Emergence of Spacetime: From Entanglement toEinstein
Year: 2020
Type: preprint
Abstract: Here I develop the connection between thermodynamics,entanglement, and gravity. I begin by showing that the classical
null energy condition (NEC) can arise as a consequence of the
second law of thermodynamics applied to local holographic screens.
This is accomplished by essentially reversing the steps of
Hawking's area theorem, leading to the Ricci convergence condition
as an input, from which an application of Einstein's equations
yields the NEC. Using the same argument, I show logarithmic quantum
corrections to the Bekenstein-Hawking entropy formula do not alter
the form of the Ricci convergence condition, but obscure its
connection to the NEC. Then, by attributing thermodynamics to the
stretched horizon of future lightcones – a timelike hypersurface
generated by a collection of radially accelerating observers with
constant and uniform proper acceleration – I derive Einstein's
equations from the Clausius relation. Based on this derivation I
uncover a local first law of gravity, connecting gravitational
entropy to matter energy and work. I then provide an entanglement
interpretation of stretched lightcone thermodynamics by extending
the entanglement equilibrium proposal. Specifically I show that the
condition of fixed volume can be understood as subtracting the
irreversible contribution to the thermodynamic entropy. Using the
AdS/CFT correspondence, I then provide a microscopic explanation of
the 'thermodynamic volume' – the conjugate variable to the
pressure in extended black hole thermodynamics – and reveal the
super-entropicity of three-dimensional AdS black holes is due to
the gravitational entropy overcounting the number of available dual
CFT states. Finally, I conclude by providing a recent generlization
of the extended first law of entanglement, and study its
non-trivial 2+1- and 1+1-dimensional limits. This thesis is
self-contained and pedagogical by including useful background
content relevant to emergent gravity.
Source: arXiv (Cornell University)
Author: Andrew Svesko
Institution: Arizona State University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3036293705