A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics

Abstract

Determining whether Planck-scale effects can stabilize black holes addresses fundamental questions about black hole evaporation and quantum gravity consistency. Here, we analyze the thermodynamic topology of Schwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction \(ηE^3/E_P\). Enforcing physical constraints (\(S'(r_h) > 0\), \(T > 0\)) via the entropy-geometry correspondence, we find a single unstable branch with \(w = -1\) and \(W = -1\) for both signs of the correction parameter. A second root suggesting stability (\(w = +1\)) is excluded due to negative mass/temperature and lies outside the perturbative regime. Thus, this class of MDRs does not yield stable Schwarzschild black holes. However, MDRs with different leading-order corrections may behave otherwise, leaving the search for Planck-scale stabilization an open endeavor.

14 pages (two columns), 2 figures, 2 tables. v2: Refs added, to appear in EPJC

References in corpus (28)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• The Area of a Rough Black Hole
• Quantum Tunneling and Back Reaction
• Black Hole Solutions as Topological Thermodynamic Defects
• Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole
• Modified cosmology from extended entropy with varying exponent
• Early and late universe holographic cosmology from a new generalized entropy
• GRBs Neutrinos as a Tool to Explore Quantum Gravity induced Lorentz Violation
• Minimal Length in Quantum Gravity, Equivalence Principle and Holographic Entropy Bound
• Exponential corrections to black hole entropy
• Universal topological classifications of black hole thermodynamics
• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• New entropies, black holes, and holographic dark energy
• Alleviating both $H_0$ and ${\sigma }_8$ tensions in Tsallis cosmology
• The lower bound violation of shear viscosity to entropy ratio due to logarithmic correction in STU model
• Entropic corrections to Friedmann equations and bouncing universe due to the zero-point length
• Black hole geometrothermodynamics and critical phenomena: a look from Tsallis entropy-based perspective
• Modified Cosmology Models from Thermodynamical Approach
• Thermodynamically consistent entropic late-time cosmological acceleration
• Beyond Special Relativity at second order
• Modified cosmology from quantum deformed entropy
• Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity
• Dispersion relations in finite-boost DSR
• Amelino-Camelia DSR effects on charged Dirac oscillators: Modulated spinning magnetic vortices
• Fundamental length scale and the bending of light in a gravitational field
• Two-body Dirac equation in DSR: results for fermion-antifermion pairs
• Topological and optical signatures of modified black-hole entropies
• Thermal properties of Klein-Gordon Oscillator in the Context of Amelino-Camelia and Magueijo-Smolin Doubly Special Relativity (DSR) frameworks