[Paper Review] Quantum corrected black holes: testing the correspondence between grey-body factors and quasinormal modes

M. V. Skvortsova|arXiv (Cornell University)|Nov 8, 2024

Relativity and Gravitational Theory4 citations

TL;DR

This study tests the correspondence between grey-body factors and quasinormal modes in three recently derived quantum-corrected black hole models using high-precision 6th-order WKB calculations. The correspondence yields grey-body factors with errors below 3% for near-extremal black holes and under 1% for moderate quantum coupling, confirming its robustness despite near-horizon quantum corrections.

ABSTRACT

Grey-body factors and quasinormal modes are two distinct characteristics of radiation near black holes, each associated with different boundary conditions. Nevertheless, a correspondence exists between them, which we use to calculate the grey-body factors of three recently constructed quantum-corrected black hole models. Our findings demonstrate that the grey-body factors are significantly influenced by the quantum corrections for some of the models under consideration, and the correspondence holds with reasonable accuracy across all three models. We confirm that the grey-body factors are less sensitive to the near-horizon corrections of the spacetime, because the grey-body factors are reproduced via the correspondence using only the fundamental mode and the first overtone.

Motivation & Objective

• To test the validity of the correspondence between grey-body factors and quasinormal modes in quantum-corrected black hole spacetimes.
• To assess the sensitivity of grey-body factors to near-horizon quantum corrections in models where quasinormal modes are already known.
• To provide accurate, high-order numerical estimates of grey-body factors for gravitational perturbations in these models, filling a gap in the literature.
• To evaluate whether the correspondence remains accurate beyond the eikonal limit and for finite multipole numbers ℓ.
• To compare results from the quasinormal mode correspondence with precise 6th-order WKB calculations as a benchmark.

Proposed method

• Utilizes the 6th-order WKB method to compute highly accurate grey-body factors for gravitational perturbations (ℓ ≥ 2) in three quantum-corrected black hole models.
• Applies the analytical correspondence formula from [18] that relates grey-body factors to the fundamental quasinormal mode ω₀ and the first overtone ω₁, valid up to ℓ⁻² order.
• Employs quasinormal mode data from [61] as input for the correspondence, ensuring consistency with prior high-accuracy calculations.
• Compares the grey-body factors derived from the correspondence with those computed via the 6th-order WKB method to quantify accuracy.
• Analyzes the behavior of effective potentials and transmission coefficients as functions of the quantum correction parameter ξ.
• Evaluates the relative error of the correspondence across different black hole models and values of ℓ and ξ.

Experimental results

Research questions

• RQ1 Does the correspondence between grey-body factors and quasinormal modes remain accurate for quantum-corrected black holes with non-trivial near-horizon geometry?
• RQ2 How sensitive are grey-body factors to quantum corrections in the spacetime metric, particularly when the effective potential is altered near the horizon?
• RQ3 To what extent do the fundamental mode and first overtone of quasinormal modes determine the grey-body factors in these models?
• RQ4 How does the accuracy of the correspondence vary with multipole number ℓ and the quantum coupling parameter ξ?
• RQ5 Can the correspondence serve as a reliable alternative to high-order WKB methods for computing grey-body factors in quantum-corrected black holes?

Key findings

• The correspondence between grey-body factors and quasinormal modes yields results with relative errors below 3% for near-extremal black holes and within 1% for moderate quantum coupling across all three models.
• Grey-body factors are significantly influenced by quantum corrections in some models, particularly where the effective potential is strongly modified, but remain less sensitive than quasinormal mode overtones to near-horizon deformations.
• For the third black hole model, despite a dramatic change in the near-horizon effective potential and an outburst in overtone frequencies with increasing n, the grey-body factors remain only moderately altered due to dependence on ω₀ and ω₁.
• The 6th-order WKB method provides a reliable benchmark, confirming that the correspondence is accurate to within a fraction of a percent for larger ℓ values.
• The correspondence holds with high precision even when the WKB approximation is not fully convergent, suggesting robustness beyond the eikonal limit.
• The study confirms that grey-body factors are more stable than quasinormal modes under small geometric deformations, especially near the horizon, validating their use as reliable probes of black hole radiation.