VII Leopoldo García-Colín Mexican Meeting on Mathematical and Experimental Physics

ROBERTO SUSSMAN: Towards a relativistic covariant interpretation of Milgrom’s acceleration

17 Feb 2020, 17:00

30m

El Colegio Nacional, México City

SYMPOSIUM ON BLACK HOLES AND GRAVITATIONAL WAVES SHORT TALKS

Description

We propose in this letter a relativistic coordinate independent
interpretation for Milgrom's acceleration $a_0=1.2\times {10}^{-8}{\text{cm/s}}^2$ through a geometric constraint obtained from the product of the Kretschmann invariant scalar times the surface area of 2--spheres defined through suitable characteristic length scales for local and cosmic regimes, described by Schwarzschild and Friedman--Lemaître--Robertson--Walker (FLRW) geometries, respectively. By demanding consistency between these regimes we
obtain an appealing expression for the empirical (so far unexplained) relation between the accelerations $a_0$ and $c{H}_0$. Imposing this covariant geometric criterion upon a FLRW model, yields a dynamical equation for the Hubble scalar whose solution matches, to a very high accuracy, the cosmic expansion rate of the $\mathrm{\Lambda }$CDM concordance model fit for cosmic times close to the present epoch. While these results are very preliminary and strictly valid only at a toy model level, we believe that they could provide relevant information in the search of alternative gravity theories or even within General Relativity itself.