合并双星中单个黑洞的质量公式

IF 0.6 4区 教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES European Journal of Physics Pub Date : 2024-01-16 DOI:10.1088/1361-6404/ad1531
Zeynep Tugce Ozkarsligil, Bayram Tekin
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引用次数: 0

摘要

我们利用牛顿物理学给出了合并中单个黑洞质量的公式,并以探测器中的三个测量量为基础:初始波频 f1、最大检测频率(啁啾频率)f2 和这两个频率之间的时间间隔 τ。牛顿万有引力为理解引力波观测的基本特征提供了一个极好的教学工具,但由于不存在引力波牛顿万有引力,因此必须用广义相对论中关于加速质量的引力辐射假设来增强它。最简单的方法是考虑一个由两个不旋转的质量(两个黑洞)组成的双星系统,它们围绕着共同的质量中心旋转。所有的计算都可以在牛顿物理学中完成,但在这个方案中需要引力波所携带的功率的广义相对论公式。结果发现了一个微妙的问题:为了使这一简单但具有教学意义的计算保持一致,采用广义相对论的最低阶功率公式会导致复杂的单个质量。在此,我们将弥补这一问题,并提出一种从微扰广义相对论中写下平均功率公式的方法。
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Mass formulas for individual black holes in merging binaries
We give formulas for individual black hole masses in a merger, by using Newtonian physics, in terms of the three measured quantities in the detector: the initial wave frequency f 1, the maximum detected frequency (chirp frequency) f 2, and the time elapse τ between these two frequencies. Newtonian gravity provides an excellent pedagogical tool to understand the basic features of gravitational wave observations, but it must be augmented with the assumption of gravitational radiation from General Relativity for accelerating masses as there is no gravitational wave Newtonian gravity. The simplest approach would be to consider a binary system of two non-spinning masses (two black holes) circling their common center of mass. All the computations can be done within Newtonian physics, but the General Relativistic formula for the power carried by gravitational waves is required in this scheme. It turns out there is a subtle point: for the consistency of this simple, yet pedagogical computation, taking the lowest order power formula from General Relativity leads to complex individual masses. Here we remedy this problem and suggest a way to write down an average power formula coming from perturbative General Relativity.
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来源期刊
European Journal of Physics
European Journal of Physics 物理-物理:综合
CiteScore
1.70
自引率
28.60%
发文量
128
审稿时长
3-8 weeks
期刊介绍: European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education. Authors submitting articles must indicate the usefulness of their material to physics education and make clear the level of readership (undergraduate or graduate) for which the article is intended. Submissions that omit this information or which, in the publisher''s opinion, do not contribute to the above mission will not be considered for publication. To this end, we welcome articles that provide original insights and aim to enhance learning in one or more areas of physics. They should normally include at least one of the following: Explanations of how contemporary research can inform the understanding of physics at university level: for example, a survey of a research field at a level accessible to students, explaining how it illustrates some general principles. Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks. Descriptions of novel laboratory exercises illustrating new techniques of general interest. Those based on relatively inexpensive equipment are especially welcome. Articles of a scholarly or reflective nature that are aimed to be of interest to, and at a level appropriate for, physics students or recent graduates. Descriptions of successful and original student projects, experimental, theoretical or computational. Discussions of the history, philosophy and epistemology of physics, at a level accessible to physics students and teachers. Reports of new developments in physics curricula and the techniques for teaching physics. Physics Education Research reports: articles that provide original experimental and/or theoretical research contributions that directly relate to the teaching and learning of university-level physics.
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