Kepler's second law for classical orbits states that planets sweep out equal areas in equal times. Is that still true in Schwarzschild spacetime, assuming orbital radii \(r>2 G M / c^{2}\) ?

(a) First suppose that "time" here means the coordinate time \(t\) in Schwarzschild coordinates.

(b) Then suppose instead that "time" means the proper time \(\tau\) of the planets themselves.