Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes
Abstract
We determine the quadrupolar logarithmic tidal response of electrically charged Einstein-Euler-Heisenberg black holes from the coupled static odd-parity gravitational and electromagnetic equations. Although the second electromagnetic invariant vanishes on the electric background, its quadratic interaction contributes to the axial fluctuation equations. At first order in the Euler-Heisenberg coupling a, a direct asymptotic recursion gives the canonical running matrix CcanEH=(9aQ2/10)(0&−Q −Q&M), defined as the coefficients multiplying the canonical source vector in the r−2log(r0/r) term. The resulting local coefficients retain the full dependence on the subextremal ratio Q/M at this perturbative order. The two quartic invariants partially cancel in both nonzero channels, while the action-normalized fields make gravitoelectromagnetic reciprocity explicit. The local extremal limit of the running matrix reproduces the corresponding two-invariant effective-field-theory result after convention conversion. Allowing independent quartic couplings further shows that identical electric background geometries can have different axial running matrices and yields algebraic inverse relations within the specified two-operator model. The calculation determines local logarithmic running within minimally coupled quartic electrodynamics; the finite horizon-matched response requires an additional global matching calculation.
Related
- The Analytical Solutions of Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
- Horizon Structure and Geodesic Properties of Simpson-Visser Black Holes in Einstein-Euler-Heisenberg Theory
- Charge-dependent scalarization of Einstein- Euler-Heisenberg black holes
- Geometric Capture and Optical Critical Curves of Purely Electric, Magnetic and Dyonic Black Holes in Einstein-Euler-Heisenberg Theory
- Charge-dependent scalarization of Einstein–Euler–Heisenberg black holes
BibTeX
@misc{becar2026tidal,
title = {{Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes}},
author = {Ramon Becar and P. A. Gonzalez and Ali Ovgun and Joel Saavedra and Yerko Vasquez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.38649},
eprint = {2609.38649},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38649},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tidal Response Beyond the Background Geometry in Einstein-Euler-Heisenberg Black Holes
AU - Ramon Becar
AU - P. A. Gonzalez
AU - Ali Ovgun
AU - Joel Saavedra
AU - Yerko Vasquez
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2609.38649
UR - https://arxiv.org/abs/2609.38649
AB - We determine the quadrupolar logarithmic tidal response of electrically charged Einstein-Euler-Heisenberg black holes from the coupled static odd-parity gravitational and electromagnetic equations. Although the second electromagnetic invariant vanishes on the electric background, its quadratic interaction contributes to the axial fluctuation equations. At first order in the Euler-Heisenberg coupling a, a direct asymptotic recursion gives the canonical running matrix C_can^EH=(9aQ^2/10)(0&−Q −Q&M), defined as the coefficients multiplying the canonical source vector in the r^−2log(r_0/r) term. The resulting local coefficients retain the full dependence on the subextremal ratio Q/M at this perturbative order. The two quartic invariants partially cancel in both nonzero channels, while the action-normalized fields make gravitoelectromagnetic reciprocity explicit. The local extremal limit of the running matrix reproduces the corresponding two-invariant effective-field-theory result after convention conversion. Allowing independent quartic couplings further shows that identical electric background geometries can have different axial running matrices and yields algebraic inverse relations within the specified two-operator model. The calculation determines local logarithmic running within minimally coupled quartic electrodynamics; the finite horizon-matched response requires an additional global matching calculation.
ER -