Related papers: Finsler gravity action from variational completion
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
Finslerian extensions of Special and General Relativity -- commonly referred to as Very Special and Very General Relativity -- necessitate the development of a unified Lorentz-Finsler geometry. However, the scope of this geometric framework…
We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Ra\~{n}ada field. We consider the most general actions that are invariant under the Lorentz, electromagnetic…
This work places the invariant $ds^2$ at the center of the gravitational interaction, interpreting it not as a purely geometric object but as the differential of proper time, endowed with direct physical meaning. Starting from the extension…
Lorentz invariance is one of the foundations of modern physics; however, Lorentz violation may happen from the perspective of quantum gravity, and plenty of studies on Lorentz violation have arisen in recent years. As a good tool to explore…
In Finsler geometry the complete lift vector fields have distinguished geometric significance. For example a vector field on a Finsler manifold is said to be conformal if its complete lift is conformal in usual sense. In this work we define…
In the paper we show that the general relativity action (and Lagrangian) in recent Einstein-Palatini formulation is equivalent to the action (and Langrangian) of a gauge field. We begin with a bit of information of the Einstein-Palatini…
We present a proposal to include Lorentz-violating effects in gravitational field by means of the Finsler geometry. In the Finsler set up, the length of an event depends both on the point and the direction in the space-time. We briefly…
General properties of vacuum solutions of $f(R)$ gravity are obtained by the condition that the divergence of the Weyl tensor is zero and $f''\neq 0$. Specifically, a theorem states that the gradient of the curvature scalar, $\nabla R$, is…
The sub-Finslerian geometry means that the metric $F$ is defined only on a given subbundle of the tangent bundle, called a horizontal bundle. In the paper, a version of the Hopf-Rinow theorem is proved in the case of sub-Finslerian…
General relativity postulates that the gravity field is defined on a Riemannian manifold. The field equations are $R^\mu_\nu = 0$ i.e. Ricci's curvature tensor vanishes. The field equations have to be augmented by natural physical…
The $f(R,T)$ gravity field equations depend generically on both the Ricci scalar $R$ and trace of the energy-momentum tensor $T$. Within the assumption of perfect fluids, the theory carries an arbitrariness regarding the choice of the…
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes…
We suggest that the vacuum field equation in Finsler spacetime is equivalent to vanishing of Ricci scalar. Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserve spherical symmetry. Supposing…
Using the Steiner-Weyl expansion formula for parallel manifolds and the so called gonihedric principle we find a large class of discrete integral invariants which are defined on simplicial manifolds of various dimensions. These integral…
The authors study a generalized notion of null geodesic defined by the Legendrian dynamics of a regular conical subbundle of the tangent bundle on a manifold. A natural extension of the Weyl tensor is shown to exist, and to depend only on…
Finsler geometry is a natural arena to investigate the physics of spacetimes with local Lorentz violating. The directional dependence of the Finsler metric provides a way to encode the Lorentz violating effects into the geometric structure…
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with…
Spinor gravity is a functional integral formulation of gravity based only on fundamental spinor fields. The vielbein and metric arise as composite objects. Due to the lack of local Lorentz-symmetry new invariants in the effective…