Newtonian gravitational waves from a continuum

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-05-15 DOI:10.1098/rspa.2023.0656
Peter Vadasz
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Abstract

Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier–Stokes equations for a general variable gravitational field g ( t , x ) , are equivalent to a form identical to the Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at a finite speed. The latter implies that Newtonian gravitation as presented in this paper is not ‘spooky action at a distance’ but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that, in analogy to the Maxwell equations, the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein’s general relativity theory, it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity, i.e. as a flat-space approximation. The latter is left for follow-up research.

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来自连续体的牛顿引力波
研究表明,引力波直接源自连续质量分布的牛顿动力学,例如可压缩流体或等效流体。研究表明,管理连续质量分布的方程,即一般可变引力场 g(t,x) 的不粘性纳维-斯托克斯方程,与电磁学中的麦克斯韦方程等价,但须符合特定条件。这种等价关系的结果是产生了以有限速度传播的引力波。后者意味着本文提出的牛顿引力不是 "远距离幽灵作用",而是类似于以有限速度传播的电磁波,尽管在积分场公式中出现了明显的形式。此外,这还证明,与麦克斯韦方程组类似,牛顿引力方程组对于以光速传播的波也是洛伦兹不变的。由于迄今为止引力波只是从爱因斯坦的广义相对论中推导出来的,因此有必要检查本文提出的牛顿引力波与广义相对论类型的引力波之间是否存在联系,至少在一定的重叠有效性限度内,即作为平空间近似。后者有待后续研究。
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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