Schwarzschild has 4 independent Killing vector fields, including a timelike one, and thus is a static metric, while Vaidya has only 3 independent Killing vector fields regarding the spherical symmetry, and consequently is nonstatic.
Metric system | United States Metric Board | Nishad Vaidya | metric system | Alex Metric | U.S. Metric Association | The Metric Marvels | Performance metric | Pallavi Vaidya | Omi Vaidya | Metric signature | Metric expansion of space | metric expansion of space | Kerr metric | Kantowski-Sachs metric | Gödel metric | Friedmann–Lemaître–Robertson–Walker metric | Fisher information metric | Ashok Vaidya |