General Relativity solutions in modified gravity
General Relativity solutions in modified gravity
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DOI：
10.1016/j.physletb.2018.04.041
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发表时间：
2018-04
影响因子：
4.4
通讯作者：
H. Motohashi;Masato Minamitsuji
中科院分区：
文献类型：
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作者：
H. Motohashi;Masato Minamitsuji
最近的引力波观测的二元黑洞合并和二元中子星星合并的LIGO和处女座合作与其光学对应物约束偏离广义相对论（GR）的强场制度和宇宙尺度与高精度，并进一步强大的约束，预计在不久的将来的观测。因此，在众多的理论中，找出本质上具有与GR相同解的修正引力理论是很重要的。我们澄清了修正引力理论允许GR解的三个条件，即，解的度量满足爱因斯坦方程的GR和常数的标量场的轮廓。我们的分析是相当普遍的，因为它应用了广泛的一类单/多场标量张量理论的修改的重力在物质分量的存在下，和任何时空几何，包括宇宙学背景以及黑洞和中子星星周围的时空，其中后者的这些条件提供了一个必要条件无毛定理。这三个条件将有助于对修正引力理论的进一步约束，因为它们将修正引力的一般理论分为三类，每一类都具有i）唯一的GR解（即，无毛的情况下），ii）只有多毛的解决方案（除了GR解决方案是通过消除之间的奇异耦合函数的欧拉-拉格朗日方程），和iii）GR和多毛的解决方案，其中最后一个两个解决方案之一，可以动态选择。
Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar–tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler–Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.