Compact binary systems in scalar-tensor gravity. III. Scalar waves and energy flux

TL;DR

This paper derives the scalar gravitational waveforms and energy flux for binary systems in scalar-tensor gravity, extending previous models to 1.5 post-Newtonian order and analyzing different binary types.

Contribution

It provides the first detailed derivation of scalar waveforms in scalar-tensor theories at 1.5 post-Newtonian order, including the energy flux for various binary configurations.

Findings

Scalar waves vanish for black hole--black hole binaries.

Scalar waveform depends on a single parameter for black hole--neutron star binaries.

Total energy flux agrees with previous lower order calculations.

Abstract

We derive the scalar waveform generated by a binary of nonspinning compact objects (black holes or neutron stars) in a general class of scalar-tensor theories of gravity. The waveform is accurate to 1.5 post-Newtonian order [$O((v/c)^3)$] beyond the leading-order tensor gravitational waves (the "Newtonian quadrupole"). To solve the scalar-tensor field equations, we adapt the direct integration of the relaxed Einstein equations formalism developed by Will, Wiseman, and Pati. The internal gravity of the compact objects is treated with an approach developed by Eardley. We find that the scalar waves are described by the same small set of parameters which describes the equations of motion and tensor waves. For black hole--black hole binaries, the scalar waveform vanishes, as expected from previous results which show that these systems in scalar-tensor theory are indistinguishable from their general relativistic counterparts. For black hole--neutron star binaries, the scalar waveform simplifies considerably from the generic case, essentially depending on only a single parameter up to first post-Newtonian order. With both the tensor and scalar waveforms in hand, we calculate the total energy flux carried by the outgoing waves. This quantity is computed to first post-Newtonian order relative to the "quadrupole formula" and agrees with previous, lower order calculations.