Rotating Thin Shells in Einstein-Gauss-Bonnet Gravity
A rotating metric solution in Einstein-Gauss-Bonnet gravity with a negative cosmological constant was recently found in the Chern-Simons point. We construct a rotating thin shell gluing two spacetimes in Einstein-Gauss-Bonnet gravity, using the Davis junction conditions. We take the inner and outer spacetimes as replicas of the same rotating metric, with different values of mass and angular momentum. We show that the only possible thin shells either are vacuum thin shells or have a non-zero pressure in one tangential direction while the remaining stress tensor components vanish. We obtain the equation of motion for the shell, which resembles the continuity equation for a shell in General Relativity (GR), even though the quantity analogous to the intrinsic mass of the shell in GR is not connected to its stress tensor. We study the special case of vacuum thin shells connecting two spacetimes with zero hair. We obtain analytically the possible trajectories of the shell, and in certain situations we observe that the solution ceases to be valid. We find cases where the vacuum shell collapses and a naked singularity is formed. There two types of static vacuum thin shell solutions, one being stable occurring when both inner and outer spacetimes are overextremal, and the other unstable occurring when the horizons of inner and outer spacetimes approach each other, and are close to extremality.