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gerald V
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- Moller himself stated that a specific modification of his tetrad-based gravitational Lagrangian is in agreement with General Relativity in the weak field limit. What limits emerge from current observational evidence?
This is a quite specific question, but maybe someone knows (part of) the answers, what would be much appreciated.
The Moller (the o is a specific Danish character) Lagrangian for gravitation reads (see for example Aldrovandi-Pereira, Teleparallel Gravity, Springer 2013) ##L = \partial_\mu h^{a\nu} \partial_\nu h_a^\mu - \partial_\mu h_a^\mu \partial_\nu h^{a \nu}##, where ##\partial## is the covariant derivative and ##h^a## are the 4 tetrad vector fields. In flat spacetime, for any of the ##h^a## the above is a pure divergence, for which reason such combination does not show up in, say, electrodynamics. But when there is curvature, the interchange of partial derivatives leads to the result, that the above Lagrangian just is the curvature scalar plus a divergence.
In a 1978 paper (On the crisis in the theory of gravitation and a possible solution, Det Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser 39, 13), Moller says that a term ##\lambda( \partial_\mu h^{a\nu} \partial_\mu h_a^\nu - 2 \partial_\mu h^{a\nu} \partial_\nu h_a^\mu)##, where ##\lambda## is some real number, can be added where ''##\lambda## can be taken of order 1 without destroying the first order agreement with Einstein's theory in the weak field case''.
##\lambda = + 1## would mean some resemblance to the Lagrangians of vector force fields, apart from one additional term.
My questions: From the recent observational results, what is the limit on ##\lambda##? Is ##\lambda = +1## still possible? Have there even theories been formulated with ##|\lambda| \ne 0##?
Thank you very much in advance, be it for answers, be it for hints if I made some mistakes.
The Moller (the o is a specific Danish character) Lagrangian for gravitation reads (see for example Aldrovandi-Pereira, Teleparallel Gravity, Springer 2013) ##L = \partial_\mu h^{a\nu} \partial_\nu h_a^\mu - \partial_\mu h_a^\mu \partial_\nu h^{a \nu}##, where ##\partial## is the covariant derivative and ##h^a## are the 4 tetrad vector fields. In flat spacetime, for any of the ##h^a## the above is a pure divergence, for which reason such combination does not show up in, say, electrodynamics. But when there is curvature, the interchange of partial derivatives leads to the result, that the above Lagrangian just is the curvature scalar plus a divergence.
In a 1978 paper (On the crisis in the theory of gravitation and a possible solution, Det Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser 39, 13), Moller says that a term ##\lambda( \partial_\mu h^{a\nu} \partial_\mu h_a^\nu - 2 \partial_\mu h^{a\nu} \partial_\nu h_a^\mu)##, where ##\lambda## is some real number, can be added where ''##\lambda## can be taken of order 1 without destroying the first order agreement with Einstein's theory in the weak field case''.
##\lambda = + 1## would mean some resemblance to the Lagrangians of vector force fields, apart from one additional term.
My questions: From the recent observational results, what is the limit on ##\lambda##? Is ##\lambda = +1## still possible? Have there even theories been formulated with ##|\lambda| \ne 0##?
Thank you very much in advance, be it for answers, be it for hints if I made some mistakes.