Recently Kaloper, Kleban and Martin reexamined the McVittie solution and argued, contrary to a very widely held belief, that the solution contains a black hole in an expanding universe. Here we corroborate their main conclusion but go on to examine, in some detail, a specific solution that asymptotes to the ΛCDM cosmology. We show that part of the boundary of the solution contains the inner bifurcation two -sphere of the Schwarzschild -de Sitter spacetime and so both the black and white hole horizons together form a partial boundary of this McVittie solution. We go on to show that the null and weak energy conditions are satisfied and that the dominant energy condition is satisfied almost everywhere in the solution. The solution is understood here by way of a systematic construction of a conformal diagram based on detailed numerical integrations of the null geodesic equations. We find that the McVittie solution admits a degenerate limit in which the bifurcation two -sphere disappears. For solutions with zero cosmological constant, we find no evidence for the development of a weak null singularity. Rather, we find that in this case there is either a black hole to the future of an initial singularity or a white hole to its past.

We present here the transformations required to recast the Robertson-Walker metric and Friedmann-Robertson-Walker equations in terms of observer-dependent coordinates for several commonly assumed cosmologies. The overriding motivation is the derivation of explicit expressions for the radius R h of our cosmic horizon in terms of measurable quantities for each of the cases we consider. We show that the cosmological time dt diverges for any finite interval ds associated with a process at R → R h , which therefore represents a physical limit to our observations. This is a key component required for a complete interpretation of the data, particularly as they pertain to the nature of dark energy. With these results, we affirm the conclusion drawn in our earlier work that the identification of dark energy as a cosmological constant does not appear to be consistent with the data.

We provide an invariant characterization of the physical properties of the Kerr spacetime. We introduce two dimensionless invariants, constructed out of some known curvature invariants, that act as detectors for the event horizon and ergosurface of the Kerr black hole. We also show that the mass and angular momentum can be extracted from local measurements of the curvature invariants, which in the weak field limit could be used to approximate the total angular momentum and mass of a system of merging black holes. Finally, we introduce a dimensionless invariant that gives a local measure of the "Kerrness" of the spacetime.

The hierarchical clustering inherent in Λcold dark matter cosmology seems to produce many of the observed characteristics of large‐scale structure. But some glaring problems still remain, including the overprediction (by a factor of 10) of the number of dwarf galaxies within the virialized population of the local group. Several secondary effects have already been proposed to resolve this problem. It is still not clear, however, whether the principal solution rests with astrophysical processes, such as early feedback from supernovae, or possibly with as yet undetermined properties of the dark matter itself. In this paper, we carry out a detailed calculation of the dwarf halo evolution incorporating the effects of a hypothesized dark matter decay, D→ D′+l, where D is the unstable particle, D′ is the more massive daughter particle and l is the other, lighter (or possibly massless) daughter particle. This process preferentially heats the smaller haloes, expanding them during their evolution and reducing their present‐day circular velocity. We find that this mechanism can account very well for the factor of 4 deficit in the observed number of systems with velocity 10–20 km s−1 compared to those predicted by the numerical simulations, if , where Δm is the mass difference between the initial and final states. The corresponding lifetime τ cannot be longer than ∼30 Gyr, but may be as short as just a few Gyr.

Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant (Λ > 0), the AdS/CFT correspondence tells us that the case Λ < 0 is still worthy of consideration. In this paper we study the McVittie solution with Λ < 0. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson -Walker case, we find that Λ < 0 ensures collapse to a Big Crunch, a feature which completely dominates the global structure.