A relativistic model of the topological acceleration effect
Abstract
It has previously been shown heuristically that the topology of the Universe affects gravity, in the sense that a test particle near a massive object in a multiply connected universe is subject to a topologically induced acceleration that opposes the local attraction to the massive object. It is necessary to check if this effect occurs in a fully relativistic solution of the Einstein equations that has a multiply connected spatial section. A Schwarzschildlike exact solution that is multiply connected in one spatial direction is checked for analytical and numerical consistency with the heuristic result. The T^{1} (slabspace) heuristic result is found to be relativistically correct. For a fundamental domain size of L, a slowmoving, negligiblemass test particle lying at distance x along the axis from the object of mass M to its nearest multiple image, where GM/c^{2} ≪ x ≪ L/2, has a residual acceleration away from the massive object of 4ζ(3)G(M/L^{3}) x, where ζ(3) is Apéry's constant. For M ∼ 10^{14}M_{⊙} and L ∼ 1020h^{1} Gpc, this linear expression is accurate to ±10% over 3\;{{h^{1} Mpc}}\ \lower.6ex{\buildrel < \over \sim }\ x\ \lower.6ex{\buildrel<\over \sim }\ 2\;{{h^{1} Gpc}}. Thus, at least in a simple example of a multiply connected universe, the topological acceleration effect is not an artefact of Newtonianlike reasoning, and its linear derivation is accurate over about three orders of magnitude in x.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 August 2012
 DOI:
 10.1088/02649381/29/16/165006
 arXiv:
 arXiv:1109.1596
 Bibcode:
 2012CQGra..29p5006O
 Keywords:

 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 12 pages, 2 figures, 1 table