Aberration in Gravito-Electromagnetism
Victor Massart and M. B. Paranjape
Abstract The dynamical effects of general relativity which go past Newtonian
gravity, specifically the expectation that gravitational effects propagate with a finite
velocity, have not been directly verified. In this article we use the formalism of
gravito-electromagnetism to compute the first dynamical corrections to Newtonian
gravity due to general relativity. We consider a system with multiple sources of
dynamical gravitational effects. The main problem that arises is that there are
different retarded times for the different sources. We use the Lagrange inversion
theorem to express all dynamical effects in terms of the instantaneous time and
then simply superpose them. We apply our results to a proposed, realizable
experimental set-up and find a dynamical effect that could be observed in a LIGOtype experiment.
Keywords Gravito-electromagnetism · Aberration · Retarded time · Lagrange
inversion theorem
1 Gravito-electromagnetism
Gravito-electromagnetism is a linearized, weak-field, non-relativistic approximation
to general relativity. The name comes from the fact that in this approximation,
gravity is almost exactly analogous to Maxwell electromagnetism. Throughout this
article we will use the notation from Jackson’s textbook [1] on electromagnetism,
V. Massart
Groupe de physique des particules, Département de physique, Montréal, QC, Canada
e-mail: victor.massart@umontreal.ca
M. B. Paranjape ()
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: paranj@lps.umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_43
465
Victor Massart and M. B. Paranjape
Abstract The dynamical effects of general relativity which go past Newtonian
gravity, specifically the expectation that gravitational effects propagate with a finite
velocity, have not been directly verified. In this article we use the formalism of
gravito-electromagnetism to compute the first dynamical corrections to Newtonian
gravity due to general relativity. We consider a system with multiple sources of
dynamical gravitational effects. The main problem that arises is that there are
different retarded times for the different sources. We use the Lagrange inversion
theorem to express all dynamical effects in terms of the instantaneous time and
then simply superpose them. We apply our results to a proposed, realizable
experimental set-up and find a dynamical effect that could be observed in a LIGOtype experiment.
Keywords Gravito-electromagnetism · Aberration · Retarded time · Lagrange
inversion theorem
1 Gravito-electromagnetism
Gravito-electromagnetism is a linearized, weak-field, non-relativistic approximation
to general relativity. The name comes from the fact that in this approximation,
gravity is almost exactly analogous to Maxwell electromagnetism. Throughout this
article we will use the notation from Jackson’s textbook [1] on electromagnetism,
V. Massart
Groupe de physique des particules, Département de physique, Montréal, QC, Canada
e-mail: victor.massart@umontreal.ca
M. B. Paranjape ()
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: paranj@lps.umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_43
465