Scalar scattering from black holes with tidal charge

Ednilton S De Oliveira

doi:10.1140/epjc/s10052-018-6316-9

Abstract

The cross sections of black holes with tidal charge predicted in the context of the Randall–Sundrum brane-world scenario are computed considering the massless scalar field. Results obtained for black holes with different tidal-charge intensities are compared in order to study how this charge modifies the black hole cross sections. Such results are also compared with the ones for Schwarzschild and extreme Reissner–Nordström black holes. The increase of the tidal-charge intensity makes the black hole absorb more and can also be measured by the narrowing of interference fringes of the differential scattering cross section. These results indicate that the effects of the tidal charge are very important in phenomena which take place near the black hole, but can be neglected in the far region. Analytical results are obtained in the high-frequency limit and are shown to excellently agree with the numeric results obtained via the partial-wave method. It is shown numerically that black holes with tidal charge obey the universality of the low-frequency absorption cross section of stationary black holes for the massless scalar field.

Highlights

Since these black holes would rapidly evaporate via Hawking radiation [11], some effort has been put on determining their greybody factors [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], once their evaporation rate depend directly on these factors
In this work we present the study of the cross sections of a black hole with tidal charge [41] predicted as a solution considering the Randall–Sundrum scenario
We see that the tidal charge acts in the same sense of the black hole mass, increasing the size of the event horizon, while the electric charge on the Reissner–Nordström solution acts in the opposite sense, once rh tends to decrease with the increase of q

Summary

Introduction

One of the most important consequences of these so called brane-world models is that microscopic black holes could be produced by particle collisions of a few TeVs at the LHC [5].1 Since these black holes would rapidly evaporate via Hawking radiation [11], some effort has been put on determining their greybody factors [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], once their evaporation rate depend directly on these factors. One of the most important consequences of these so called brane-world models is that microscopic black holes could be produced by particle collisions of a few TeVs at the LHC [5].1 Since these black holes would rapidly evaporate via Hawking radiation [11], some effort has been put on determining their greybody factors [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26], once their evaporation rate depend directly on these factors. This system is described by the following metric on the 3-brane:

Classical and semi-classical scattering

Geodesic limit

Glory approximation

Wave scattering

Numeric results

Final remarks