DOI: 10.1140/epjc/s10052-026-16186-x ISSN: 1434-6052
A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics
Mohsen Khodadi, Nosratolla Jafari, Shahin Mamedov 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 ofSchwarzschild black holes under Planck-scale modified kinematics, using a cubic entropy correction derived from a well-known phenomenological MDR with leading correction
$$\eta E^3/E_P$$
η
E
3
/
E
P
. Enforcing physical constraints (
$$S'(r_h) > 0$$
S
′
(
r
h
)
>
0
,
$$T > 0$$
T
>
0
) via the entropy-geometry correspondence, we find a single unstable branch with
$$w = -1$$
w
=
-
1
and
$$W = -1$$
W
=
-
1
for both signs of the correction parameter. A second root suggesting stability (
$$w = +1$$
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.