Computing inspirals in Kerr in the adiabatic regime: I. The scalar case
Computing inspirals in Kerr in the adiabatic regime: I. The scalar case
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在绝热状态下计算克尔的启发：I. 标量情况
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Hughes
中科院分区：
文献类型：
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作者：
S. Drasco;E. Flanagan;S. Hughes
丽莎的一个关键来源将是紧凑物体进入大质量黑洞的螺旋。最近Mino已经证明，在绝热极限下，这些源的引力波形可以通过对辐射反作用力使用延迟和超前度规扰动之差的一半的梯度来计算。使用后牛顿展开，我们认为，由此产生的波形应该是足够准确的信号检测与丽莎。数据分析模板将需要更高的准确性，超越绝热性;这仍然是一个重大挑战。我们描述了一个明确的计算过程，获得波形的基础上米诺的结果，一个点粒子耦合到标量场的情况下。我们推导出一个明确的表达式的时间平均的时间导数的卡特常数，并验证该表达式正确地预测，圆形轨道保持圆形，而辐射反应的影响下发展。推导使用的模式扩展，绿色的功能和约束测地线轨道的克尔时空，我们详细审查的详细属性。本文约四分之三是综述，四分之一是新材料。其目的是用一个统一的符号，对克尔时空中的标量辐射反应给出一个完整而完备的处理，从克尔度规开始，到运动的所有三个常数的时间演化公式结束，这些公式足够明确，可以立即用在数值代码中。
A key source for LISA will be the inspiral of compact objects into massive black holes. Recently Mino has shown that in the adiabatic limit, gravitational waveforms for these sources can be computed by using for the radiation reaction force the gradient of one half the difference between the retarded and advanced metric perturbations. Using post-Newtonian expansions, we argue that the resulting waveforms should be sufficiently accurate for signal detection with LISA. Data-analysis templates will require higher accuracy, going beyond adiabaticity; this remains a significant challenge. We describe an explicit computational procedure for obtaining waveforms based on Mino's result, for the case of a point particle coupled to a scalar field. We derive an explicit expression for the time-averaged time derivative of the Carter constant, and verify that the expression correctly predicts that circular orbits remain circular while evolving under the influence of radiation reaction. The derivation uses detailed properties of mode expansions, Green's functions and bound geodesic orbits in the Kerr spacetime, which we review in detail. This paper is about three quarters review and one quarter new material. The intent is to give a complete and self-contained treatment of scalar radiation reaction in the Kerr spacetime, in a single unified notation, starting with the Kerr metric, and ending with formulae for the time evolution of all three constants of the motion that are sufficiently explicit to be used immediately in a numerical code.