH) is mathematically the vacuum solution of Einstein’s field equations; and astrophysically, its full description can be attained with the three parameters of Arnowitt-Deser-Misner (ADM) mass (M), charge (Q), and angular momentum (a) when in equilibrium. With the advent of gravitational-wave (GW) astronomy, we can now exploit perturbed BHs as GW sources. With this in mind, we concern ourselves with the quasinormal mode (QNM), which is a fundamental feature of the damped “ringdown” phase through which a perturbed system passes as it returns to equilibrium. The corresponding quasinormal frequencies (QNFs) are complex, where the real part represents the physical oscillation frequency and the imaginary part expresses the damping.
For spherically-symmetric BHs, the QNM wavefunction can be separated into its radial
and angular components, where the latter can be expressed fully through spherical harmonic. For the radial equations were Schrodinger-like, and illustrated by Regge-Wheeler and Zerilli equations for Bosonic perturbations as well as a long history studies including of our previous works on Fermionic perturbations. As we have the radial equations corresponding to all kinds of spins (at least from spin-0, spin-1/2,..to spin-2) in spherically-symmetric BHs, we may do the systematically asymptotic studies on them, and the large angular momentum (l) limit were studied in this work.
There are several Well-established procedures for the study on QNFs, such as the Poschl-Teller (PT) approximation method, the modified Wentzel-Kramers-Brillouin (WKB) approximation, as well as more recently constructed AIM methods. It is however that the illustrated methods are most accurate in the eikonal limit, but not confirmed to work as well in the large-l limit. As such, we studied the large-l QNFs by Dolan and Ottewill’s (DO) method in the current work, which based on applying the BH contexts and the radial equations to the negative power order of the angular momentum parameter L (O(L^{−k})). As such, the DO method is well-suited for our purpose due to its physically-motivated foundations and the ease with which it lends itself to computations within the eikonal limit.
Key results
– We perform a complete study of DO method for perturbations of spin s ∈ {0, 1/2, 1, 3/2, 2} in 4D Schwarzschild, Reissner-Nordstrom, and Schwarzschild de Sitter spacetimes.
– We presented our expansions and results by using DO methods to the orders of (O(L^{−6})) for all the cases in the current work, which reflecting a marked improvement on several extant attempts at pursuing the DO method in the literature.
Journal : https://journals.aps.org/…/10.1103/PhysRevD.104.024009
