Nearly indistinguishable: charged black holes in general and entangled relativity
Abstract
Entangled Relativity (ER) is a parameter-free alternative to General Relativity (GR), with classical departures fixed by the action and no adjustable scalar coupling. We investigate whether its static charged spacetimes can nevertheless be distinguished from Reissner–Nordström (RN) black holes through orbital motion. For the neutral test-particle model adopted here, ER motion is geodesic in the Einstein frame. We compare null and timelike orbits using the areal radius and show that the two theories have the same first post-Newtonian pericentre advance at the same mass, charge, and leading-order orbital scale. Noiseless fits and Gaussian-noise Monte Carlo experiments then allow both models to adjust the same six black-hole and orbital parameters. The main result is a strong observational degeneracy after refitting: throughout the common black-hole charge range, including q = |Q|/M = 1, RN reproduces the ER time series with very small residuals. These residuals are nonzero, and sufficiently low noise reveals an ER fitting advantage, but even the highest noise tested corresponds to only about 0.02 µas at the scale of Sgr A*. The simulated orbits also probe a much stronger field than S301. The scale comparison therefore indicates no realistic prospect of discrimination with current S301 astrometry, even for very highly charged black holes in the common charge range. Two ER boundary configurations with q greater than 1 are distinguishable at the simulated noise levels because RN black holes must satisfy q ≤ 1 and cannot compensate by adjusting their other parameters. Overall, this degeneracy exists despite ER having no tunable parameter to suppress its deviations from GR.
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BibTeX
@misc{yuan2026nearly,
title = {{Nearly indistinguishable: charged black holes in general and entangled relativity}},
author = {Jianqing Yuan and Arnaud Crepinge and Olivier Minazzoli and Xue-Mei Deng and Teng Xu},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05835250v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nearly indistinguishable: charged black holes in general and entangled relativity
AU - Jianqing Yuan
AU - Arnaud Crepinge
AU - Olivier Minazzoli
AU - Xue-Mei Deng
AU - Teng Xu
PY - 2026
DA - 2026/10/22
PB - HAL
UR - https://hal.science/hal-05835250v1
AB - Entangled Relativity (ER) is a parameter-free alternative to General Relativity (GR), with classical departures fixed by the action and no adjustable scalar coupling. We investigate whether its static charged spacetimes can nevertheless be distinguished from Reissner–Nordström (RN) black holes through orbital motion. For the neutral test-particle model adopted here, ER motion is geodesic in the Einstein frame. We compare null and timelike orbits using the areal radius and show that the two theories have the same first post-Newtonian pericentre advance at the same mass, charge, and leading-order orbital scale. Noiseless fits and Gaussian-noise Monte Carlo experiments then allow both models to adjust the same six black-hole and orbital parameters. The main result is a strong observational degeneracy after refitting: throughout the common black-hole charge range, including q = |Q|/M = 1, RN reproduces the ER time series with very small residuals. These residuals are nonzero, and sufficiently low noise reveals an ER fitting advantage, but even the highest noise tested corresponds to only about 0.02 µas at the scale of Sgr A*. The simulated orbits also probe a much stronger field than S301. The scale comparison therefore indicates no realistic prospect of discrimination with current S301 astrometry, even for very highly charged black holes in the common charge range. Two ER boundary configurations with q greater than 1 are distinguishable at the simulated noise levels because RN black holes must satisfy q ≤ 1 and cannot compensate by adjusting their other parameters. Overall, this degeneracy exists despite ER having no tunable parameter to suppress its deviations from GR.
ER -