# Thermodynamics of Spacetime: The Einstein Equation of State?

1. Jul 23, 2009

### mtak0114

Hi,

I have recently been delving into Quantum gravity related material... and I came accross a paper by Ted Jacobson "Thermodynamics of Spacetime: The Einstein Equation of State" http://arxiv.org/abs/gr-qc/9504004 and as far as I understand the argument it is very impressive who would have thought that three seemingly unrelated theories could be so closely tied (GR, thermo and QFT). But I have two questions:

1) Why starting from the 2nd law which assumes an arrow of time can we extract a theory which is time reversal invariant GR? (this is probably closely related to the work of Hawking which I am unfamiliar with)

2) His interpretation of heat puzzles me:

specifically he identifies $$Q$$ (the heat) with $$T^{\alpha\beta}$$ (the energy momentum tensor.)

cheers

M

2. Jul 23, 2009

### Naty1

This seems dependent on the holographic principle/conjecture...and all these things tie together when entropy is considered as information...

entropy is a measure of hidden information (not macroscopically observable) with heat and entropy closely related.

wiki has some insights at: http://en.wikipedia.org/wiki/Laws_of_black_hole_mechanics

I hesitate to make any other comments as I would be as likely to mislead as enlighten.

Leonard Susskind has good discussion on this general subject, THE BLACK HOLE WAR, in various places under thermo/heat/entropy as does Charles Seife, DECODING THE UNIVERSE, including pages 70 to 85...