I`ve just stumbled about a sentence which says that high curvature of spacetime

Question

I`ve just stumbled about a sentence which says that high curvature of spacetime implies that any matter present is at high temperature.

This somehow confuses me, so my probably dumb question(s) are:

1) How is this general (?) relationship between the temperature of matter and curvature of spacetime derived or explained? Just looking at Einsteins field equations, I dont see why there cant be some cold mass just "sitting there" leading to large curvature ...

2) Is this relationship generally valid or is its domain of applicability restricted somehow? For example has the curvature of spactime to be so large that quantum effects kick in and it has something to do with the uncertainty principle?

Explanation / Answer

There's no way to generally identify (some function of) curvature with temperature. Ron Maimon (below) is secretly eager to give examples illustrating this pont. There is a nice "dictionary" relating black holes and thermodynamics, where the surface area of the event horizon is entropy and black hole "surface gravity" is temperature. In its classic form it applies only to black holes, but it's incredibly interesting and important, so it's worth studying: http://en.wikipedia.org/wiki/Black_hole_thermodynamics http://en.wikipedia.org/wiki/Surface_gravity#Surface_gravity_of_a_black_hole http://www.physics.umd.edu/grt/taj/776b/lectures.pdf Naturally people have tried to generalize these ideas from black holes to other solutions of Einstein's equations. Ted Jacobson has an interesting argument that derives Einstein's equations from the equation dQ=TdS connecting heat, entropy, and temperature: http://arxiv.org/abs/gr-qc/9504004 As he notes, "The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with dQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon." A Rindler horizon is different from an event horizon; roughly speaking, it's the boundary separating the part of spacetime an accelerating observer can see from the part he will never see. Simplest example: if you're in a rocket in Minkowski spacetime and you fire your thrusters so that you feel a constant g force in the same direction, your velocity will approach the speed of light but never get there, yet some photons coming from behind you will never catch up with you, so there will be some objects behind you that you'll never get to see, even if you look over your shoulder. The imaginary surface separating the spacetime points you'll see from those you won't is called the Rindler horizon. But Jacobson is considering a subtler 'local' version of the Rindler horizon, and considering it in curved spacetime. Since Erik Verlinde's work on 'entropic gravity' there have been further attempts to relate general relativity and thermodynamics. Some of these are reviewed in this paper by T. Padmanabhan: http://arxiv.org/abs/0911.5004 I haven't really read this paper, though. In short, there's a bunch of tantalizing relations between gravity and thermodynamics, but they don't proceed by saying "temperature is some function of curvature".

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.