Hyperelliptic disk solution (imaginary)

 

The video shows the imaginary part of the Ernst potential for a family of disk solutions where the matter consists of two streams of counter-rotating dust (the real part can be seen in Hyperelliptic disk solution (real part)). We show the transition between the Newtonian limit (flat spacetime) to the extreme relativistic limit where the central redshift diverges. The situation is equatorially symmetric (the imaginary part is an odd function in ζ ) and asymptotically flat (the imaginary part tends to 0 at infinity). The potential is smooth in the exterior of the disk and has a jump there. See LN 29/2006

for details.

J. Frauendiener and C. Klein