Quantum production of black holes

Stephen D.H Hsu

doi:10.1016/s0370-2693(03)00012-1

Abstract

We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. Classical solutions describing black hole production resulting from two particle scattering at non-zero impact parameter, combined with our formalism, indicate a geometric cross section for the quantum process. In TeV gravity scenarios these solutions may exhibit large curvatures, but (modulo a mild assumption about quantum gravity) corrections to the semi-classical cross section are small.

Highlights

Proposed models with extra dimensions solve the hierarchy problem by bringing the fundamental scale of gravity down to the electroweak scale [1]
In [2]-[7] it was asserted that the cross section is geometrical, determined by the impact parameter at which the particle pair at closest approach is within the Schwarschild radius associated with the center of mass energy √s
Eardley and Giddings [9] have analyzed classical solutions in general relativity which describe two particle high energy collisions at non-zero impact parameter. They demonstrate the existence of a closed trapped surface for any collision with sufficiently small impact parameter

Summary

Introduction

Proposed models with extra dimensions solve the hierarchy problem by bringing the fundamental scale of gravity ( referred to as the Planck scale) down to the electroweak scale [1]. In [2]-[7] it was asserted that the cross section is geometrical, determined by the impact parameter at which the particle pair at closest approach is within the Schwarschild radius associated with the center of mass energy √s If this is the case, black holes would be copiously produced at LHC and in cosmic ray collisions. Eardley and Giddings [9] have analyzed classical solutions in general relativity which describe two particle high energy collisions at non-zero impact parameter (see [10]-[14]) They demonstrate the existence of a closed trapped surface for any collision with sufficiently small impact parameter (at fixed center of mass energy). We explain the importance of large curvatures to the quantum corrections from an effective field theory point of view

Path Integral Formalism

Quantum corrections