Unconventional Gravitational Excitation of a Schwarzschild Black Hole

TL;DR

This paper investigates the continuum spectrum of Schwarzschild black holes, revealing unexpected behaviors near a special frequency and identifying new unconventional damped modes through numerical and analytical methods.

Contribution

It uncovers a previously overlooked continuum spectrum and identifies unconventional damped modes near the algebraically special frequency.

Findings

Continuum spectrum exists on the negative imaginary axis.

Unconventional damped modes are confirmed near the special frequency.

Numerical and analytical methods agree on the new modes.

Abstract

Besides the well-known quasinormal modes, the gravitational spectrum of a Schwarzschild black hole also has a continuum part on the negative imaginary frequency axis. The latter is studied numerically for quadrupole waves. The results show unexpected striking behavior near the algebraically special frequency $\Omega=-4i$. This reveals a pair of unconventional damped modes very near $\Omega$, confirmed analytically.