Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Towards an S-matrix Description of Gravitational Collapse

D. Amati, M. Ciafaloni, G. Veneziano

TL;DR

The paper tackles the problem of describing gravitational collapse within a quantum string-gravity framework by constructing an S-matrix that evolves from large-impact-parameter scattering ($b \gg G\sqrt{s}$) down toward the collapse regime, uncovering a critical impact parameter $b_c = O(G\sqrt{s})$ where perturbation theory breaks down.The authors develop an effective-action approach that resums the eikonal series in powers of $R^2/b^2$, derive a reduced 2D action for transverse and longitudinal fields, and connect the results to a shock-wave picture via Lipatov's framework, yielding a unitary S-matrix with calculable elastic and inelastic components.They find that for $b>b_c$ the S-matrix is essentially unitary with a TT-graviton spectrum and a controllable deflection angle; as $b\to b_c$, the spectrum is cut off at $\sim 1/R$ and elastic absorption grows exponentially; below $b_c$ the solutions become complex, adding further absorption and suggesting a tunneling-like transition rather than horizon formation.Overall, the work provides a self-consistent quantum description of high-energy gravitational collapse within an effective-action framework, linking perturbative eikonal corrections to non-perturbative collapse and opening avenues to connect with black-hole thermodynamics and information considerations.

Abstract

Extending our previous results on trans-Planckian ($Gs \gg \hbar$) scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters ($b \gg G\sqrt{s}>λ_s$) down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value $b = b_c = O(G\sqrt{s})$, signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) $b = b_c$, and present some ideas and results on its extension all the way to the $ b \to 0$ region. We find that for $b<b_c$ the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.

Towards an S-matrix Description of Gravitational Collapse

TL;DR

The paper tackles the problem of describing gravitational collapse within a quantum string-gravity framework by constructing an S-matrix that evolves from large-impact-parameter scattering ($b \gg G\sqrt{s}$) down toward the collapse regime, uncovering a critical impact parameter $b_c = O(G\sqrt{s})$ where perturbation theory breaks down.The authors develop an effective-action approach that resums the eikonal series in powers of $R^2/b^2$, derive a reduced 2D action for transverse and longitudinal fields, and connect the results to a shock-wave picture via Lipatov's framework, yielding a unitary S-matrix with calculable elastic and inelastic components.They find that for $b>b_c$ the S-matrix is essentially unitary with a TT-graviton spectrum and a controllable deflection angle; as $b\to b_c$, the spectrum is cut off at $\sim 1/R$ and elastic absorption grows exponentially; below $b_c$ the solutions become complex, adding further absorption and suggesting a tunneling-like transition rather than horizon formation.Overall, the work provides a self-consistent quantum description of high-energy gravitational collapse within an effective-action framework, linking perturbative eikonal corrections to non-perturbative collapse and opening avenues to connect with black-hole thermodynamics and information considerations.

Abstract

Extending our previous results on trans-Planckian () scattering of light particles in quantum string-gravity we present a calculation of the corresponding S-matrix from the region of large impact parameters () down to the regime where classical gravitational collapse is expected to occur. By solving the semiclassical equations of a previously introduced effective-action approximation, we find that the perturbative expansion around the leading eikonal result diverges at a critical value , signalling the onset of a new (black-hole related?) regime. We then discuss the main features of our explicitly unitary S-matrix -- and of the associated effective metric -- down to (and in the vicinity of) , and present some ideas and results on its extension all the way to the region. We find that for the physical field solutions are complex-valued and the S-matrix shows additional absorption, related to a new production mechanism. The field solutions themselves are, surprisingly, everywhere regular, suggesting a quantum-tunneling -- rather than a singular-geometry -- situation.

Paper Structure

This paper contains 18 sections, 125 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Eikonal Expansion and effective action
  3. H-diagram: Amplitude and emission field
  4. The reduced effective action
  5. Shock-wave interpretation
  6. Axisymmetric solutions
  7. Particle-particle scattering at $b=0$
  8. Central collision of two homogeneous beams
  9. Extension to $b>0$ and critical impact parameter
  10. Solutions for $b>0$ and perturbative expansion
  11. The on-shell action and its singularities
  12. The effective metric
  13. Momentum space formulation
  14. Effective action and equations of motion
  15. Arguments for the existence of a critical $b/R$ ratio
  16. ...and 3 more sections

Figures (5)

  • Figure 1: The leading eikonal rescattering series. Crosses denote on-shell propagation
  • Figure 2: Diagrammatic structure of $2n$-loop irreducible contributions to the eikonal
  • Figure 3: Regge-Gribov H-diagram, yielding the first subleading correction to the eikonal; dashed (wavy) lines denote exchanged (emitted) gravitons corresponding to the fields $a_0$ and $\bar{a}_0$ ($h_0$ or $\phi_0$)
  • Figure 4: Regge-Gribov double-H diagram, contributing at order $R^4/b^4$ to the eikonal; dashed (wavy) lines denote exchanged (emitted) gravitons
  • Figure 5: Typical Regge-Gribov rescattering diagram, contributing at higher orders to the eikonal; dashed (wavy) lines denote exchanged (emitted) gravitons which have mostly transverse (longitudinal) propagators.