LAUSR

A modified Hamilton–Jacobi equation with Lorentz-violating scalar field in the curved spacetime is used to research tunneling radiation from the horizons of Reissner–Nordstr $$\ddot{\mathrm{o}}$$ m de Sitter black hole. We investigate the influence of different etheric-like vector $$u^\alpha $$ on the solution of the modified Hamilton–Jacobi equation by using both the semi-classical approximation and beyond the semi-classical approximation. We find that the solution of the modified Hamilton–Jacobi equation strongly depends on the choices of $$u^\alpha $$ . As $$u^\alpha =\delta ^\alpha _t u^t$$ , the Lorentz-violating scalar field can enhances black holes’ Hawking temperature but reduces its entropy. However, the case will reverses as $$u^\alpha =\delta ^\alpha _r u^r$$ . Our conclusions are applicable to other spherically symmetric charged black holes.