Spherically symmetric, static vacuum solution in aether scalar tensor theory with MOND term
Abstract
Aether scalar tensor (AeST) theory is a relativistic theory of gravity that recovers Modified Newtonian Dynamics (MOND), a proposed alternative to dark matter, in the quasistatic weak-field regime. In this work, we include the MOND term in the theory’s free function, which has been neglected in previous studies. By doing so, and studying vacuum solutions in a static, spherically symmetric spacetime, we find that the MOND term induces deviations from flat spacetime at unphysically large distances—greater than the radius of the observable universe (>1010 ly), while the metric remains Minkowski-flat within galactic scales (≲ 106 ly), where no MOND behavior is observed. In contrast, removing the MOND term yields a flat spacetime throughout the entire domain. We also observe the screening effects of the parameter λs, which controls the strength and range of the deviation, although it has no significant effect in the absence of the MOND term.
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