大规模布兰斯-迪克理论的详细一阶后牛顿分析：数值约束和 β 参数的含义,Physical Review D

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大规模布兰斯-迪克理论的详细一阶后牛顿分析：数值约束和 β 参数的含义
Physical Review D ( IF 4.6 ) Pub Date : 2024-02-21 , DOI: 10.1103/physrevd.109.044045
Matheus F. S. Alves , Júnior D. Toniato , Davi C. Rodrigues

大规模布兰斯-迪克（BD）理论是最简单的广义相对论扩展之一。它通常被认为是其他引力理论的弱场极限。在这里，我们对大量 BD 理论进行了详细的后牛顿分析。我们首先按照 Will-Nordtvedt 参数化后牛顿 (PPN) 形式主义扩展大量 BD 场方程，无需点粒子近似。发现了标准 PPN 形式中不存在的单一势。这种新的潜力阻碍了 PPN 立即得出结论。接下来，我们进行完整的一阶后牛顿分析并明确导出所有守恒量。通过要求 BD 质量足够大来要求存在牛顿极限后，我们发现，正如预期的那样，

γ = 1

; 但没有有效的

β

可以具有与标准相同的物理作用的参数

β

在 PPN 形式主义中。所有其他标准 PPN 参数都可以毫无问题地扩展到大规模 BD 情况，并且具有相同的广义相对论值。最后，我们考虑两种不同物理背景下近星体进角和 BD 质量的数值关系，即水星围绕太阳的轨道和恒星 S2 围绕银河系中预期的超大质量黑洞的轨道。

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Detailed first-order post-Newtonian analysis of massive Brans-Dicke theories: Numerical constraints and the meaning of theβparameter

Massive Brans-Dicke (BD) theory is among the simplest general relativity extensions. It is commonly found as the weak-field limit of other gravitational theories. Here we do a detailed post-Newtonian analysis of massive BD theories. We start by expanding the massive BD field equations following the Will-Nordtvedt parametrized post-Newtonian (PPN) formalism, without point-particle approximations. A single potential that is not present in the standard PPN formalism is found. This new potential hinders immediate PPN conclusions. To proceed, we do a complete first-order post-Newtonian analysis and explicitly derive all the conserved quantities. After demanding that there exists a Newtonian limit by requiring the BD mass to be sufficiently large, we find, as expected, that

γ = 1

; but there is no effective

β

parameter that can have the same physical role of the standard

β

in PPN formalism. All the others standard PPN parameters can be extended to the massive BD case without issues and are shown to have the same values of general relativity. At last, we consider numerical relations on the periastron advance and the BD mass in two different physical contexts, the orbit of Mercury about the Sun and the orbit of the star S2 about the expected supermassive black hole in the Milky Way.

更新日期：2024-02-23

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