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.

Post-Newtonian limit of generalized scalar-torsion theories of gravity

“…One then continues with the third order solution. To determine the PPN parameter α 1 , we use the gauge invariant formulation of the PPN formalism [82]. Here a different gauge is chosen, in which the third velocity order of the metric component 3 h 0i only depends on the combination V i + W i and reads…”

“…Calculations have been performed using xPPN [39]. Alternatively, one could make use of the gauge-invariant approach to the PPN formalism [36,40]; the resulting equations for the constant coefficients we obtain are identical.…”

“…It has been widely used to restrict several classes of gravity theories based on curvature [65][66][67][68][69][70][71][72] and torsion [73][74][75][76][77][78], as well as to gravity theories based on multiple metrics [79][80][81]. Recently, a gauge-invariant approach to the PPN formalism has been developed, which consolidates its mathematical foundation as a tool to study gravity theories by the way how they describe the geometry of spacetime [82].…”

xPPN: an implementation of the parametrized post-Newtonian formalism using xAct for Mathematica

“…4], which has the advantage that it simplifies the gauge transformation of the PPN potentials compared to the original formulation. Another approach to simplify the issue of gauge transformations is to resort to a formulation which makes use of gauge-invariant perturbation theory, thereby resolving the necessity of gauge considerations and simplifying the application of the PPN procedure [32]. Such modifications may be included by changing the expansion of the metric in terms of PPN potentials.…”

Post-Newtonian limit of generalized symmetric teleparallel gravity

“…It has been widely used to restrict several classes of gravity theories based on curvature [65][66][67][68][69][70][71][72] and torsion [73][74][75][76][77][78], as well as to gravity theories based on multiple metrics [79][80][81]. Recently, a gauge-invariant approach to the PPN formalism has been developed, which consolidates its mathematical foundation as a tool to study gravity theories by the way how they describe the geometry of spacetime [82].…”