Charge-activated birefringence of an Einstein-tensor-coupled vector field on Reissner--Nordström black holes
Abstract
We study the propagation of a neutral vector test field non-minimally coupled to the Einstein tensor on a Reissner--Nordström black hole. The interaction vanishes on a vacuum background, so electric charge is required to activate the curvature-induced response. The parity potentials have one symmetry: reversing the sign of the coupling exchanges the electric and magnetic susceptibilities. Because of this symmetry, the two polarizations respond identically at first order in the coupling. The dominant propagation-level effect is therefore a common shift of the effective photon sphere and of the shadow radius, not a birefringent splitting. The variation of shadow size can mimic the charge variation of a black hole. When the coupling is weak, polarization splitting appears only in the second-order term, distinguishing this interaction from corrections involving only charge. We follow this ordering through full-frequency absorption and scattering, the semiclassical glory, and ray-traced double shadows. The absorption parity asymmetry and the shadow rim splitting probe the difference between the effective potentials. The polarization-summed backward scattering isolates the helicity-reversing response, which is zero without the coupling. At the positive-coupling boundary the splitting grows but stays finite. Beyond it the even-parity potential has a pole outside the horizon. In the high-multipole limit, the two boundaries of the stability window both correspond to the thresholds of bound-state instability, but their physical properties differ: the negatively coupled boundary forms a regular potential well, while the positively coupled boundary marks the breaking of regularity. A Frobenius analysis shows a forced logarithmic branch at that pole. Without an additional physical connection condition, the continuation across the pole is not unique.
Related
- Charge-Activated Birefringence and Shadow Mimicry around Reissner-Nordström Black Holes
- Nonoscillatory gravitational quasinormal modes of Reissner–Nordström–de Sitter spacetime
- Reissner-Nordstrom in the Bertotti-Robinson-Bonnor-Melvin electromagnetic field
- Stochastic motion of massless particles near event horizons in Schwarzschild and Reissner-Nordström spacetimes
- Flexible numerical characteristic gluing to extremal Reissner-Nordström black holes
BibTeX
@misc{wan2026chargeactivated,
title = {{Charge-activated birefringence of an Einstein-tensor-coupled vector field on Reissner--Nordström black holes}},
author = {Mao-Yuan Wan and Chen Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16650},
eprint = {2610.16650},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16650},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Charge-activated birefringence of an Einstein-tensor-coupled vector field on Reissner--Nordström black holes
AU - Mao-Yuan Wan
AU - Chen Wu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.16650
UR - https://arxiv.org/abs/2610.16650
AB - We study the propagation of a neutral vector test field non-minimally coupled to the Einstein tensor on a Reissner--Nordström black hole. The interaction vanishes on a vacuum background, so electric charge is required to activate the curvature-induced response. The parity potentials have one symmetry: reversing the sign of the coupling exchanges the electric and magnetic susceptibilities. Because of this symmetry, the two polarizations respond identically at first order in the coupling. The dominant propagation-level effect is therefore a common shift of the effective photon sphere and of the shadow radius, not a birefringent splitting. The variation of shadow size can mimic the charge variation of a black hole. When the coupling is weak, polarization splitting appears only in the second-order term, distinguishing this interaction from corrections involving only charge. We follow this ordering through full-frequency absorption and scattering, the semiclassical glory, and ray-traced double shadows. The absorption parity asymmetry and the shadow rim splitting probe the difference between the effective potentials. The polarization-summed backward scattering isolates the helicity-reversing response, which is zero without the coupling. At the positive-coupling boundary the splitting grows but stays finite. Beyond it the even-parity potential has a pole outside the horizon. In the high-multipole limit, the two boundaries of the stability window both correspond to the thresholds of bound-state instability, but their physical properties differ: the negatively coupled boundary forms a regular potential well, while the positively coupled boundary marks the breaking of regularity. A Frobenius analysis shows a forced logarithmic branch at that pole. Without an additional physical connection condition, the continuation across the pole is not unique.
ER -