97 research outputs found
Eleven spherically symmetric constant density solutions with cosmological constant
Einstein's field equations with cosmological constant are analysed for a
static, spherically symmetric perfect fluid having constant density. Five new
global solutions are described.
One of these solutions has the Nariai solution joined on as an exterior
field. Another solution describes a decreasing pressure model with exterior
Schwarzschild-de Sitter spacetime having decreasing group orbits at the
boundary. Two further types generalise the Einstein static universe.
The other new solution is unphysical, it is an increasing pressure model with
a geometric singularity.Comment: 19 pages, 5 figures, 1 table, revised bibliography, corrected eqn.
(3.11), typos corrected, two new reference
Bounds on M/R for static objects with a positive cosmological constant
We consider spherically symmetric static solutions of the Einstein equations
with a positive cosmological constant which are regular at the
centre, and we investigate the influence of on the bound of M/R,
where M is the ADM mass and R is the area radius of the boundary of the static
object. We find that for any solution which satisfies the energy condition
where and are the radial and
tangential pressures respectively, and is the energy density, and
for which the inequality
\frac{M}{R}\leq\frac29-\frac{\Lambda R^2}{3}+\frac29 \sqrt{1+3\Lambda R^2},
holds. If it is known that infinitely thin shell solutions uniquely
saturate the inequality, i.e. the inequality is sharp in that case. The
situation is quite different if Indeed, we show that infinitely
thin shell solutions do not generally saturate the inequality except in the two
degenerate situations and . In the latter
situation there is also a constant density solution, where the exterior
spacetime is the Nariai solution, which saturates the inequality, hence, the
saturating solution is non-unique. In this case the cosmological horizon and
the black hole horizon coincide. This is analogous to the charged situation
where there is numerical evidence that uniqueness of the saturating solution is
lost when the inner and outer horizons of the Reissner-Nordstr\"{o}m solution
coincide.Comment: 14 pages; Improvements and corrections, published versio
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