Axisymmetric black hole in a non–commutative gauge theory: Classical and quantum gravity effects

This work explores both classical and quantum aspects of an axisymmetric black hole within a non–commutative gauge theory. The rotating solution is derived using a modified Newman–Janis procedure. The analysis begins with the horizon structure, ergospheres, and angular velocity. The thermodynamic properties are examined through surface gravity, focusing on the Hawking temperature, entropy, and heat capacity. In addition, the remnant mass is calculated. The Hawking radiation is treated as a tunneling process for bosonic and fermionic particles, along with the corresponding particle creation density. Geodesic motion is explored, emphasizing null geodesics, radial accelerations, the photon sphere, and black hole shadows. Finally, the gravitational lensing in the strong deflection limit is investigated.