2026/07/12 by Mohsen Khodadi, Nosratolla Jafari, Shahin Mamedov
#gr-qc #hep-th
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 \(ηE3/EP\). Enforcing physical constraints (\(S'(rh) > 0\), \(T > 0\)) 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.