Non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter: Plasma lensing and thermodynamics analysis

The focus of this paper is to examine the properties of thermodynamics and weak gravitational lensing about the geometry of black holes within the context of a non-commutative Schwarzschild black hole surrounded by Perfect fluid dark matter. We examine the geometric mass and thermal temperature in this context to discuss the stability of the black hole solution. We examine the phase transition and stability while calculating the specific heat. We also research the black hole's energy emission process. We deduce that our researched black hole solution is thermally stable based on its thermodynamic features. Furthermore, we analyze uniform and non-uniform plasma by calculating the deflection angle, and we examine gravitational lensing in the weak plasma field. It is observed that in uniform plasma, the deflection angle is larger than in non-uniform plasma. We also looked at the image magnification caused by source brightness and found that the source image is enlarged more in uniform plasma than in non-uniform plasma.