Peculiar velocities in dynamic spacetimes

Abstract

We investigate the asymptotic behavior of peculiar velocities in certain physically significant time-dependent gravitational fields. Previous studies of the motion of free test particles have focused on the \emph{collapse scenario}, according to which a double-jet pattern with Lorentz factor $\gamma \to \infty$ develops asymptotically along the direction of complete gravitational collapse. In the present work, we identify a second \emph{wave scenario}, in which a single-jet pattern with Lorentz factor $\gamma \to \infty$ develops asymptotically along the direction of wave propagation. The possibility of a connection between the two scenarios for the formation of cosmic jets is critically examined.Comment: 17 pages, 1 figure; v2: minor stylistic improvement

Twisted gravitational waves in the presence of a cosmological constant

“…For plane gravitational wave spacetimes, this cosmic jet property was first demonstrated in Ref. [15] and further studied in Ref. [16].…”

“…In certain dynamic spacetime regions, geodesics tend to line up, as measured by static fiducial observers, and thus produce a cosmic jet whose speed asymptotically approaches the speed of light [14,15]. For plane gravitational wave spacetimes, this cosmic jet property was first demonstrated in Ref.…”

“…An example of the latter situation has been discussed in detail, in connection with the phenomenon of cosmic jets [14], in Section IV of Ref. [15]. Conformally flat Kundt solutions with a cosmological constant are treated in Ref.…”

“…A plane gravitational wave admits parallel null rays, so that the four principal null directions of the Weyl tensor coincide and are all parallel to the direction of propagation of the plane wave and hence perpendicular to the uniform wave front. With respect to the static observers in these spacetimes, timelike geodesics exhibit the cosmic jet property, where the jet motion is parallel to the direction of motion of the plane wave [15,16]. However, the nonuniformity of the wave front in the case of nonplanar TGWs implies that the resulting cosmic jet direction is oblique with respect to the direction of wave propagation [16].…”

Vacuum gravitational fields with a null Killing vector

“…In recent years the "cosmic jet" property was intensively investigated: Test particles can gain (or lose) energy in time-dependent gravitational fields, e.g. plane waves [27,28]. It would be interesting to study this question also for the nonplanar waves presented in this article.…”