# Temperature of space-time?

Well, I was wondering if anyone knows of any way to relate the concept of temperture with space-time, at least intuitively. Is there an energy-density type argument one could use? Are there equations in GR that have a similar form as those of entropy and temerature relationships? I have sort of a simple-minded approach to this idea, that a gas can be approximated as a continuous, isotropic substance with properties of temperature, pressure, and density, and therefore energy-density. Can one get similar properties of space-time (pressure, density, temperature)?

## Answers and Replies

pervect
Staff Emeritus
I'm not aware of any standard approach that gives a "temperature" to space-time. Black holes - yes. Space-time, no.

In order to give a temperature to space-time, one would have to define (in advance) or wind up with (as a consequence of the definition) an entropy for space-time - i.e. how many possible states does some amount of space-time contain.

I'm not aware of any standard approach that gives a "temperature" to space-time. Black holes - yes. Space-time, no.

In order to give a temperature to space-time, one would have to define (in advance) or wind up with (as a consequence of the definition) an entropy for space-time - i.e. how many possible states does some amount of space-time contain.

exactly

I guess this isn't cannonical physics. If one could solve for a stable configuration of space-time that behaves like a particle, then I guess we could consider all the possible configurations of space-time for a given amount of space-time. I've been asking myself recently if space-time and a point particle are mutually exclusive. In other words, what if ther is no space-time at the center of a particle, and in fact a particle is like a "boundary" of space-time? Then there must be some sort of configuration of space-time (or state) that meets the boundary condition at that point (perhaps a "hole" in space-time, or an Einstein-Rosen bridge). Yeah, sorry for all this speculation, I don't like to speculate, but I can't stop these thoughts.

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One way to approach the problem is to take the temperature of the matter that is in a region of spacetime and require the spacetime to be in equilibrium with it. Can spacetime be considered as a kind of medium in which stuff exists, or does it not have to be in thermal equilibrium with matter? One interesting aspect to this is that the only way for spacetime to absorb and emit energy is through gravitational interactions.

wabbit
it's a great question...but we already know that spacetime has a temperature (xbar = 3K). Furthermore, the WMAP data demonstrate that there are even slight local variations in this mean temperature. So, since the empirical data are quite reproducible, the next question is, as Jonny_trig speculates (correctly, I would argue), to create a mathematical model that successfully incorporates the empirical data w/ the theory.