Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.38742

Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity

Abhishek Rout
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study odd-parity perturbations of Reissner-Nordström black holes in dynamical Chern-Simons gravity. The dCS action is parity invariant because $\vartheta\,{}^{*}RR$ is the product of two pseudoscalars; nevertheless, the pseudoscalar perturbation has odd parity and enters only the axial sector at linear order and so lifts the axial--polar isospectrality of general relativity. We derive the finite-charge couplings between the pseudoscalar and the axial gravitational and electromagnetic perturbations directly from the linearized field equations. Both directions are governed by the radial kernel $(Mr-Q^2)Δ/r^8$, and at nonzero charge the pseudoscalar couples to $Ψ+χΨ_e$, with $χ=2Q/[r\sqrt{(l-1)(l+2)}]$. After diagonalizing the Einstein--Maxwell sector, we compute branch-resolved quasinormal-mode shifts with exterior complex scaling for the photon-sphere modes and Frobenius shooting for the near-extremal zero-damping modes. For the Schwarzschild $l=2$ fundamental mode we obtain $β\,δω=-0.7733-0.3946\,i$ (units $M=α=1$). Off resonance, the gravitational-led shift scales as $ζ\,l^3$ at $Q=0$ but as $ζ\,l^2/Q$ at fixed nonzero charge and large $l$. The electromagnetic-led branch becomes exactly degenerate with the pseudoscalar mode at $Q_c=2M\sqrt{l(l+1)+1}/[l(l+1)+2]$, where the pseudoscalar potential coincides with the polar partner of the electromagnetic-led potential; there the breaking is $\mathcal{O}(\sqrtζ)$, $M|Δω|\simeq2.4\sqrtζ$ for $l=2$, and the shift reverses sign across $Q_c$. Near extremality the photon-sphere shifts remain finite, whereas the non-degenerate fundamental gravitational-led zero-damping mode is suppressed, $δω/ω\simeq6.0\times10^{3}\,ζ\,(1-Q^2/M^2)$ for $l=2$.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Abhishek Rout. 2026-10-28. Isospectrality breaking in the axial quasinormal modes of Reissner-Nordström black holes in dynamical Chern-Simons gravity. https://arxiv.org/abs/2610.38742

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-force in hyperbolic black hole encounters

Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform ongoing efforts to construct an accurate description of the general-relativistic binary dynamics via an effective-one-body description or other approaches. Existing self-force methods are to a large extent specialised to bound, inspiral orbits. Here we derive the first-order conservative self-force correction to the scattering angle, show its agreement with recent post-Minkowsian results, and develop a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. In the method, the metric perturbation is reconstructed from a Hertz potential that satisfies (mode-by-mode) a certain inhomogeneous version of the Teukolsky equation. The crucial ingredient in this formulation are certain jump conditions that the (multipole modes of the) Hertz potential must satisfy along the worldline of the small body's orbit. We present a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime. To begin developing the numerical infrastructure, a scalar-field evolution code on a Schwarzschild background (in 1+1D) is developed. Following this, results for the conservative scalar self-force corrections to the scatter angle are calculated. We continue by constructing a Teukolsky evolution code on a Schwarzschild background. This produces numerically unstable solutions due to unphysical homogeneous solutions of the Teukolsky equation at the horizon and null infinity being seeded by numerical error. This can be resolved by a change of variables to a Regge-Wheeler-like field. We then present a full numerical implementation of this method for circular and scatter orbits in Schwarzschild.

gr-qc↗
arXiv2026

Quasinormal Ringing of de Sitter Braneworlds

Compared with the Poincaré braneworld, the de Sitter (dS) braneworld aligns more closely with the present universe characterized by a small but finite cosmological constant; to explore the quasinormal ringing properties within the dS brane scenario, we investigate gravitational perturbations in both thin and thick dS brane configurations. Analysis of the perturbation equations reveals that the effective potential along the extra dimension exhibits the shape of a Pöschl-Teller potential, asymptotically approaching a constant value (mass gap) at infinity, and in particular this mass gap can be reduced. Analytical calculations further indicate that the gravitational perturbations, apart from the zero mode, possess a series of discrete, purely imaginary quasinormal modes in the late stages, implying that these perturbations decay without oscillation over time; the analytical findings also demonstrate that the brane structure primarily determines the distribution of the quasinormal spectrum while preserving the purely imaginary nature of the quasinormal frequencies. Subsequently, we further simulate the gravitational wave signal by numerically evolving the perturbation equations, which yields late-stage results consistent with the analytical predictions. Interestingly, these quasinormal modes carry information about the cosmological constant on the brane, which provides a potential new pathway for the study of cosmology in the dS brane scenario.

gr-qc↗
arXiv2026

Beyond quasinormal modes: a complete mode decomposition of black hole perturbations

We show that retarded Green's functions of black hole spacetimes can be expressed as a convergent mode sum everywhere in spacetime. At late times a quasinormal mode sum converges, while at early times a Matsubara (or, Euclidean) mode sum converges. The two regions are separated by a lightcone which scatters from the black hole potential. The Matsubara sum is a Fourier series on the Euclidean thermal circle associated to the early time region. We illustrate our results for Pöschl-Teller, BTZ, and Schwarzschild. In the case of Schwarzschild, we express the branch cut contribution as a convergent sum of de Sitter quasinormal modes as $Λ\to 0^+$, and exploit recent exact solutions to the Heun connection problem. In each case we analytically show convergence by studying the asymptotics of residue sums and also provide numerical demonstrations.

gr-qc↗