https://doi.org/10.1140/epjc/s10052-018-6344-5
Regular Article - Theoretical Physics
Premetric teleparallel theory of gravity and its local and linear constitutive law
1
Institute of Mathematics, The Hebrew University of Jerusalem and Jerusalem College of Technology, 91160, Jerusalem, Israel
2
Theoretical Physics Laboratory, Nuclear Safety Institute, Russian Academy of Sciences, B. Tulskaya 52, 115191, Moscow, Russia
3
Theoretical Physics Institute, University of Alberta, Edmonton, AB, T6G 2E1, Canada
4
Institute for Theoretical Physics, University of Cologne, 50923, Cologne, Germany
* e-mail: hehl@thp.uni-koeln.de
Received:
23
August
2018
Accepted:
13
October
2018
Published online:
9
November
2018
We continue to investigate the premetric teleparallel theory of gravity (TG) with the coframe (tetrad) as gravitational potential. We start from the field equations and a local and linear constitutive law. We create a Tonti diagram of TG in order to disclose the structure of TG. Subsequently we irreducibly decompose the 6th order constitutive tensor under the linear group. Moreover, we construct the most general constitutive tensors from the metric and the totally antisymmetric Levi-Civita symbol, and we demonstrate that they encompass nontrivial axion and skewon type pieces. Using these tools, we derive for TG in the geometric-optics approximation propagating massless spin 0, 1, and 2 waves, including the special case of Einstein’s general relativity.
© The Author(s), 2018
