Abstract
We formulate Penrose’s Weyl curvature hypothesis from an aspect of spacetime thermodynamics, which has been proposed by Jacobson. Using the evolution equation for the shear tensor of a null congruence in a local Rindler frame, we show that the entropy variation can be expressed in terms of the Weyl curvature. This result supports Penrose’s hypothesis, which claims that entropy of the gravitational field is somehow linked to the Weyl curvature. We point out that Penrose’s hypothesis corresponds to Clausius’ relation for a quasi-equilibrium state in spacetime thermodynamics.
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