Correction of Bekenstein–Hawking entropy of Kiselev black holes surrounded by quintessence owing to Lorentz breaking

We consider a rotational symmetry solution for a Kiselev black hole that is wrapped in dark energy and defined by the equation of state. In the spacetime of the Kiselev black hole, considering Lorentz-breaking, the action of the scalar field is corrected, and the variational principle is applied to obtain the corrected scalar field equation in this black hole spacetime. The WKB approximation theory and black hole quantum tunneling radiation theory are applied to study the quantum tunneling rate, Hawking temperature, and entropy of the black hole, resulting in new expressions for the Hawking temperature and Bekenstein–Hawking entropy of the black hole. Finally, an in-depth discussion is presented on the employed research methods and obtained results.