Buchdahl bound, photon ring, ISCO and radial acceleration in Einstein-\ae{}ther theory

Document detail

ID

oai:arXiv.org:2411.02550

Topic

General Relativity and Quantum Cos... Astrophysics - Astrophysics of Gal...

Author

Hsu, Yi-Hsiung Lasenby, Anthony Barker, Will Durakovic, Amel Hobson, Michael

Year

2024

listing date

11/13/2024

Keywords

e\ae{} theory

Metrics

Abstract

Spherically symmetric Einstein-{\ae}ther (E{\AE}) theory with a Maxwell-like kinetic term is revisited.

We consider a general choice of the metric and the \ae{}ther 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 \ae{}ther field to be time-like in the coordinate basis.

We derive the vacuum solution and confirm that the innermost stable circular orbit (ISCO) and photon ring are enlarged relative to general relativity (GR).

Buchdahl's theorem in E\AE{} 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 E\AE{} radial acceleration relations run parallel in the low pressure limit.

Our analysis of E\AE{} theory may offer novel insights into its interesting phenomenological generalization: \AE{}ther--scalar--tensor theory ({\AE}ST).

;Comment: 15 pages, 4 figures

Hsu, Yi-Hsiung,Lasenby, Anthony,Barker, Will,Durakovic, Amel,Hobson, Michael, 2024, Buchdahl bound, photon ring, ISCO and radial acceleration in Einstein-\ae{}ther theory