Conservation laws, gravitational waves, and mass losses in the Dicke-Brans-Jordan theory of gravity

In the Dicke-Brans-Jordan theory of gravity, far away from a bounded system, orbiting test particles measure the total, active gravitational mass M while orbiting test black holes measure the "tensor" mass MT. Their difference (M-MT) is the scalar mass MS. In this paper, conservation laws for MS, MT, and M are delineated and are used to show the following: (i) A spin-2 gravitational plane wave carries tensor mass, but does not carry scalar mass; the flux of tensor mass is proportional to the square of the time-integrated amplitude of the Riemann tensor |∫Ψ₄dt|². (ii) A spin-0 gravitational plane wave carries both tensor mass (flux proportional to the square of the time-integrated Riemann amplitude |∫Φ₂₂dt|²) and scalar mass (flux proportional to the Riemann amplitude Φ₂₂---or, equivalently, proportional to the second time derivatives of the amplitude of the scalar field ∂²φ∂t²). (iii) The tensor mass in a gravitational wave curves up the background spacetime through which the wave propagates; the scalar mass does not. (iv) The tensor mass in a wave is positive-definite; the scalar mass is not. (v) If a dynamical spherical system emits gravitational waves that change its scalar mass by ΔMS in time τ (ΔMS may be positive or negative), then these waves will also reduce its tensor mass by an amount ≥(ΔMS)²τ. The response of gravitational-wave antennas to scalar waves is discussed. It is shown that, whereas antennas of negligible self-gravity respond only to the tidal forces of the wave (Φ₂₂), antennas with significant self-gravity respond about equally to the tidal forces Φ₂₂ and the oscillating Cavendish gravitation constant φ. Because of the unique phase and amplitude relations of Φ₂₂ and φ, the two responses are coherent---and can even cancel each other perfectly for a "carefully designed" detector.