https://doi.org/10.1140/epjc/s10052-025-15097-7
Regular Article - Theoretical Physics
Restricted gravity: Lagrangian formalism and explicit solutions
1
Department of Liberal Arts, Tech University of Korea, 15073, Siheung-Si, Korea
2
Konkuk Institute of Science and Technology, Konkuk University, 05029, Seoul, Korea
3
School of Physics and Astronomy, Seoul National University, 08826, Seoul, Korea
4
Center for Quantum Spacetime, Sogang University, 04107, Seoul, Korea
Received:
20
March
2025
Accepted:
17
November
2025
Published online:
28
November
2025
It is well known that, making the Abelian projection of Einstein’s theory one can obtain the restricted gravity which is simpler than Einstein’s theory but describes the core dynamics of Einstein’s gravity. In this paper we present the Lagrangian formalism of the restricted gravity which makes the restricted gravity a self consistent field theory by itself, independent of Einstein’s theory. With this we present interesting solutions of the restricted gravity, in particular the gravitational cosmic string, the Bertotti–Robinson spacetime, the axisymmetric pp-wave, and the conformally flat waves with flat wavefront. Moreover, we show that in the restricted gravity the Rosen–Bondi gravitational plane wave could be described by two Maxwellian potentials. This could play important role in quantum gravity. We discuss the physical implications of the restricted gravity.
© The Author(s) 2025
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