Null Wave Front and Ryu–Takayanagi Surface

Entropy

Yasusada Nambu¹  Jun Tsujimura¹ 

[1] Department of Physics, Graduate School of Science, Nagoya University, Chikusa, Nagoya 464-8602, Japan;

关键词: Ryu–Takayanagi surface;    null geodesics;    wave front;    extremal surface;    wave optics;   

DOI  :  10.3390/e22111297

来源: DOAJ

【 摘 要 】

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

【 授权许可】

Unknown