Gravitational field of a spinning radiation beam pulse in higher dimensions

We study the gravitational field of a spinning radiation beam pulse in a higher-dimensional spacetime. We derive first the stress-energy tensor for such a beam in a flat space-time and find the gravitational field generated by it in the linear approximation. We demonstrate that this gravitational field can also be obtained by boosting the Lense-Thirring metric in the limit when the velocity of the boosted source is close to the velocity of light. We then find an exact solution of the Einstein equations describing the gravitational field of a polarized radiation beam pulse in a spacetime with arbitrary number of dimensions. In a $D$-dimensional spacetime this solution contains [$D/2$] arbitrary functions of one variable (retarded time $u$), where [$d$] is the integer part of $d$. For the special case of a four-dimensional spacetime we study effects produced by such a relativistic spinning beam on the motion of test particles and light.

Figure 1

The relativistic gyraton with $m=0$, $j=0.7$ passes through the center of a set of particles initially located at the radius 1. The gravitational field of the gyraton is turned on during the interval ($-1/2$, $1/2$) (two solid circular curves). During this interval the particles position is twisted. After this the particles are moving radially outward with a uniform speed.

Figure 2

Motion of particles for the gyraton parameters $m=0.25$, $j=0$. For this case there is no twist, and particles move to the center with constant radial velocity. They pass the center, $r=0$ after the gyraton, and passing the caustic starts their expansion.

Figure 3

A special case ($m=1$, $j=1$) when the centrifugal repulsion compensates exactly the Newtonian attraction.

Figure 4

The case when both of the parameters $m$ and $j$ do not vanish, but the attraction dominates ($m=1.5$, $j=1$).

Figure 5

The case when both of the parameters $m$ and $j$ do not vanish, but the repulsion dominates ($m=0.7$, $j=1$).

Figure 6

A special case when the repulsion dominates ($m=0$, $j=0.6$). After the gyraton passes throughout the center, the particles located at the inner circle $r_1=0.8$ get higher positive radial velocity than the particle which initially were located at $r_0=1.0$. The inner particles (their world sheet is shown by a light surface) cross the outer particles (darker surface). At the moment of the intersection a caustic is formed.