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Quantum-corrected gravitational collapse and multi-messenger signatures: Beyond spherical symmetry in loop quantum gravity

Hoang Van Quyet

Abstract

We present a comprehensive theoretical framework for multi-messenger signatures arising from quantum-corrected gravitational collapse within an extended Ashtekar-Olmedo-Singh (AOS) loop quantum gravity model incorporating perturbative asymmetries. By developing a consistent perturbation theory for non-spherical modes on the quantum-corrected spherically symmetric background, we resolve the fundamental tension between spherical symmetry assumptions and gravitational wave emission requirements. Our analysis demonstrates that quantum geometric effects naturally seed asymmetric perturbations during the bounce phase, leading to observable gravitational wave bursts with mass-dependent frequencies in the range $f_{\rm gw} \sim 10^{-3}$--$10^{3}$ Hz and distinctive electromagnetic counterparts via quantum field effects in curved spacetime. Through self-consistent calculations based on the effective AOS framework, we compute the coupling between quantum bounce dynamics and perturbative modes, yielding gravitational wave strains $h \sim 10^{-23}$--$10^{-21}$ at 100 Mpc for primordial black holes with masses $M \sim 1$--$100$ $M_{\odot}$. The electromagnetic emission mechanism is analyzed through detailed calculations of dynamic Casimir effects and coherent field amplification in time-dependent quantum geometry. Our parameter sensitivity analysis reveals detection prospects that are critically dependent on primordial black hole abundance constraints, with realistic event rates of $\mc{R} \sim 10^{-3}$--$10^{-1}$ yr$^{-1}$ within current observational limits. These results provide testable predictions for quantum gravity theories while extending previous work beyond spherical symmetry assumptions.

Quantum-corrected gravitational collapse and multi-messenger signatures: Beyond spherical symmetry in loop quantum gravity

Abstract

We present a comprehensive theoretical framework for multi-messenger signatures arising from quantum-corrected gravitational collapse within an extended Ashtekar-Olmedo-Singh (AOS) loop quantum gravity model incorporating perturbative asymmetries. By developing a consistent perturbation theory for non-spherical modes on the quantum-corrected spherically symmetric background, we resolve the fundamental tension between spherical symmetry assumptions and gravitational wave emission requirements. Our analysis demonstrates that quantum geometric effects naturally seed asymmetric perturbations during the bounce phase, leading to observable gravitational wave bursts with mass-dependent frequencies in the range -- Hz and distinctive electromagnetic counterparts via quantum field effects in curved spacetime. Through self-consistent calculations based on the effective AOS framework, we compute the coupling between quantum bounce dynamics and perturbative modes, yielding gravitational wave strains -- at 100 Mpc for primordial black holes with masses -- . The electromagnetic emission mechanism is analyzed through detailed calculations of dynamic Casimir effects and coherent field amplification in time-dependent quantum geometry. Our parameter sensitivity analysis reveals detection prospects that are critically dependent on primordial black hole abundance constraints, with realistic event rates of -- yr within current observational limits. These results provide testable predictions for quantum gravity theories while extending previous work beyond spherical symmetry assumptions.

Paper Structure

This paper contains 23 sections, 46 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Extended Theoretical Framework
  3. Beyond Spherical Symmetry: Perturbative Extension of AOS Model
  4. Quantum Geometric Seeding of Asymmetric Perturbations
  5. Mass-Dependent Bounce Dynamics and Frequency Scaling
  6. Gravitational Wave Generation from Asymmetric Perturbations
  7. Electromagnetic Counterparts: Quantum Field Theory Treatment
  8. Relativistic Blast Wave Analysis
  9. Numerical Results and Detection Prospects
  10. Computational Implementation
  11. Gravitational Wave Signatures and Mass Scaling
  12. Multi-messenger Coordination and Environmental Dependence
  13. Realistic Detection Rates and PBH Abundance Constraints
  14. Parameter Space Analysis and Optimization
  15. Discussion and Future Prospects
  16. ...and 8 more sections

Figures (3)

  • Figure 1: Gravitational wave signatures from quantum bounce events showing mass-dependent frequency evolution. (a) Time-domain strain amplitude $h(t)$ for PBH masses $M=1, 10, 50, 100\,M_{\odot}$. (b) Frequency spectrum showing characteristic peaks at $f_{\rm gw} \propto M^{-1/6}$. (c) Instantaneous frequency evolution demonstrating chirp-like behavior distinct from classical mergers. (d) Detector sensitivity comparison with LIGO/Virgo noise curves.
  • Figure 2: Multi-messenger observation timeline and environmental dependence. (a) Gravitational wave signal followed by electromagnetic counterparts across multiple wavebands. (b) Sky localization accuracy evolution with coordinated observations. (c) Detection probability as function of environmental density $n_{\rm ext}$. (d) Observational strategy optimization for different PBH masses.
  • Figure 3: Parameter sensitivity analysis and detection optimization. (a) Gravitational wave frequency scaling with PBH mass compared to detector sensitivity bands. (b) Electromagnetic power scaling demonstrating environmental dependence. (c) Multi-messenger detection confidence contours in the $M$-$D$ plane, with red line indicating current detection limits ($M > 30\,M_\odot$, $D < 100\,$Mpc). (d) Required detector sensitivity improvements for confident detection.