The overwhelming empirical evidence supporting the Einstein Equivalence Principle, discussed in the previous chapter, has convinced many theorists that only metric theories of gravity have a hope of being completely viable. Even the most carefully formulated nonmetric theory – the Belinfante – Swihart theory – was found to be in conflict with the Moscow Eötvös experiment. Therefore, here, and for the remainder of this book, we shall turn our attention exclusively to metric theories of gravity.

In Section 3.1, we review the concept of universal coupling, first defined in Section 2.5. Armed with EEP and universal coupling, we then develop, in Section 3.2, the mathematical equations that describe the behavior of matter and nongravitational fields in curved spacetime. Every metric theory of gravity possesses these equations.

Metric theories of gravity differ from each other in the number and type of additional gravitational fields they introduce and in the field equations that determine their structure and evolution; nevertheless, the only field that couples directly to matter is the metric itself. In Section 3.3, we discuss general features of metric theories of gravity, and present an additional principle, the Strong Equivalence Principle that is useful for classifying theories and for analyzing experiments.

Universal Coupling

The validity of the Einstein Equivalence Principle requires that every nongravitational field or particle should couple to the same symmetric, second rank tensor field of signature –2.