Particle collisions near a three-dimensional warped AdS black hole

In this paper we consider the warped AdS$_{3}$ black hole solution of topologically massive gravity with a negative cosmological constant, and we investigate the possibility that it acts as a particle accelerator by analyzing the energy in the center of mass (CM) frame of two colliding particles in the vicinity of its horizon, which is known as the Ba\~nados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum $(L_c)$ of the particle decreases when the parameter that controls the stretching deformation ($\nu$) increases. Also, we show that despite the particle with $L_c$ can exist for certain values of the conserved energy outside the horizon, it will never reach the event horizon; therefore, the black hole can not act as a particle accelerator with arbitrarily high CM energy on the event horizon. However, such particle could also exist inside the outer horizon being the BSW process possible on the inner horizon. On the other hand, for the extremal warped AdS$_{3}$ black hole, the particle with $L_c$ and energy $E$ could exist outside the event horizon and the CM energy blows up on the event horizon if its conserved energy fulfill the condition $E^{2}>\frac{(\nu^{2}+3)l^{2}}{3(\nu^{2}-1)}$, being the BSW process possible.