Arrow of Time

Penrose conjectures that the entropy of the vacuum geometrodynamical field is proportional to it's conformal curvature. This is still not a precise statement of course. "Wood" (Einstein) sources, i.e. Tuv create local Ricci curvature. Apparently the FLRW cosmological metric has zero conformal "Marble" (Einstein) curvature and it has a "cosmological fluid" everywhere when. On the other hand, the event horizon of a vacuum black hole is only conformal curvature and it has entropy S according to the Bekenstein formula

S = A/4

A = 4pi(2M)^2 = area of event horizon of the SSS black hole.

Lp^2 = 1

in Planck units where h = c = G = kB = 1

This can be generalized to the rotating Kerr metric.

Therefore, one reason to reject an SSS solution to GR with a singular point source Tuv and a timelike NAKED future singularity is that it has no entropy. If all future singularities were naked then the second law of thermodynamics might not be possible.

Penrose's idea for the cosmic arrow of time is that the Big Bang has zero gravity entropy because all the curvature from it is Ricci curvature. Even the dark zero point energy makes only Ricci curvature. Ordinary matter is only ~ 4% of all the stuff so that the usual stat mech arguments for increasing phase space volumes in say kinetic theory of gases cannot explain the actual cosmic arrow of time. Matter is a relatively small effect. The largest effect is from the increase in gravity entropy as the conformal curvature of the universe increases from black hole event horizon formation. That is, there is a close connection between cosmic censorship and the second law of thermodynamics for the universe as a whole. The final singularities of clumping matter have large entropy from the future event horizons. In contrast, the initial Big Bang singularity has zero entropy.

## Sunday, May 14, 2006

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