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Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions

Andrea Addazi, Massimo Bianchi, Gabriele Veneziano

TL;DR

This paper addresses whether ultra-Planckian string collisions reveal black-hole formation and evaporation within a consistent quantum framework. It contrasts ACV/AGK’s unitarization via virtual corrections and gravi-reggeon cuts with DGILS’ tree-level, high-multiplicity amplitudes, identifying a tension that arises from neglecting virtual soft gravitons in the latter. By introducing IR-safe gravitational jet cross sections and incorporating soft real and virtual gravitons, the authors show that BH-like final-state properties—soft, abundant quanta with a thermal-like energy distribution around the Hawking temperature—can appear in inclusive observables without full thermalization at the current level. The findings point toward a unitary S-matrix description of trans-Planckian gravity and outline concrete steps to sharpen the connection between high-energy scattering and black-hole evaporation.

Abstract

We revisit possible glimpses of black-hole formation by looking at ultra-planckian string-string collisions at very high final-state multiplicity. We compare, in particular, previous results using the optical theorem, the resummation of ladder diagrams at arbitrary loop order, and the AGK cutting rules, with the more recent study of $2 \rightarrow N$ scattering at $N \sim s M_P^{-2} \gg 1$. We argue that some apparent tension between the two approaches disappears once a reinterpretation of the latter's results in terms of suitably defined infrared-safe cross sections is adopted. Under that assumption, the typical final state produced in an ultra-planckian collision does indeed appear to share some properties with those expected from the evaporation of a black hole of mass $\sqrt{s}$, although no sign of thermalization is seen to emerge at this level of approximation.

Glimpses of black hole formation/evaporation in highly inelastic, ultra-planckian string collisions

TL;DR

This paper addresses whether ultra-Planckian string collisions reveal black-hole formation and evaporation within a consistent quantum framework. It contrasts ACV/AGK’s unitarization via virtual corrections and gravi-reggeon cuts with DGILS’ tree-level, high-multiplicity amplitudes, identifying a tension that arises from neglecting virtual soft gravitons in the latter. By introducing IR-safe gravitational jet cross sections and incorporating soft real and virtual gravitons, the authors show that BH-like final-state properties—soft, abundant quanta with a thermal-like energy distribution around the Hawking temperature—can appear in inclusive observables without full thermalization at the current level. The findings point toward a unitary S-matrix description of trans-Planckian gravity and outline concrete steps to sharpen the connection between high-energy scattering and black-hole evaporation.

Abstract

We revisit possible glimpses of black-hole formation by looking at ultra-planckian string-string collisions at very high final-state multiplicity. We compare, in particular, previous results using the optical theorem, the resummation of ladder diagrams at arbitrary loop order, and the AGK cutting rules, with the more recent study of scattering at . We argue that some apparent tension between the two approaches disappears once a reinterpretation of the latter's results in terms of suitably defined infrared-safe cross sections is adopted. Under that assumption, the typical final state produced in an ultra-planckian collision does indeed appear to share some properties with those expected from the evaporation of a black hole of mass , although no sign of thermalization is seen to emerge at this level of approximation.

Paper Structure

This paper contains 14 sections, 112 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The ACV approach: a reminder
  3. Different regimes in $b,R_S, \ell_s$ parameter space
  4. The string-gravity regime via the AGK cutting rules
  5. The classicalization approach to high-energy, high-multiplicity gravitational scattering
  6. A tension between the two approaches
  7. Virtual soft gravitons
  8. Real soft gravitons
  9. A reinterpretation of the DGILS result and resolution of its tension with ACV/AGK
  10. Summary and outlook
  11. A brief review of the AGK rules
  12. Building the $B_{0}$ factor
  13. Derivation of $B_0$ for massive and massless particles
  14. Special kinematics for massless particles

Figures (4)

  • Figure 1: Rough phase diagram for transplanckian string-string collisions. In Region I and III calculations are essentially under control. They both border with region II where BH formation is expected on the ground of classical collapse criteria Eardley:2002reKohlprath:2002yhYoshino:2004mmGiddings:2004xy.
  • Figure 2: $2\rightarrow N$ graviton amplitudes with virtual soft gravitons corrections and emission of real soft gravitons from the external legs.
  • Figure 5: Representation of the $2\rightarrow N-{\rm jet}$ process. The $N$ hard ($E \ge \bar{E}$) gravitons are represented by solid outgoing lines, the IR gravitons ($E < \bar{E}$) by red dotted lines and the virtual gravitons by wiggly lines.
  • Figure 6: The $2\rightarrow 2$ amplitude with n-gravi-reggeons exchanged is parted in two $\mathcal{A}^{a,b}_{n}$ subamplitudes, diagrammatically schematizing the Integral (\ref{['expr']}).