What question did this study set out to answer?

This research aims to develop a singularity-free black hole solution using Planck-scale suppression, focusing on the S(r) framework.

June 27, 2026Open Access

Regular Black Holes from Planck-Scale Suppression: Complete Analysis of the S(r) Framework

Key Points

This research aims to develop a singularity-free black hole solution using Planck-scale suppression, focusing on the S(r) framework.
Introduced a novel metric function suppressing singularities at r=0, confirming finite curvature invariants.
Conducted thermodynamic analysis to determine phase transitions in black hole behavior.
Computed quasinormal modes using the WKB method and predicted black hole shadow radius deviations.
Kretschmann scalar K(0) = 24M²/r₀⁶ is finite, confirming singularity resolution.
Thermodynamic analysis reveals phase transition at r_H ≈ 1.5r₀ with positive heat capacity for small black holes.
Predictions for black hole shadow radius deviate by 5-10% for Sgr A* and M87*, testable with EHT observations.

Abstract

We present a novel singularity-free black hole solution based on Planck-scale suppression of the metric function. The suppression factor S (r) = 1 - exp (-r³/r₀³) ensures finite curvature invariants at r = 0 while recovering Schwarzschild geometry at large distances. Key results: 1. Kretschmann scalar K (0) = 24M²/r₀⁶ is finite, proving singularity resolution. 2. Thermodynamic analysis reveals a phase transition at rH ≈ 1. 5r₀ with positive heat capacity for small black holes. 3. Quasinormal modes computed via WKB method show deviations from Schwarzschild, testable by future gravitational wave detectors. 4. Black hole shadow radius predictions deviate by 5-10% for Sgr A* and M87*, within reach of EHT observations. This 11-page manuscript includes 2 figures, 1 comparison table, and 15 references. The S (r) framework provides a minimal, parameter-free mechanism for regularizing black hole singularities without exotic matter, offering falsifiable predictions for astrophysical observations. Final version v1. 0 prepared for submission to Physical Review D. No scientific changes from development versions, only formatting finalization. Keywords: regular black holes, singularity resolution, Planck scale, S (r) framework, black hole thermodynamics, quasinormal modes

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