Fokker Lagrangian and Coordinate Condition in General Relativity

Lagrangian Formulation of General Relativity

Canonical Lagrangian Dynamics and General Relativity

Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase space. We identify a “Lagrangian one-form” to replace the standard symplectic one-form, which we use to construct the canonical constraints and an associated...

Necessary and sufficient condition for hydrostatic equilibrium in general relativity

We present explicit examples to show that the ‘compatibility criterion’ [recently obtained by us towards providing equilibrium configurations compatible with the structure of general relativity] which states that: for a given value of σ[≡ (P0/E0) ≡ the ratio of central pressure to central energy-density], the compactness ratio u[≡ (M/R), whereM is the total mass andR is the radius of the config...

Fokker–Planck equation with fractional coordinate derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

Boundary conditions from boundary terms, Noether charges and the trace K lagrangian in general relativity.

We present the Lagrangian whose corresponding action is the trace K action for General Relativity. Although this Lagrangian is second order in the derivatives, it has no second order time derivatives and its behavior at space infinity in the asymptotically flat case is identical to other alternative Lagrangians for General Relativity, like the gamma-gamma Lagrangian used by Einstein. We develop...