Non-commutativity in Hayward spacetime

Abstract

In this work, we propose a new black hole solution, namely, a Hayward-like metric incorporating corrections due to non-commutativity by taking into account ∂r ∧ ∂θ Moyal twist. We begin by deriving this solution using the non-commutative gauge theory framework. The general properties of the metric are then analyzed, including the event horizon structure and the Kretschmann scalar. Analogous to the standard Hayward solution, the modified black hole remains regular, provided that additional dependence on the angle θ. Next, we examine the thermodynamic properties, computing the Hawking temperature, entropy, and heat capacity. From the temperature profile, we verify that there is no physical remnant mass when T(Θ,l) → 0, indicating a complete evaporation process. Quantum radiation is analyzed by considering both bosonic and fermionic particle modes, with an estimation of the particle creation density provided for each case. The effective potential is evaluated perturbatively to accomplish the analysis of quasinormal modes and the time-domain response for scalar perturbations. The study of null geodesics is explored to enable the characterization of the photon sphere and black hole shadows. Furthermore, the Gaussian curvature is determined to assess the stability of critical orbits, followed by an analysis of gravitational lensing using the Gauss-Bonnet theorem. Finally, the constraints (bounds) on the parameters Θ (non-commutativity) and l (“Hayward parameter”) are derived based on solar system tests, including the perihelion precession of Mercury, light deflection, and the Shapiro time delay effect.