Spin 1/2 quasinormal mode frequencies in Schwarzschild-AdS spacetime

TL;DR

This paper derives an asymptotic formula for Dirac quasinormal mode frequencies in Schwarzschild-AdS spacetime, providing corrections to the leading behavior and confirming the results with numerical calculations, relevant for AdS/CFT applications.

Contribution

It presents the first asymptotic formula for Dirac quasinormal modes in Schwarzschild-AdS_D, including subleading corrections, and validates it against numerical data.

Findings

Asymptotic formula for quasinormal frequencies derived

Agreement between analytical and numerical frequencies confirmed

Provides insights for AdS/CFT correspondence applications

Abstract

We find the asymptotic formula for quasinormal mode frequencies omega_n of the Dirac equation in a Schwarzschild-AdS_D background in space-time dimension D > 3, in the large black-hole limit appropriate to many applications of the AdS/CFT correspondence. By asymptotic, we mean large overtone number n with everything else held fixed, and we find the O(n^0) correction to the known leading O(n) behavior of omega_n. The result has the schematic form omega_n =~ n Delta(omega) + A ln(n) + B, where Delta(omega) and A are constants and B depends logarithmically on the (D-2)-dimensional spatial momentum k parallel to the horizon. We show that the asymptotic result agrees well with exact quasinormal mode frequencies computed numerically.