The most general metric tensor that can represent a static isotropic gravitational field (i.e., in empty space) is called the standard isotropic metric. There are a number of forms in which this metric can be written, including "standard" form
"isotropic form"
and "harmonic form"
References
Weinberg, S. "The General Static Isotropic Metric." §8.1 in Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, pp. 175-179, 1972.
