See studies by C. B. Cone (1952) and W. D. Hudson (1970).
Price graduated from Stuyvesant High School in 1960, and went on to earn a dual degree in physics and engineering from Cornell University in 1965. He earned his Ph.D. in 1971 from Caltech under the supervision of Kip Thorne. He has spent most of his career at the University of Utah, but in 2004 joined Center for Gravitational Wave Astronomy at the University of Texas at Brownsville.
Price is probably best known for a 1972 result now known as Price's theorem. This is usually informally stated as follows: any inhomogeneities in the spacetime geometry outside a black hole will be radiated away. (Any such inhomogeneities can be quantified as nonzero higher multipole moments.) Price's theorem explains how the no hair theorem is enforced. Price also made pioneering numerical simulations which established (nonrigorously) a precise scenario for the emission of gravitational radiation during the merger of two compact objects (such as two black holes). Subsequent work has largely confirmed the scenario which was first developed in his work. These simulations have provided a major impetus for the development of gravitational wave detectors such as LIGO.
Price is the coauthor of three well known books in general relativity.