Thermodynamics of Black Holes with non-commutative corrections to the Einstein-Gauss-Bonnet theory in 4D
Black Holes. Black Hole Thermodynamics; Einstein–Gauss–Bonnet gravity; Noncommutativity.
This work investigates the thermodynamics of spherically symmetric four-dimensional
black holes modified simultaneously by Einstein–Gauss–Bonnet (EGB) gravity and the non-
commutative geometry of spacetime, two extensions motivated by the search for quantum
corrections to General Relativity. Starting from a review of the Schwarzschild solution and
its thermal instability, a dimensional regularization is used to introduce the Gauss–Bonnet
term, while a Lorentzian smeared mass distribution implements noncommutativity, yielding
a regularized metric. The combined action of these corrections significantly modifies the
temperature, entropy, and heat capacity, leading to the emergence of thermal stability at
small horizon scales. The results indicate the formation of a stable remnant associated with
a minimum radius dependent on α and θ, emphasizing the joint role of these corrections
in the final stage of black hole evaporation.