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Asymptotic Limit of Null Hypersurfaces

Luca Ciambelli

TL;DR

The paper develops a Carrollian framework for null hypersurfaces in asymptotically flat spacetimes within the Bondi-Sachs gauge, showing that the Raychaudhuri constraint asymptotically reproduces the Bondi mass-loss formula as a conservation law for a Carrollian stress tensor. It introduces and analyzes the null Brown-York stress tensor on finite-distance null hypersurfaces, then demonstrates that its Carrollian boundary limit yields a Carrollian stress tensor at null infinity. A central result is the precise matching between the canonical phase space on finite-distance null hypersurfaces and the Ashtekar-Streubel phase space at null infinity, establishing a concrete link between bulk null dynamics and asymptotic flat-space holography. By working in a simplified framework with a time-independent boundary metric, the subleading equations reveal the Bondi mass-loss structure and the emergence of radiative data via the News tensor, while the holographic stress tensor encodes the Bondi mass and radiative content. Overall, the work lays a robust foundation for connecting finite-distance Carrollian physics with celestial holography and flat-space gravitation, suggesting future explorations into angular-momentum dynamics, phase-space quantization, and soft-theorem correspondences.

Abstract

We study null hypersurfaces approaching null infinity in asymptotically flat spacetimes within the Bondi-Sachs gauge. The null Raychaudhuri constraint is shown to asymptote to the Bondi mass-loss formula, interpreted as a stress tensor conservation law. This stress tensor, the null Brown-York tensor, yields a Carrollian stress tensor at null infinity from the bulk. Furthermore, we establish that the canonical phase space on finite-distance null hypersurfaces asymptotes to the Ashtekar-Streubel phase space. This connection between finite-distance null physics and null infinity unveils promising insights.

Asymptotic Limit of Null Hypersurfaces

TL;DR

The paper develops a Carrollian framework for null hypersurfaces in asymptotically flat spacetimes within the Bondi-Sachs gauge, showing that the Raychaudhuri constraint asymptotically reproduces the Bondi mass-loss formula as a conservation law for a Carrollian stress tensor. It introduces and analyzes the null Brown-York stress tensor on finite-distance null hypersurfaces, then demonstrates that its Carrollian boundary limit yields a Carrollian stress tensor at null infinity. A central result is the precise matching between the canonical phase space on finite-distance null hypersurfaces and the Ashtekar-Streubel phase space at null infinity, establishing a concrete link between bulk null dynamics and asymptotic flat-space holography. By working in a simplified framework with a time-independent boundary metric, the subleading equations reveal the Bondi mass-loss structure and the emergence of radiative data via the News tensor, while the holographic stress tensor encodes the Bondi mass and radiative content. Overall, the work lays a robust foundation for connecting finite-distance Carrollian physics with celestial holography and flat-space gravitation, suggesting future explorations into angular-momentum dynamics, phase-space quantization, and soft-theorem correspondences.

Abstract

We study null hypersurfaces approaching null infinity in asymptotically flat spacetimes within the Bondi-Sachs gauge. The null Raychaudhuri constraint is shown to asymptote to the Bondi mass-loss formula, interpreted as a stress tensor conservation law. This stress tensor, the null Brown-York tensor, yields a Carrollian stress tensor at null infinity from the bulk. Furthermore, we establish that the canonical phase space on finite-distance null hypersurfaces asymptotes to the Ashtekar-Streubel phase space. This connection between finite-distance null physics and null infinity unveils promising insights.

Paper Structure

This paper contains 15 sections, 121 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Bondi-Sachs Gauge
  3. Asymptotic Null Hypersurfaces
  4. Constructing Null Hypersurfaces
  5. Asymptotic Expansion
  6. Intrinsic Carrollian Data
  7. Einstein Equations
  8. Simplified Framework
  9. Intrinsic Carrollian Data
  10. Einstein Equations
  11. Holographic Stress Tensor
  12. Covariant Phase Space
  13. Final Words
  14. Acknowledgements
  15. Intrinsic Carrollian Analysis

Figures (1)

  • Figure 1: Foliations of asymptotically AdS (left) and asymptotically flat (right) spacetimes with family of hypersurfaces with the same causal nature as the asymptotic boundary of interest. For AdS, the boundary is timelike, while for flat, the boundary is null.