Gravitational Waves in Brans-Dicke Theory : Analysis by Test Particles around a Kerr Black Hole

TL;DR

This paper investigates gravitational waves in Brans-Dicke theory emitted by test particles falling into Kerr black holes, analyzing waveform characteristics and the dominance of scalar modes under various conditions.

Contribution

It provides a detailed analysis of scalar and tensor gravitational wave modes in Brans-Dicke theory around Kerr black holes, highlighting when scalar modes dominate.

Findings

Scalar gravitational waves weakly depend on black hole rotation

Scalar modes dominate only in highly spherical collapse scenarios

Scalar modes do not generally exceed tensor modes unless d ls 750 or 20,000 depending on spin

Abstract

Analyzing test particles falling into a Kerr black hole, we study gravitational waves in Brans-Dicke theory of gravity. First we consider a test particle plunging with a constant azimuthal angle into a rotating black hole and calculate the waveform and emitted energy of both scalar and tensor modes of gravitational radiation. We find that the waveform as well as the energy of the scalar gravitational waves weakly depends on the rotation parameter of black hole $a$ and on the azimuthal angle. Secondly, using a model of a non-spherical dust shell of test particles falling into a Kerr black hole, we study when the scalar modes dominate. When a black hole is rotating, the tensor modes do not vanish even for a ``spherically symmetric" shell, instead a slightly oblate shell minimizes their energy but with non-zero finite value, which depends on Kerr parameter $a$. As a result, we find that the scalar modes dominate only for highly spherical collapse, but they never exceed the tensor modes unless the Brans-Dicke parameter $\omega_{BD} \lsim 750 $ for $a/M=0.99$ or unless $\omega_{BD} \lsim 20,000 $ for $a/M=0.5$, where $M$ is mass of black hole. We conclude that the scalar gravitational waves with $\omega_{BD} \lsim$ several thousands do not dominate except for very limited situations (observation from the face-on direction of a test particle falling into a Schwarzschild black hole or highly spherical dust shell collapse into a Kerr black hole). Therefore observation of polarization is also required when we determine the theory of gravity by the observation of gravitational waves.