Quasinormal modes for integer and half-integer spins within the large angular momentum limit

Abstract

While independent observations have been made regarding the behaviour of effective quasinormal mode (QNM) potentials within the large angular momentum limit, we demonstrate analytically here that a uniform expression emerges for non-rotating, higher-dimensional, and sphericallysymmetric black holes (BHs) in this regime for fields of integer and half-integer spin in asymptotically flat and dS BH contexts; a second uniform expression arises for these QNM potentials in AdS BH spacetimes. We then proceed with a numerical analysis based on the multipolar expansion method recently proposed by Dolan and Ottewill to determine the behaviour of quasinormal frequencies (QNF) for varying BH parameters in the eikonal limit. We perform a complete study of Dolan and Ottewill's method for perturbations of spin s ∈ {0, 1/2, 1, 3/2, 2} in 4D Schwarzschild, Reissner-Nordström, and Schwarzschild de Sitter spacetimes, clarifying expressions and presenting expansions and results to higher orders (O(L −6 )) than many of those presented in the literature (∼ O(L −2 )). We find good agreement with known results of QNFs for low-lying modes; in the large-ℓ regime, our results are highly consistent with those of Konoplya's 6th-order WKB method.We confirm a universality in the trends of physical features recorded in the literature for the lowlying QNFs (that the real part grows indefinitely, the imaginary tends to a constant as ℓ → ∞, etc.) as we approach large values of ℓ within these spacetimes, and explore the consequent interplay between BH parameters and QNFs in the eikonal limit.

Asymptotic quasinormal frequencies of different spin fields in d-dimensional spherically-symmetric black holes

“…Its dependencies include n (the 'overtone' number) and (the 'multipolar' or angular momentum number), the asymptotic limits of which represent regimes of interest in QNM studies. We explore the properties of QNFs subjected to → ∞ within reference [54]; here, we focus on the n → ∞ regime.…”

“…Moreover, we must recognise that proof of the stability of perturbing fields within the extremal Reissner-Nordström BH spacetime is still outstanding (see section VIII of reference [4]), which implies any results within the extremal Reissner-Nordström BH context must be approached with some scrutiny. Despite this, the extremal Reissner-Nordström case remains a fascinating BH spacetime with extensive applications ranging from numerical development (see reference [54] and references therein) to supersymmetry (SUSY) considerations [62,63], the latter of which shall be addressed in section 4.…”

Asymptotic quasinormal frequencies of different spin fields in $d$-dimensional spherically-symmetric black holes

“…We explore the properties of QNFs subjected to → ∞ within Ref. [53]; here, we focus on the n → ∞ regime.…”

“…Despite this, the extremal Reissner-Nordström case remains a fascinating BH spacetime with extensive applications ranging from numerical development (see Ref. [53] and references therein) to supersymmetry (SUSY) considerations [61,62], the latter of which shall be addressed in section IV.…”