Abstract
We present an extension to the gauge-invariant formulation of the parameterized post-Newtonian (PPN) formalism, which allows its application to symmetric teleparallel gravity theories. In its original formulation, the gauge-invariant PPN formalism makes use of a gauge-invariant perturbative expansion of tensor fields; however, one of the fundamental gravitational field variables in symmetric teleparallel gravity theories is a flat, torsion-free connection, hence not a tensor field. Since connections transform differently from tensor fields under diffeomorphisms, we introduce here an adapted notion of gauge-invariant perturbation variables for the symmetric teleparallel connection, and show how the lowest order terms can be expressed in terms of the common PPN potentials.
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Funding
The author gratefully acknowledges the full support by the Estonian Research Council through the Personal Research Funding project PRG356, as well as the European Regional Development Fund through the Center of Excellence TK133 “The Dark Side of the Universe.”
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Paper presented at the Fourth Zeldovich meeting, an international conference in honor of Ya.B. Zeldovich held in Minsk, Belarus, on September 7–11, 2020. Published by the recommendation of the special editors: S.Ya. Kilin, R. Ruffini, and G.V. Vereshchagin.
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Hohmann, M. Gauge-Invariant Post-Newtonian Perturbations in Symmetric Teleparallel Gravity. Astron. Rep. 65, 952–956 (2021). https://doi.org/10.1134/S1063772921100140
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DOI: https://doi.org/10.1134/S1063772921100140