On Deformed Phase Space Black Holes

Abstract

We revisit the Schwarzschild black hole in the context of noncommutative phase space. By mapping the horizon area operator into a two-dimensional harmonic oscillator structure, we derive the modifications induced by phase space noncommutativity. The formalism is developed using the generalized Bopp shift on the canonical coordinates and momenta. We computed the modified area spectrum, black hole mass levels, transition frequencies, Hawking temperature, and entropy, highlighting the physical implications of the deformation parameters $\hat{I}¸$ and $\hat{I}\cdot$ on the thermodynamical properties of the deformed black hole. Finally, we conjecture a connection between the noncommutative contribution to the entropy and Barrow's entropy.

16 pages, no figures