Gauge-invariant approach to the parametrized post-Newtonian formalism

Abstract

We present an approach to the parametrized post-Newtonian (PPN) formalism which is based on gauge-invariant higher order perturbation theory. This approach divides the components of the metric perturbations into gauge-invariant quantities, which carry information about the physical system under consideration, and pure gauge quantities, which describe the choice of the coordinate system. This separation generally leads to a simplification of the PPN procedure, since only the gauge-invariant quantities appear in the field equations and must be determined by solving them. Another simplification arises from the fact that the gauge-invariant approach supersedes the necessity to first choose a gauge for solving the gravitational field equations and later transforming the obtained solution into the standard PPN gauge, as it is conventionally done in the PPN formalism, whose standard PPN gauge is determined only after the full solution is known. In addition to the usual metric formulation, we also present a tetrad formulation of the gauge-invariant PPN formalism. To illustrate their practical application, we demonstrate the calculation of the PPN parameters of a well-known scalar-tensor class of theories.

arXiv commentLaTeX, 21 pages, no figures; published version

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Cited by in corpus (10)

• Teleparallel Gravity: From Theory to Cosmology
• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Post-Newtonian limit of Teleparallel Horndeski gravity
• General cosmological perturbations in teleparallel gravity
• Note on gauge invariance of second order cosmological perturbations
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
• xPPN: An implementation of the parametrized post-Newtonian formalism using xAct for Mathematica
• Gauge-invariant post-Newtonian perturbations in symmetric teleparallel gravity
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity