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arXiv · 2608.19264

Renormalization group improved black holes in non-commutative momentum-dependent spacetime geometry

Gema Ilham Baskara Darman·Ar Rohim·Anto Sulaksono
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Abstract

We investigate black holes (BHs) in momentum-dependent spacetime geometry and assess its quantum Reissner-Nordstr\"om (RN) consistency with the weak gravity conjecture (WGC). Quantum corrections are introduced through the non-commutative momentum space algebra as the quantization process, and spacetime renormalization approach as a map between momentum and spacetime spaces. For the Schwarzschild case, thermodynamic analysis indicates the existence of a hot (non-zero temperature) BH remnant when evaporation stops (the entropy becomes zero), obeying a complementary third law for black hole thermodynamics. We extend this framework to the RN solution and examine its extremal limit. For large BHs with $M \gg M_P$ ($M_P$ for Planck mass), the quantum-improved RN geometry exhibits a non-zero Hawking temperature in the extremal case, consistent with the WGC, which stipulates that extremal states should not be exactly stable or cold. The resulting momentum-dependent metric and thermodynamic properties are shown to reproduce the results derived from the Poincar\'e algebra (classical model) in the infrared (IR) regime.

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Gema Ilham Baskara Darman, Ar Rohim, Anto Sulaksono. 2026-08-18. Renormalization group improved black holes in non-commutative momentum-dependent spacetime geometry. https://arxiv.org/abs/2608.19264

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