Einstein's equations from entanglement entropy

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http://urn.fi/URN:NBN:fi-fe201804208590
Title: Einstein's equations from entanglement entropy
Author: Kastikainen, Jani
Contributor: University of Helsinki, Faculty of Science, Department of Physics
Publisher: Helsingin yliopisto
Date: 2018
Language: eng
URI: http://urn.fi/URN:NBN:fi-fe201804208590
http://hdl.handle.net/10138/273527
Thesis level: master's thesis
Discipline: Theoretical Physics
Teoreettinen fysiikka
Teoretisk fysik
Abstract: Since the inception of the AdS/CFT correspondence in 1997 there has been great interest in the holographic description of quantum gravity in terms of conformal field theory. Studying how classical gravity emerges in this framework helps us to understand the quantum foundations of general relativity. A fundamental concept is entanglement entropy which has a classical interpretation in terms of areas of minimal surfaces in general relativity, due to Ryu and Takayanagi. This thesis is a review on how Einstein's equations can be derived up to second order from the Ryu-Takayanagi formula in the context of AdS/CFT correspondence. It also serves as an introduction to entanglement entropy in quantum field theories and holography, while providing necessary mathematical ingredients to understand the derivation. We also review a related derivation, based on the entanglement equilibrium hypothesis, and discuss its extensions to higher order theories of gravity.


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