Black Hole Thermodynamics with Non-Commutative Corrections in the 4D Einstein-Gauss-Bonnet Theory
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 noncommutative 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.