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Hyperbolic Octonion Formulation of Gravitational Field Equations

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Abstract

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.

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Acknowledgements

I thank to the reviewers for their valuable suggestions and constructive feedbacks which substantially helped improving the quality of the paper.

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  1. Department of Physics, Science Faculty, Anadolu University, 26470, Eskişehir, Turkey

    Süleyman Demir

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  1. Süleyman Demir
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Correspondence to Süleyman Demir.

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Demir, S. Hyperbolic Octonion Formulation of Gravitational Field Equations. Int J Theor Phys 52, 105–116 (2013). https://doi.org/10.1007/s10773-012-1307-3

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  • DOI: https://doi.org/10.1007/s10773-012-1307-3

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