Theories of gravitation with nonminimal coupling of matter and the gravitational field

Anisotropic cosmological models with nonminimally coupled magnetic field

“…The Lagrangian of such a theory contains the three U(1) gauge-invariant scalars R ikmn F ik F mn , R ik g mn F im F kn and RF mn F mn with coefficients proportional to the square of the Compton wavelength of the electron. Subsequently, a non-minimal coupling of gravity and electromagnetism has been discussed by a number of authors in different settings [8,9,10,11,12,13,14,15,16,17,18]. Non-minimally extended theories were used as a framework to discuss potential limitations of the equivalence principle [19,20,21]).…”

Mass–Energy–Momentum: Only there Because of Spacetime?

“…Weinstein [1996]): the newly introduced scalar field φ indirectly couples to all matter fields via directly coupling to the metric g µν ; which in turn directly couples to all matter fields. 30 The definition of minimal coupling to the metric via the absence of coupling to the curvature tensor can be found in Goenner [1984]. He argues that the common definition of minimal coupling, namely that general relativistic field equations can be obtained from special relativistic ones by demanding that η µν → g µν and ∂ µ → ∇ µ , where η µν is the Minkowski metric and ∇ µ compatible to g µν , is unique only for first-order differential equations, and hence not generally applicable.…”

pp-waves in modified gravity

“…In particular, there are many mathematically admissible interaction terms of the general form RF 2 that one can consider [147]. Such coupling terms can explicitly be written in the following forms: F ∧ F ab * Ω ab , F ∧ F ab Ω ab , F a ∧ R a ∧ * F or F a ∧ R a ∧ F [7,148] where R a is the Ricci 1-form R a = R ab θ b that can be defined in terms of the contraction R a ≡ i b Ω b a . The pp-wave solution to the nonminimal coupling involving the term of the particular form F ∧ F ab * Ω ab has been recently studied in [7] based on the Lagrangian of the form…”