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Abstract For a Lorentzian invariant theory, the entanglement entropy should be a function of the domain of dependence of the subregion under consideration. More precisely, it should be a function of the domain of dependence and the appropriate cut-off. In this paper, we refine the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant ic/6 with c the central charge. The gravitational dual of the `covariant' timelike entanglement entropy is finally presented following this method. Content from this work may be used under the terms of the Creative Commons Attribution 3. 0 licence. Any further distribution of this work must maintain attribution to the author (s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.
He et al. (Thu,) studied this question.