Quantum entanglement and Hawking temperature

The European Physical Journal C

S. Shankaranarayanan¹  S. Santhosh Kumar¹ 

[1] School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), 695016, Thiruvananthapuram, Kerala, India;

关键词: Entropy;    Black Hole;    Scalar Field;    Entanglement Entropy;    Event Horizon;   

DOI  :  10.1140/epjc/s10052-016-4241-3

来源: Springer

【 摘 要 】

The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there has been an intense activity to understand the thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment and the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black holes—which are simple yet macroscopic systems—and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole’s horizon with regard to the system energy. This is yet other numerical evidence leading to understanding the key features of black-hole thermodynamics from the viewpoint of quantum information theory.

【 授权许可】

CC BY