The rate of entropy change: gravitational effects

The covariant form of entropy change (or balance) is expressed in the metric of the Schwarzschild line element. In this metric the rate of entropy change depends only on the time component of the metric tensor; it is then different at different points in space and appears to be slower in the presence than in the absence of a gravitational field. The linear equations originated by the internal entropy sources depend on both the time and radial components of the metric tensor and the transport processes behave anisotropically, being slower along the radial coordinate than in the directions of the others. The extent of rate reduction is expressed by the kinetic (transport) quantities which assume different values at different points in space.