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We have investigated quantum entropy of a static black hole arising from themassless scalar field with Lorentz violation induced by the coupling toEinstein tensor. Our results show that the coupled massless scalar fieldcontributes to the classical Bekenstein-Hawking term in the black hole entropy.The corrected classical Bekenstein-Hawking entropy is not one quarter of theevent horizon area of the original background black hole, but of acorresponding effective metric related to the coupling. It means that theclassical Bekenstein-Hawking entropy depends not only on the black holeparameter, but also on the coupling which reduces Lorentz violation.

Black hole entropy arising from massless scalar field with Lorentz violation induced by the coupling to Einstein tensor