GTA Seminar | Speaker: Filipe Costa (IST-UL, Lisbon)

Title: Reference frames in General Relativity, gravitomagnetism, and the galactic missing mass problem

Abstract: Interpreting the solutions of the Einstein field equations is, in general, a challenging task, part of the difficulties lying in the significance of the coordinate system. I will present an extension of the International Astronomical Union (IAU) reference system to the exact theory, namely how to set up reference frames non-rotating with respect to distant inertial objects. We show this to be possible in spacetimes admitting shearfree congruences of time-like curves whose vorticity and acceleration asymptotically vanish, corresponding to a restricted form of the metric tensor. The construction shall be exemplified in the FLRW, Kerr, NUT, van Stockum rotating cylinder, and spinning string solutions. We also use it to debunk the Balasin-Grumiller and akin galactic models, claiming to explain the galactic rotation curves through gravitomagnetic effects without the need for dark matter. Such models are seen to originate (among other pathologies) precisely from an invalid choice of reference frame. 
For the description of gravitomagnetic effects in the exact theory, we use the 1+3 "quasi-Maxwell" formalism; generalizing it to null geodesics, and employing the Gauss-Bonnet theorem, we show, on general grounds, that relativistic effects cannot account for the galactic missing mass problem, addressing the recent extensive debate in the literature. 

References: Costa et al Phys. Rev. D 108, 044056 (2023) [arXiv:2303.17516], Phys. Rev. D 110, 064056 (2024) [arXiv:2312.12302].