Abstract
In this paper we consider the warped hbox {AdS}_{3} black hole solution of topologically massive gravity with a negative cosmological constant, and we study 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 Bañnados, Silk and West (BSW) process. Mainly, we show that the critical angular momentum (L_c) of the particle decreases when the warping parameter(nu ) increases. Also, we show that despite the particle with L_c being able to exist for certain values of the conserved energy outside the horizon, it will never reach the event horizon; therefore, the black hole cannot act as a particle accelerator with arbitrarily high CM energy on the event horizon. However, such a particle could also exist inside the outer horizon, with the BSW process being possible on the inner horizon. On the other hand, for the extremal warped hbox {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 fulfills the condition E^{2}>frac{(nu ^{2}+3)l^{2}}{3(nu ^{2}-1)}, with the BSW process being possible.
Highlights
In Refs. [16,17] the authors found that the particle with the critical angular momentum could exist inside the outer horizon of the BTZ black hole regardless of the particle energy with the BSW process being possible on the inner horizon for the non-extremal BTZ black hole
In Ref. [18], the authors studied the collision of two particles on an event horizon and outside of the BTZ black hole, and they showed that in principle the center of mass (CM) energy of two ingoing particles can be arbitrarily large on an event horizon, if either of the two particles has a critical angular momentum and the other has a non-critical angular momentum, the critical particles never reach the event horizon
We will show that the BSW effect is possible on the outer horizon in the extremal warped AdS3 black hole, and the particle with critical angular momentum can reach the degenerate horizon when a condition on its energy is fulfilled, which resembles to what occurs in the extremal Kerr-AdS black hole; in the extremal Kerr-AdS black hole two conditions must be fulfilled [9]; besides, this effect is possible on the inner horizon for the non-extremal warped AdS3 black hole
Summary
The models of gravity in three spacetime dimensions and their modifications have attracted remarkable interest in the last decade. Where τσμ = 1/√−g is the Levi–Civita tensor and ν is a dimensionless coupling constant, which is related to the graviton mass μ by ν = μl/3 This model, in contrast to GR in three spacetime dimensions, has a propagating degree of freedom which corresponds to a massive graviton. The metric describing the spacelike stretched black holes [36,37,38,39] in ADM form is given by ds2 = −N 2(r )dt2 + 2 R2(r ) dφ + Nφ(r )dt 2. An important feature of these black holes is that the Killing vector ∂t is spacelike everywhere in the spacetime and its ergoregion extends to infinity; observers cannot follow the orbits of ∂t in the exterior region. It is worth noting that the warped AdS3 space arises in other contexts, for instance see [41,65,66,67,68,69,70,71,72,73,74]
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