A note on geodesics in inhomogeneous expanding spacetimes

Abstract

There are several solutions of Einstein field equations that describe an inhomogeneity in an expanding universe. Among these solutions, the McVittie metric and its generalizations have been investigated through decades, though a full understanding of them is still lacking. In this note, we explore the trajectories of photons and massive particles in generalized McVittie spacetimes. In the case of massless particles, we show that no circular orbits are possible for those models that admit cosmological singularities. We also analyze the trajectory of particles for a specific generalized McVittie spacetime that is conformal to the Schwarzschild metric. By integrating the equations of motion in the Newtonian approximation, we show that particles behave in quite distinctive ways in different cosmological black hole solutions. We conclude that the analysis of the geodetic motion in inhomogeneous expanding metrics can help to discriminate those solutions that represent real cosmological black holes in the universe.

Lagrangian density and local symmetries of inhomogeneous hyperconical universes

“…If this approach is considered for the spatial components of the hyperconical metric, g rr = −a(t) 2 /(1 − r 2 /t 2 ), it locally approaches to the Schwarzschild components, g rr = −a(t) 2 /(1 − 2Gm(r)/r), as expected for inhomogeneous metrics (e.g. LTB and McVittie metrics [33,35]). Summarising, inhomogeneous metric with a locally valid GR leads to Ω Λ = ρ Λ /ρ crit = 0, but if that metric is projected on a flat FRW metric (forcing GR to be generally valid), the inhomogeneity is absorbed as an acceleration and dark energy is Ω Λ = 0.6937181(2) ([ [17]]).…”

“…Differences are also found comparing with the McVittie metric, which is an asymptotically spatially flat FLRW metric for largest distances. [35] To compare with similar FLRW metrics, we can see that the t -isochronous hypersurface is similar to a paraboloid, in contrast to the homogeneous hypersphere given by the t-isochronous (Fig. 1).…”

Black Hole Philosophy

“…The reason is the expansion of the universe as the object moves around the black hole: the object never arrives back at the same point in space. This has been investigated in some detail by Pérez et al (2019).…”

“…There is another interesting consequence of the cosmological expansion. A force that pulls away the orbiting object naturally appears and increases with the expansion velocity (Nandra et al 2012, Pérez et al 2019. In a universe with accelerated expansion and a cosmological horizon, there will be a time, in the far future, where everything except the orbiting object would be causally disconnected from the black hole.…”

ISCOs and OSCOs in the presence of positive cosmological constant

“…Some previous work on these OSCOs has been performed both in quite abstract settings [2][3][4], and within the more limited frameworks of accretion disks [5,6], tori [7], galaxies [8,9], ring systems [10], and axisymmetric spacetimes [11]. Further afield, related calculations have also been reported in modified gravity [12], inhomogeneous FLRW cosmologies [13], and higher dimensions [14][15][16], but we feel there is still more to be said in this regard. In this article we shall emphasize simple calculations, robust estimates of the relevant distances scales, and the broad astrophysical relevance of these OSCOs.…”