journal club on aspects of information, quantum theory, and gravity
25 Mar 2025
The swirling universe solution is an exact solution of Einstein’s field equation, it is stationary and axially symmetric space-time that is fully characterized by one parameter, the swirling parameter, which is to be understood as the background rotation. The “swirling” name actually came from a preliminary study on the effects of the background on the motion of test particles. This space-time possesses some interesting characteristics, like the space-time frame-dragging that changes its sign with respect to the equatorial plane and the geometry of the ergoregions, which, differently from the well-known Kerr space-time, are two disconnected, non-compact patches, above and below the equatorial plane, that extend all the way to infinity. In this talk, I will demonstrate that the equations of motion for a test particle in the swirling universe can be decoupled using the Hamilton-Jacobi formalism, where a fourth constant of motion is obtained, a method akin to the Carter constant for the Kerr geometry; thus, the geodesic equations can then be analytically integrated using elementary and elliptic functions. A typical orbit is then bounded in the radial direction and escapes to infinity in the z-direction. However, once a Schwarzschild black hole is immersed into a swirling universe, the geodesic equations can no longer be decoupled, and hence, a numerical approach is required to study the motion of test particles, suggesting the emergence of chaotic orbits. Furthermore, this solution has been generalized to include external electromagnetic fields as well, in a solution that is coined as the “electromagnetic-swirling universe”. The motion of charged particles in this novel solution can also be analytically integrated using a similar fashion.