Study On Hawking Radiation And Shadows Of Black Holes In Extended Phase Space

General relativity successfully predicted and described black holes,and people have never stopped studying them.Among them,the discovery of Hawking radiation of black holes is an important discovery in the discipline of theoretical physics,which closely links general relativity,quantum mechanics and thermodynamics,and establishes black hole thermodynamics.And more recently in black hole thermodynamics,by treating the cosmological constant as a dynamical variable,one introduces the concept of thermodynamic pressure and interprets a negative cosmological constant as a thermodynamic pressure,thus the phase space is extended,the laws of black hole thermodynamics are refined,and a rich phase structure is exhibited.Although many interesting physical phenomena are obtained in this extended thermodynamic phase space,the behaviour of black hole Hawking tunneling radiation in the extended phase space is still unknown.On the other hand,treating the cosmological constant as dynamical to study the effect of its variation on the black hole shadow may provide a proof to treat the cosmological constant as a dynamical variable.In this paper,the cosmological constant is treated as a dynamical variable to study the Hawking radiation of black holes in extended phase space and the effect on the light trajectory and shadow of the black hole when the value of the cosmological constant changes.The main findings and conclusions of this paper are as follows:(1)The black hole thermodynamic phase space is extended by treating the cosmological constant as a dynamical variable and interpreting it as the thermodynamic pressure P.The Parikh-Wilczek quantum tunneling method is used to solve for the probability of a black hole particle crossing the event horizon in the extended phase space in order to explore the behaviour of Hawking radiation in a broader physical context.Three different black holes are used as models to study the behaviour of black hole Hawking radiation.The results show that even in extended phase space,where the thermodynamic pressure is taken into account in the calculation of the tunneling rate of particles crossing the apparent horizon,the resulting particle emission spectra are not purely thermal and deviate from the purely thermal spectrum,similar to the results obtained by Parikh et al.The Hawking radiation serves as evidence that black hole thermodynamics is valid,side-by-side justifying the interpretation of the negative cosmological constant as a thermodynamic pressure concept.This further completes the theoretical framework of black hole thermodynamics,while enriching the phase structure of black holes.This provides a theoretical basis for a deeper understanding of the connection between black holes,quantum field theory and gravitational theory in one aspect.(2)The effects of changes in cosmological constants and charge values on light trajectories and black hole shadows near the Reissner-Nordstrom Ad S black hole are investigated by means of theoretical analysis and numerical simulations.The effective potential energy function is derived from the geodesic equation and the light trajectories and black hole shadow images are plotted under static accretion.We find that as the cosmological constant increases,the values of the black hole event horizon radius and the critical collision parameter increase and the black hole expands outwards,but the position of the photon ring remains unchanged,while as the charge increases,the values of the black hole event horizon radius,the shadow radius and the critical collision parameter decrease and the photon ring of the black hole contracts inwards.Furthermore,as the cosmological constant increases,the radius of the black disk is larger and the deflection of light near the black hole is greater,while the increase in charge leads to an increase in the curvature of spacetime near the black hole,which in turn leads to more curved light and a greater intensity of shadow observations.