Effect of the self-gravity of shells on a high energy collision in a rotating Ba\~{n}ados-Teitelboim-Zanelli spacetime

Abstract

We consider a collision of two dust thin shells with a high center-of-mass (CM) energy including their self-gravity in a Ba\~{n}ados-Teitelboim-Zanelli (BTZ) spacetime. The shells divide the BTZ spacetime into three domains and the domains are matched by the Darmois-Israel junction conditions. We treat only the collision of two shells which corotate with a background BTZ spacetime because of the junction conditions. The counterpart of the corotating shell collision is a collision of two particles with vanishing angular momenta. We compare the dust thin shell collision and the particle collision in order to investigate the effects of the self-gravity of colliding objects on the high CM energy collision. We show that the self-gravity of the shells affects the position of an event horizon and it covers the high-energy collisional event. Therefore, we conclude that the self-gravity of colliding objects suppresses its CM energy and that any observer who stands outside of the event horizon cannot observe the collision with an arbitrary high CM energy.