Buchdahl bound, photon ring, innermost stable circular orbit, and radial acceleration in Einstein-æther theory
Phys. Rev. D 111, 124032 – Published 20 June, 2025
DOI: https://doi.org/10.1103/4y9j-wyrf
Abstract
Spherically symmetric Einstein-æther (EÆ) theory with a Maxwell-like kinetic term is revisited. We consider a general choice of the metric and the æther field, finding that (i) there is a gauge freedom allowing one always to use a diagonal metric; and (ii) the nature of the Maxwell equation forces the æther field to be timelike in the coordinate basis. We derive the vacuum solution and confirm that the innermost stable circular orbit and photon ring are enlarged relative to general relativity (GR). Buchdahl’s theorem in EÆ theory is derived. For a uniform physical density, we find that the upper bound on compactness is always lower than in GR. Additionally, we observe that the Newtonian and EÆ radial acceleration relations run parallel in the low pressure limit. Our analysis of EÆ theory may offer novel insights into its interesting phenomenological generalization: Æther-scalar-tensor theory.
