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 λ_s, which controls the strength and range of the deviation, although it has no significant effect in the absence of the MOND term.