Soft-photon theorem near static spherical horizons in generic dimensions
Abstract
We study Maxwell theory near a nonextremal bifurcate Killing horizon in a general static, spherically symmetric spacetime of dimension D>3. We impose near-horizon boundary conditions in a regular Eddington--Finkelstein chart that retain both radiative and Coulombic data, and construct the associated horizon phase space and large-U(1) charge. At null infinity, the radiative falloff depends on the spacetime dimension and involves half-integer powers in odd D, whereas a nonextremal horizon at finite radius supports radiative data with an ordinary integer-power expansion. Expanding the horizon fields in Killing frequency and spherical harmonics, we derive the associated soft-photon relation from the large-U(1) Ward identity. For comparison, we express the flat-space leading soft-photon theorem using the same spherical harmonics and commutator normalization as the horizon modes. In D=4, the two relations have the same soft-frequency dependence and the same angular dependence of the hard-charge terms, whereas for D>4 the flat-space relation contains additional dimension-dependent frequency and angular factors.
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BibTeX
@misc{zhang2026softphoton,
title = {{Soft-photon theorem near static spherical horizons in generic dimensions}},
author = {Kai-Yu Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07498},
eprint = {2610.07498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07498},
}
RIS
TY - UNPB
TI - Soft-photon theorem near static spherical horizons in generic dimensions
AU - Kai-Yu Zhang
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07498
UR - https://arxiv.org/abs/2610.07498
AB - We study Maxwell theory near a nonextremal bifurcate Killing horizon in a general static, spherically symmetric spacetime of dimension D>3. We impose near-horizon boundary conditions in a regular Eddington--Finkelstein chart that retain both radiative and Coulombic data, and construct the associated horizon phase space and large-U(1) charge. At null infinity, the radiative falloff depends on the spacetime dimension and involves half-integer powers in odd D, whereas a nonextremal horizon at finite radius supports radiative data with an ordinary integer-power expansion. Expanding the horizon fields in Killing frequency and spherical harmonics, we derive the associated soft-photon relation from the large-U(1) Ward identity. For comparison, we express the flat-space leading soft-photon theorem using the same spherical harmonics and commutator normalization as the horizon modes. In D=4, the two relations have the same soft-frequency dependence and the same angular dependence of the hard-charge terms, whereas for D>4 the flat-space relation contains additional dimension-dependent frequency and angular factors.
ER -