Black hole quasinormal modes and isospectrality in Deser-Woodard nonlocal gravity

TL;DR

This paper studies black hole perturbations in a nonlocal gravity model, finding that axial modes match General Relativity while polar modes differ due to scalar field effects, breaking isospectrality.

Contribution

It demonstrates how nonlocal gravity modifies polar gravitational perturbations and breaks isospectrality, providing new insights into black hole oscillation spectra in such theories.

Findings

Axial modes are unaffected by nonlocal corrections, identical to GR.

Polar modes are altered when scalar fields are excited, breaking isospectrality.

Similar results hold for the DW-I model, confirming the robustness of findings.

Abstract

We investigate the gravitational perturbations of the Schwarzschild black hole in the nonlocal gravity model recently proposed by Deser and Woodard (DW-II). The analysis is performed in the localized version in which the nonlocal corrections are represented by some auxiliary scalar fields. We find that the nonlocal corrections do not affect the axial gravitational perturbations, and hence the axial modes are completely identical to those in General Relativity (GR). However, the polar modes get different from their GR counterparts when the scalar fields are excited at the background level. In such a case the polar modes are sourced by an additional massless scalar mode and, as a result, the isospectrality between the axial and the polar modes breaks down. We also perform a similar analysis for the predecessor of this model (DW-I) and arrive at the same conclusion for it.