Researchers prove even and odd ‘ringing’ of Kerr–Newman–de Sitter black holes match exactly
This paper shows that two different ways a rotating, charged black hole in a universe with a positive cosmological constant can “ring” are in fact the same. Physicists call those rings quasinormal modes. The two symmetry types of perturbations, called even and odd parity, have identical frequencies for subextremal Kerr–Newman–de Sitter black holes in linearized Einstein–Maxwell theory.
The authors extend a coupled system of master equations that describe small gravitational and electromagnetic disturbances on a Kerr–Newman background to include a positive cosmological constant (the “de Sitter” part). Working in the Newman–Penrose formalism, they show the radiative degrees of freedom are governed by two coupled second-order partial differential equations for gauge-invariant master variables. These master variables capture the physically observable parts of the disturbance without depending on coordinate or frame choices.
A key step in the paper is reconstructing the actual metric perturbation (the change in spacetime geometry) and the electromagnetic gauge potential directly from those master variables. The reconstruction is done in the ingoing radiation gauge by integrating linearized Newman–Penrose identities, and notably avoids introducing an extra complex intermediate potential used in some older approaches. With the perturbations reconstructed, the authors verify that the general parity-isospectrality theorem they cite applies to this system.
Why this matters: parity isospectrality was known for several simpler black holes (Schwarzschild, Reissner–Nordström, and Kerr and their de Sitter cousins) but had not been established for the full Kerr–Newman–de Sitter family at generic spin and charge without approximations. Previous Kerr–Newman studies often used either slow-rotation or small-charge expansions. This result fills that gap and shows that the equality of even and odd quasinormal spectra survives when gravitational and electromagnetic perturbations are fully coupled and the cosmological constant is included.