What question did this study set out to answer?

This research aims to show that singularities in black holes can be resolved using modified gravity at Planck scale.

June 20, 2026Open Access

Resolution of Black Hole Singularities via Planck-Scale Modified Gravity

Key Points

This research aims to show that singularities in black holes can be resolved using modified gravity at Planck scale.
Introduced a suppression function S(r) = r³/(r³ + lp³) to regularize Schwarzschild singularity
Included a mathematical proof using the Kretschmann scalar K(r) vs r/lp plot
Analytically verified conservation laws and performed weak energy condition analysis for regions beyond the Planck scale.
Kretschmann scalar K(0)=80M²/lp⁶ is finite at the center of the black hole, confirming singularity resolution
The modified theory reduces singularity effects while recovering General Relativity at larger distances
A small violation of the weak energy condition occurs near the Planck core, consistent with black hole literature.

Abstract

Version 12. 13 - Professor Review Draft Graph + Email Fixed Major Updates: 1. Added Figure 1: Numerical plot of Kretschmann scalar K (r) vs r/lp showing K (0) =80M²/lp⁶ finite at center, providing mathematical proof of singularity resolution for the proposed S (r) model. 2. Full derivation of Einstein tensor G_μν and stress-energy tensor T_μν included. Conservation law ∇_μT^μν = 0 verified analytically. 3. Weak Energy Condition WEC analysis added for r > 2lp region. Small violation near Planck core consistent with regular black hole literature Bardeen 1968, Hayward 2006. 4. Corrected author email to: mdakizulislam1@gmail. com Key Result: The suppression function S (r) = r³/ (r³ + lp³) successfully regularizes Schwarzschild singularity. Kretschmann scalar remains finite K (0) =80M²/lp⁶ as r→0, while recovering GR at r >> lp. Status: Preliminary mathematical draft v12. 13 for Professor review. Core equation S (r) unchanged since v1. 0 17 June 2026. DOI: 10. 5281/zenodo. 20749914

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