Abstract
In this paper, the Lorentz-violating scalar field equation is generalized in curved spacetime, and we find that the aether-like terms modify the scalar field equation, so that the effect can correct the properties near the event horizon of black hole spacetime. We then obtain the modified Hamilton-Jacobi equation by semi-classical approximation, and investigate the Hawking radiation and black hole thermodynamics in Schwarzschild black hole spacetime. The results show that the effects of aether-like terms increase the temperature of black hole, but reduce the entropy of black hole as <inline-formula><tex-math id="M200">\begin{document}${{ u}^\alpha } = {\text{δ}}_t^\alpha {u^t}, {\text{δ}}_r^\alpha {u^r}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182050_M200.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20182050_M200.png"/></alternatives></inline-formula>. This work can help to understand the properties of Lorentz-violating in curved spacetime.
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