标题： 布兰斯-迪克理论中的引力波：围绕克尔黑洞的测试粒子分析 显示英文标题

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

摘要： 分析落入克尔黑洞的测试粒子，我们研究了布兰斯-迪克理论中的引力波。 首先我们考虑一个以恒定方位角落入旋转黑洞的测试粒子，并计算了引力辐射的标量模式和张量模式的波形和辐射能量。 我们发现，标量引力波的波形以及能量对黑洞的旋转参数$a$和方位角弱相关。 其次，使用一个非球形测试粒子尘埃壳体落入克尔黑洞的模型，我们研究了标量模式占主导的情况。 当黑洞旋转时，即使对于“球对称”壳体，张量模式也不会消失，相反，略微扁平的壳体使其能量最小，但具有非零的有限值，该值取决于克尔参数$a$。 结果表明，只有在高度球形坍缩的情况下，标量模式才占主导地位，但它们永远不会超过张量模式，除非布兰斯-迪克参数$\omega_{BD} \lsim 750 $对$a/M=0.99$或者除非$\omega_{BD} \lsim 20,000 $对$a/M=0.5$，其中$M$是黑洞的质量。 我们得出结论，具有$\omega_{BD} \lsim$几千的标量引力波除非在非常有限的情况下不会占主导地位（例如从测试粒子落入施瓦茨希尔德黑洞的正面方向观测，或高度球形的尘埃壳体坍缩成克尔黑洞）。因此，在通过引力波观测确定引力理论时，也需要观测偏振。 显示英文摘要

摘要： 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.