Date&Time  Mon Jul 27 2020 (14:00  15:00) 

Speaker  Shuichi Yokoyama 
Affiliation  YITP Kyoto 
Title  Flow equation, black hole, and singularity 
Abstract  I will speak about recent progress on the study of holography by means of flow equation and general relativity. After I briefly review the flow equation approach and explain some of its consequences, I will move on to the application of this approach to realize a holographic geometry which is expected to describe a black hole. The resulting geometry has some striking properties as follows. i) It is an asymptotic Antide Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. As a derivative of this research, we discovered a precise formula for a conserved quantity associated with a Killing vector available on a general curved spacetime. Important consequences of this new formula are that i) well known black holes in general relativity have nonzero matter energy momentum tensor at singularity, which means that any block hole is not a vacuum solution, ii) a mass for a compact star with internal structure cannot be written only by a surface integral. 
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