9 problems

Gauge-invariant decomposition conjecture. There exist a tensor field ${\cal H}_{ab}$ and a vector field $X^a$ such that

Let ${{\mathscr M}}_{\epsilon}$ be a physical spacetime, let ${{\mathscr M}}$ be its background spacetime, and let $h_{ab}$ be a perturbative metric tensor pulled back from…

The paper considers a perturbative procedure for constructing gauge-invariant variables in a two-parameter perturbation scheme, and confirms its applicability through third order.…

Consider generic stiffness tensor fields $c_i$, density fields $\rho_i$, and Riemannian metrics $g_i$ in the setting of the stated Riemannian anisotropic elasticity problem, and le…

Curvature-contraction conjecture. To derive an exactly gauge-invariant Lagrangian by this procedure, it is necessary to contract independently gauge-invariant field-strength (curva…

Higher-order gauge-transformation conjecture. There exists a vector field $\hat\sigma_{(n)}^a$ such that

Decomposition conjecture. There exist a tensor field ${\cal H}_{ab}$ and a vector field $X^a$ such that

Universal decomposition conjecture. The above assumption for the decomposition of the linear-order metric perturbation is correct for any background spacetime.

Let $X^{a}$ be a vector field constructed from some components of the linear-order metric perturbation, with gauge transformation rule given by the second equation in the linear me…