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Application of Lorentz transformations to the Schwarzschild metric

25 March 2026, Version 5
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

The gravitational field of a spherical body moving uniformly and rectilinearly is considered. The corresponding metric for weak gravity is obtained by applying the Lorentz transformations to the linearized isotropic Schwarzschild metric. The change in the flow of time obtained from the geodetic equations is consistent with the annual fluctuations in the frequency of the signal from Pioneer 10.

Keywords

Lorentz transformations
Schwarzschild metric
geodesics
Pioneer 10

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Version History

Mar 25, 2026 Version 5

Version Notes

1. Abstract supplemented. 2. The introduction now includes a discussion of the consistency of the proposed analysis with gauge theories of gravity. Relevant references are provided. 3. A complete solution of the geodetic equations and its sequential reduction to the equations used to analyze the Pioneer 10 signal are given, taking into account the relationship between the values included in it. 4. The estimate of the amplitude of annual fluctuations of the frequency of the Pioneer 10 signal in terms of additional acceleration and its error has been clarified. Changed one of the evaluation points.

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The content is available under CC BY 4.0 [opens in a new tab]

DOI

10.33774/coe-2024-267zc-v5
D O I: 10.33774/coe-2024-267zc-v5 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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