The solution of a modified Hamilton–Jacobi equation with Lorentz-violating scalar field

• Published in: General relativity and gravitation Vol. 52; no. 11
• Main Authors: Zhang, Jie, Liu, Menquan, Liu, Zhie, Sha, Bei, Tan, Xia, Liu, Yuzhen
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Nature B.V
• Subjects: Approximation; Astronomy; Astrophysics and Cosmology; Black holes; Classical and Quantum Gravitation; Differential Geometry; Entropy; Gravity; Mathematical analysis; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Radiation; Relativity Theory; Research Article; Scalars; Theoretical; Hawking radiation; Hamilton–Jacobi equation; Modified scalar field equation
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-020-02762-3

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 o ¨ m de Sitter black hole. We investigate the influence of different etheric-like vector u α 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 α . As u α = δ t α u t , the Lorentz-violating scalar field can enhances black holes’ Hawking temperature but reduces its entropy. However, the case will reverses as u α = δ r α u r . Our conclusions are applicable to other spherically symmetric charged black holes.