Joule-Thomson expansion and Optical behaviour of Reissner-Nordstr\"om-Anti-de Sitter black holes in Rastall gravity surrounded by a Quintessence field

This paper deals with the thermodynamics, Joule-Thomson expansion and optical behaviour of a Reissner-Nordstr\"om-anti-de Sitter black hole in Rastall gravity surrounded by a quintessence field. The black hole solution obtained in this framework is different from a corresponding black hole in General Relativity. The black hole metric function, as well as the Hawking temperature, is affected by the presence of energy-momentum conservation violation. The presence of energy-momentum conservation violation also affects the isenthalpic and inversion temperature curves, and with an increase in the Rastall parameter, the inversion temperature rises slowly. The impacts of other parameters, such as charge, structural constant etc., are investigated and compared. The black hole shadow, as well as the energy emission rate of the black hole, decreases with an increase in the Rastall parameter. Hence, the black holes evaporate slowly in presence of energy-momentum conservation violation.