Wormholes, naked singularities and universes of ghost radiation

Both the static and homogeneous metrics describing the spherically symmetric gravitational field of a crossflow of incoming and outgoing null dust streams are generalized for the case of the two-component ghost radiation. Static solutions represent either naked singularities or the wormholes recently found by Hayward. The critical value of the parameter separating the two possibilities is given. The wormhole is allowed to have positive mass. The homogeneous solutions are open universes.Comment: 5 pages, 10 figures, minor changes to match the published versio

Brane-world cosmology with black strings

We consider the simplest scenario when black strings / cigars penetrate the cosmological brane. As a result, the brane has a Swiss-cheese structure, with Schwarzschild black holes immersed in a Friedmann-Lema\^{\i}tre-Robertson-Walker brane. There is no dark radiation in the model, the cosmological regions of the brane are characterized by a cosmological constant $\Lambda$ and flat spatial sections. Regardless of the value of $\Lambda$, these brane-world universes forever expand and forever decelerate. The totality of source terms in the modified Einstein equation sum up to a dust, establishing a formal equivalence with the general relativistic Einstein-Straus model. However in this brane-world scenario with black strings the evolution of the cosmological fluid strongly depends on $\Lambda$. For $\Lambda \leq 0$ it has positive energy density $\rho$ and negative pressure $p$ and at late times it behaves as in the Einstein-Straus model. For (not too high) positive values of $\Lambda$ the cosmological evolution begins with positive $\rho$ and negative $p$, but this is followed by an epoch with both $\rho$ and $p$ positive. Eventually, $\rho$ becomes negative, while $p$ stays positive. A similar evolution is present for high positive values of $\Lambda$, however in this case the evolution ends in a pressure singularity, accompanied by a regular behaviour of the cosmic acceleration. This is a novel type of singularity appearing in brane-worlds.Comment: 6 pages, 4 figures; expanded version, references added, to appear in Physical Review

How river rocks round: resolving the shape-size paradox

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.Comment: 11 pages, 5 figure

Formulas on hyperbolic volume

This paper collects some important formulas on hyperbolic volume. To determine concrete values of volume function is a very hard question requiring the knowledge of various methods. Our goal to give a non-elementary integral on the volume of the orthosceme (obtain it without using the Schl\"afli differential formula), using edge-lengthes as the only parameters.Comment: 7 figure