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<p>A state-of-the-art review of the different deformations of space–time measured over more than a hundred years within the framework of general relativity in the weak-field regime is presented. The general relativity phenomena considered in this low field context include gravitational waves, the Lense-Thiring effect, gravitational lensing, gravitation around the Earth or the Sun. This overview of various deformations highlights the different active components of the perturbation tensor of the metric <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6050_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\({h}_{\mu \nu }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>h</mi> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. The authors demonstrate that each phenomenon corresponds to one or more distinct components of this tensor. They also show that the various components can be interpreted, within the elastic analogy of space–time, as coherent components of an associated strain tensor <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6050_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\varepsilon }_{\mu \nu }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ε</mi> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> in terms of elongation, compression or angular distortion of an equivalent elastic medium modeling the behavior of space–time. Through this synthetic ensemble approach and elastic analogy, it becomes evident—for the first time—that some components of the tensor <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6050_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\({h}_{\mu \nu }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>h</mi> <mrow> <mi>μ</mi> <mi>ν</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> remain to be identified and measured potentially corresponding to new phenomena or modified versions of general relativity in the weak-field limit.</p>

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Elastic Medium Analogy of Spacetime: hµv Metric Perturbation Tensor Analysis and Theoretical Implications

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • David Izabel,
  • Yves Remond,
  • Matteo Luca Ruggiero

摘要

A state-of-the-art review of the different deformations of space–time measured over more than a hundred years within the framework of general relativity in the weak-field regime is presented. The general relativity phenomena considered in this low field context include gravitational waves, the Lense-Thiring effect, gravitational lensing, gravitation around the Earth or the Sun. This overview of various deformations highlights the different active components of the perturbation tensor of the metric \({h}_{\mu \nu }\) h μ ν . The authors demonstrate that each phenomenon corresponds to one or more distinct components of this tensor. They also show that the various components can be interpreted, within the elastic analogy of space–time, as coherent components of an associated strain tensor \({\varepsilon }_{\mu \nu }\) ε μ ν in terms of elongation, compression or angular distortion of an equivalent elastic medium modeling the behavior of space–time. Through this synthetic ensemble approach and elastic analogy, it becomes evident—for the first time—that some components of the tensor \({h}_{\mu \nu }\) h μ ν remain to be identified and measured potentially corresponding to new phenomena or modified versions of general relativity in the weak-field limit.