Multipole analysis for linearized $$f(R,{\mathcal {G}})$$ f(R,G) gravity with irreducible Cartesian tensors

• Main Authors: Bofeng Wu, Chao-Guang Huang
• Format: Article
• Language: English
• Published: SpringerOpen 2019-06-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-019-6992-0
• ISSN: 1434-6044; 1434-6052

Abstract The field equations of $$f(R,{\mathcal {G}})$$ f(R,G) gravity are rewritten in the form of obvious wave equations with the stress–energy pseudotensor of the matter fields and the gravitational field as its source under the de Donder condition. The linearized field equations of $$f(R,{\mathcal {G}})$$ f(R,G) gravity are the same as those of linearized f(R) gravity, and thus, their multipole expansions under the de Donder condition are also the same. It is also shown that the Gauss–Bonnet curvature scalar $${\mathcal {G}}$$ G does not contribute to the effective stress–energy tensor of gravitational waves in linearized $$f(R,{\mathcal {G}})$$ f(R,G) gravity, though $${\mathcal {G}}$$ G plays an important role in the nonlinear effects in general. Further, by applying the 1 / r expansion in the distance to the source to the linearized $$f(R,{\mathcal {G}})$$ f(R,G) gravity, the energy, momentum, and angular momentum carried by gravitational waves in linearized $$f(R,{\mathcal {G}})$$ f(R,G) gravity are provided, which shows that $${\mathcal {G}}$$ G , unlike the nonlinear term $$R^2$$ R2 in the gravitational Lagrangian, does not contribute to them either.