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General relativity as the equation of state of spin foam · Around

2012

General relativity as the equation of state of spin foam

Smolin, Lee

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Building on recent significant results of Frodden, Ghosh and Perez (FGP) and Bianchi, I present a quantum version of Jacobson's argument that the Einstein equations emerge as the equation of state of a quantum gravitational system.

I give three criteria a quantum theory of gravity must satisfy if it is to allow Jacobson's argument to be run.
I then show that the results of FGP and Bianchi provide evidence that loop quantum gravity satisfies two of these criteria and argue that the third should also be satisfied in loop quantum gravity.
I also show that the energy defined by FGP is the canonical energy associated with the boundary term of the Holst action.

Built on

J.D. Bjorken, Asymptotic sum rules at infinite momentum
1970
Earlier work this paper cites.
W.G. Unruh, Notes on black hole evaporation
1976
Earlier work this paper cites.
P. Candelas and D.W. Sciama, Irreversible thermodynamics of black holes,
1979
Earlier work this paper cites.
Ted Jacobson, Thermodynamics of space-time: the Einstein equation of state,
1995
Earlier work this paper cites.
S. Carlip and C. Teitelboim, The off-shell black hole,
1995
Earlier work this paper cites.

Similar

[42] S. Massar and R. Parentani, How the change in horizon area drives black hole evaporation,
2000
Cited alongside, same era.
Viqar Husain and Seth Major, Gravity and BF theory defined in bounded regions,
2000
Cited alongside, same era.
Ted Jacobson, Renaud Parentani, Horizon Entropy
2003
Cited alongside, same era.
T. Padmanabhan, Thermodynamical Aspects of Gravity: New insights
Original
2010
Cited alongside, same era.
Ernesto Frodden, Amit Ghosh and Alejandro Perez, A local first law for black hole thermodynamics
Original
Cited in the paper.
Eugenio Bianchi, Entropy of non-extremal black holes from loop gravity
Original
Cited in the paper.
Eugenio Bianchi and Wolfgang Wieland, Horizon energy as the boost boundary term in general relativity and loop gravity
Cited in the paper.
L. Smolin, Newtonian gravity in loop quantum gravity
Original
Cited in the paper.
A. Ghosh and A. Perez, Black hole entropy and isolated horizons thermodynamics
Original
Cited in the paper.
Alejandro Perez, personal communication
Cited in the paper.

Then

Conrady, Florian, and Freidel, Laurent, On the semiclassical limit of 4d spin foam models
Original
2010
Later among the works it cites.
Erik P. Verlinde, On the Origin of Gravity and the Laws of Newton
Original
2011
Later among the works it cites.
Raf Guedens, Ted Jacobson and Sudipta Sarkar, Horizon entropy and higher curvature equations of state
Original
2012
Closest in time.
For recent reviews of spin foam models please see Alejandro Perez, The Spin Foam Approach to Quantum Gravity
Original
2019
Closest in time.

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