Particle Collisions on Stringy Black Hole Background

TL;DR

This paper investigates particle collisions near Sen black holes, revealing conditions for arbitrarily high energies in extremal cases and upper bounds in nonextremal cases, considering back-reaction effects and gravitational radiation.

Contribution

It provides a detailed analysis of collision energies around Sen black holes, including extremal and nonextremal cases, and assesses the impact of back-reaction and gravitational radiation.

Findings

Arbitrarily high center-of-mass energy possible in extremal Sen black holes with specific conditions.

Nonextremal black holes have an upper limit on collision energy due to particle angular momentum constraints.

Gravitational radiation significantly reduces the maximum achievable collision energy.

Abstract

The collision of two particles in the background of a Sen black hole is studied. With the equations of motion of the particles, the center-of-mass energy is investigated when the collision takes place at the horizon of a Sen black hole. For an extremal Sen black hole, we find that the center-of-mass energy will be arbitrarily high with two conditions: (1) spin $a\neq 0$ and (2) one of the colliding particles has the critical angular momentum $l_{\text{c}}=2$. For a nonextremal Sen black hole, we show that, in order to obtain an unlimited center-of-mass energy, one of the colliding particles should have the critical angular momentum $l'_{\text{c}}=2 r_{+}/a$ ($r_{+}$ is the radius of the outer horizon for a nonextremal black hole). However, a particle with the angular momentum $l=l'_{\text{c}}$ could not approach the black hole from outside of the horizon through free fall, which implies that the collision with arbitrarily high center-of-mass energy could not take place. Thus, there is an upper bound of the center-of-mass energy for the nonextremal black hole. We also obtain the maximal center-of-mass energy for a near-extremal black hole and the result implies that the Planck-scale energy is hard to be approached. Furthermore, we also consider the back-reaction effects. The result shows that, neglecting the gravitational radiation, it has a weak effect on the center-of-mass energy. However, we argue that the maximum allowed center-of-mass energy will be greatly reduced to below the Planck-scale when the gravitational radiation is included.