English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

It has previously been shown heuristically that the topology of the Universeaffects gravity, in the sense that a test particle near a massive object in amultiply connected universe is subject to a topologically induced accelerationthat opposes the local attraction to the massive object. This effectdistinguishes different comoving 3-manifolds, potentially providing atheoretical justification for the Poincar\'e dodecahedral space observationalhypothesis and a dynamical test for cosmic topology. It is necessary to checkif this effect occurs in a fully relativistic solution of the Einsteinequations that has a multiply connected spatial section. A Schwarzschild-likeexact solution that is multiply connected in one spatial direction is checkedfor analytical and numerical consistency with the heuristic result. The T$^1$(slab space) heuristic result is found to be relativistically correct. For afundamental domain size of $L$, a slow-moving, negligible-mass test particlelying at distance $x$ along the axis from the object of mass $M$ to its nearestmultiple image, where $GM/c^2 \ll x \ll L/2$, has a residual acceleration awayfrom the massive object of $4\zeta(3) G(M/L^3)\,x$, where $\zeta(3)$ isAp\'ery's constant. For $M \sim 10^14 M_\odot$ and $L \sim 10$ to $20\hGpc$,this linear expression is accurate to $\pm10%$ over $3\hMpc \ltapprox x\ltapprox 2\hGpc$. Thus, at least in a simple example of a multiply connecteduniverse, the topological acceleration effect is not an artefact ofNewtonian-like reasoning, and its linear derivation is accurate over aboutthree orders of magnitude in $x$.

A relativistic model of the topological acceleration effect