Master functions of Reissner-Nordstrom black hole perturbations and their Darboux transformation
arXiv:2505.04407 · doi:10.1103/148b-pfqr
Abstract
Lenzi and Sopuerta developed a new method to construct master functions for the perturbation of vacuum black holes. We extend this method to black holes coupled with electromagnetic field and cosmological constant by allowing the master functions to be linear combinations of the metric and electromagnetic-potential perturbations, as well as their first-order derivatives. Requiring these master functions satisfy wave equations with yet-to-be-determined effective potentials, we reduce the linearized Einstein--Maxwell system to a set of algebraic-differential constraints. Solving these constraints reveals four master function branches in each parity sector: two standard branches, which coincide with the Zerilli-Moncrief formalism, and two Darboux branches, characterized by their effective potentials. Within each parity sector, a Darboux transformation exists which connects the standard and Darboux branches, preserving the quasinormal mode spectrum and confirming their physical equivalence.
12 pages, No figures, minor revision to V1
References in corpus (6)
- Observation of gravitational waves from two neutron star-black hole coalescences
- Analysis of Ringdown Overtones in GW150914
- Search for intermediate mass black hole binaries in the third observing run of Advanced LIGO and Advanced Virgo
- Second and higher-order perturbations of a spherical spacetime
- Darboux Covariance: A Hidden Symmetry of Perturbed Schwarzschild Black Holes
- Gravito-electromagnetic perturbations of MOG black holes with a cosmological constant: Quasinormal modes and Ringdown waveforms