On new regular quadratic Gaussian black hole: Photon sphere, shadow and gravitational lensing

Gaussian black holes constitute an important class of regular black holes, characterized by their spherically symmetric and static nature. These solutions emerge from the framework of Einstein’s equations, particularly when incorporating the effects of the cosmological constant, which plays a crucial role in the overall dynamics of the universe. By examining the null geodesics, we have sought to elucidate the form of the shadow generated by an innovative regular pure quadratic Gaussian black hole. This study contributes to the broader discourse on black hole physics and the implications of their unique structures on observable phenomena. A comprehensive study has been undertaken to explore the relationship between black hole shadows and the configuration of the event horizon, focusing on the impact of Gaussian distribution and black hole mass. The findings of this research contribute to a more nuanced comprehension of how these variables influence the properties of the horizon, the photon sphere, and the effective potential associated with black holes. In addition, our study delves into the effects of gravitational lensing produced by a quadratic Gaussian black hole. The findings demonstrate how variations in the black hole’s parameters can alter several observable characteristics associated with the gravitational lensing effect.