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Classical Black Hole Production in High-Energy Collisions

Douglas M. Eardley, Steven B. Giddings

TL;DR

The paper analyzes classical black hole formation in ultra-relativistic D-dimensional collisions by modeling each particle as a gravitational shock wave and reducing horizon formation to a boundary-value problem for Poisson's equation in the transverse space. It extends prior zero-impact-parameter results to nonzero impact parameter and provides an explicit $D=4$ trapped-surface construction via a conformal map, yielding a robust lower bound on the production cross-section and mass estimates for the resulting black hole. The results support the feasibility of black hole production at high energies and lay groundwork for a semiclassical treatment, while outlining the challenges and directions for higher-dimensional analysis and differential cross-section calculations. Overall, the work strengthens the theoretical foundations for predicting black hole production in TeV-scale gravity scenarios and informs experimental searches and cosmic-ray bounds.

Abstract

We investigate classical formation of a D-dimensional black hole in a high energy collision of two particles. The existence of an apparent horizon is related to the solution of an unusual boundary-value problem for Poisson's equation in flat space. For sufficiently small impact parameter, we construct solutions giving such apparent horizons in D=4. These supply improved estimates of the classical cross-section for black hole production, and of the mass of the resulting black holes. We also argue that a horizon can be found in a region of weak curvature, suggesting that these solutions are valid starting points for a semiclassical analysis of quantum black hole formation.

Classical Black Hole Production in High-Energy Collisions

TL;DR

The paper analyzes classical black hole formation in ultra-relativistic D-dimensional collisions by modeling each particle as a gravitational shock wave and reducing horizon formation to a boundary-value problem for Poisson's equation in the transverse space. It extends prior zero-impact-parameter results to nonzero impact parameter and provides an explicit trapped-surface construction via a conformal map, yielding a robust lower bound on the production cross-section and mass estimates for the resulting black hole. The results support the feasibility of black hole production at high energies and lay groundwork for a semiclassical treatment, while outlining the challenges and directions for higher-dimensional analysis and differential cross-section calculations. Overall, the work strengthens the theoretical foundations for predicting black hole production in TeV-scale gravity scenarios and informs experimental searches and cosmic-ray bounds.

Abstract

We investigate classical formation of a D-dimensional black hole in a high energy collision of two particles. The existence of an apparent horizon is related to the solution of an unusual boundary-value problem for Poisson's equation in flat space. For sufficiently small impact parameter, we construct solutions giving such apparent horizons in D=4. These supply improved estimates of the classical cross-section for black hole production, and of the mass of the resulting black holes. We also argue that a horizon can be found in a region of weak curvature, suggesting that these solutions are valid starting points for a semiclassical analysis of quantum black hole formation.

Paper Structure

This paper contains 5 sections, 40 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Trapped surfaces in shock-wave geometries
  3. Explicit construction for $D=4$
  4. Further results and directions
  5. Conclusions

Figures (1)

  • Figure 1: The intersection curve ${\cal C}$ of the marginally trapped surface ${\cal S}$ with the collision plane ($u=0=v$). Several curves ${\cal C}$, for various impact parameters $b$, are superposed; spacetime dimension is $D=4$. Distances are in units of $G\sqrt s = 2G\mu$; in these units $r_h=2$. Incoming particle pairs appear in the horizontal line $x^2=0$ at pair separation $b$; wider pairs therefore correspond to smaller curves ${\cal C}$. Values of $b$ are 0$+$, 0.6$\times$, 1.2$*$, 1.4$\square$, 1.55$\bullet$, and 1.609$\circ$, the last being maximal.