• Corpus ID: 236950438

The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry

@inproceedings{Javaloyes2021TheEF,
  title={The Einstein-Hilbert-Palatini formalism in Pseudo-Finsler Geometry},
  author={Miguel Angel Javaloyes and Miguel S{\'a}nchez Caja and Fidel F. Villase{\~n}or},
  year={2021}
}
A systematic development of the so-called Palatini formalism is carried out for pseudo-Finsler metrics L of any signature. Substituting in the classical Einstein-Hilbert-Palatini functional the scalar curvature by the Finslerian Ricci scalar constructed with an independent nonlinear connection N, the metric and affine equations for (N, L) are obtained. In Lorentzian signature with vanishing mean Landsberg tensor Lani, both the Finslerian Hilbert metric equation and the classical Palatini… 

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References

SHOWING 1-10 OF 53 REFERENCES

Variational formulation of general relativity from 1915 to 1925 “Palatini's method” discovered by Einstein in 1925

Among the three basic variational approaches to general relativity, the metric-affine variational principle, according to which the metric and the affine connection are varied independently, is

Finsler gravity action from variational completion

In the attempts to apply Finsler geometry to construct an extension of general relativity, the question about a suitable generalization of the Einstein equations is still under debate. Since Finsler

Finsler geometric extension of Einstein gravity

We present our Finsler spacetime formalism which extends the standard formulation of Finsler geometry to be applicable in physics. Finsler spacetimes are viable non-metric geometric backgrounds for

Anisotropic tensor calculus

  • M. Javaloyes
  • Mathematics, Computer Science
    International Journal of Geometric Methods in Modern Physics
  • 2019
It is shown that the Chern connection of a Finsler metric can be interpreted as the Levi-Civita connection and the anisotropic curvature tensor is introduced, which is a way of handling tensors that depends on the direction remaining always in the same class.

Anisotropic connections and parallel transport in Finsler spacetimes

. The general notion of anisotropic connections ∇ is revisited, including its precise relations with the standard setting of pseudo-Finsler metrics, i.e., the canonic nonlinear connection and the

Ricci flat Finsler metrics by warped product.

In this work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, S. and Zhao (2018), with another "warping", one that is consistent with static spacetimes. We

Randers pp -waves

In this work we study Randers spacetimes of Berwald type and analyze Pfeifer and Wohlfarth's vacuum field equation of Finsler gravity for this class. We show that in this case the field equation is

On a class of critical Riemann–Finsler metrics

A generalized Einstein–Hilbert functional in Finsler geometry is defined and its Euler–Lagrange equation is derived, which depends on not only the Ricci scalar but also the mean Landsberg curvature.

Curvature Computations in Finsler Geometry Using a Distinguished Class of Anisotropic Connections

We show how to compute tensor derivatives and curvature tensors using affine connections. This allows for all computations to be obtained without using coordinate systems, in a way that parallels the
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