Scalar-Tensor Theory and General Relativity

The various versions of the scalar-tensor theory (e.g., the theories of Jordan, Hoyle, and Brans-Dicke) are derived from a general variational principle. It is shown that scalar-conformal transformations not only interconvert the various current versions of the scalar-tensor theory (i.e., Brans-Dicke theory ⇄ Hoyle steady-state theory), but also convert the scalar-tensor variational principle into the variational principle of general relativity. The scalar-tensor formalism is therefore implicitly embodied in the theory of general relativity, thus illustrating the considerable freedom available in specifying the nature and physical content of the "matter tensor" in the Einstein equation.