4 research outputs found
The effect of a massive object on an expanding universe
A tetrad-based procedure is presented for solving Einstein's field equations
for spherically-symmetric systems; this approach was first discussed by Lasenby
et al. in the language of geometric algebra. The method is used to derive
metrics describing a point mass in a spatially-flat, open and closed expanding
universe respectively. In the spatially-flat case, a simple coordinate
transformation relates the metric to the corresponding one derived by McVittie.
Nonetheless, our use of non-comoving (`physical') coordinates greatly
facilitates physical interpretation. For the open and closed universes, our
metrics describe different spacetimes to the corresponding McVittie metrics and
we believe the latter to be incorrect. In the closed case, our metric possesses
an image mass at the antipodal point of the universe. We calculate the geodesic
equations for the spatially-flat metric and interpret them. For radial motion
in the Newtonian limit, the force acting on a test particle consists of the
usual inwards component due to the central mass and a cosmological
component proportional to that is directed outwards (inwards) when the
expansion of the universe is accelerating (decelerating). For the standard
CDM concordance cosmology, the cosmological force reverses direction
at about . We also derive an invariant fully
general-relativistic expression, valid for arbitrary spherically-symmetric
systems, for the force required to hold a test particle at rest relative to the
central point mass.Comment: 14 pages, 2 tables, 5 figures; new version, to match the version
published in MNRA
The effect of an expanding universe on massive objects
We present some astrophysical consequences of the metric for a point mass in
an expanding universe derived in Nandra, Lasenby & Hobson, and of the
associated invariant expression for the force required to keep a test particle
at rest relative to the central mass. We focus on the effect of an expanding
universe on massive objects on the scale of galaxies and clusters. Using
Newtonian and general-relativistic approaches, we identify two important
time-dependent physical radii for such objects when the cosmological expansion
is accelerating. The first radius, , is that at which the total radial
force on a test particle is zero, which is also the radius of the largest
possible circular orbit about the central mass and where the gas pressure
and its gradient vanish. The second radius, , which is \approx r_F/1.6m\Lambda$CDM concordance model, at the
present epoch we find that these radii put a sensible constraint on the typical
sizes of both galaxies and clusters at low redshift. For galaxies, we also find
that these radii agree closely with zeroes in the radial velocity field in the
neighbourhood of nearby galaxies, as inferred by Peirani & Pacheco from recent
observations of stellar velocities. We then consider the future effect on
massive objects of an accelerating cosmological expansion driven by phantom
energy, for which the universe is predicted to end in a `Big Rip' at a finite
time in the future at which the scale factor becomes singular. In particular,
we present a novel calculation of the time prior to the Big Rip that an object
of a given mass and size will become gravitationally unbound.Comment: 16 pages, 5 tables, 6 figures; new version, to match the version
published in MNRA
Making sense of the bizarre behaviour of horizons in the McVittie spacetime
The bizarre behaviour of the apparent (black hole and cosmological) horizons
of the McVittie spacetime is discussed using, as an analogy, the
Schwarzschild-de Sitter-Kottler spacetime (which is a special case of McVittie
anyway). For a dust-dominated "background" universe, a black hole cannot exist
at early times because its (apparent) horizon would be larger than the
cosmological(apparent) horizon. A phantom-dominated "background" universe
causes this situation, and the horizon behaviour, to be time-reversed.Comment: 8 pages, 3 figure