The Einstein–Hilbert–Palatini formalism in pseudo-Finsler geometry

  1. Javaloyes, Miguel Ángel 1
  2. Sánchez Sánchez, Miguel Ángel 2
  3. Fernández Villaseñor, Fidel 2
  1. 1 Departamento de Matemáticas, Universidad de Murcia, Spain
  2. 2 Departamento de Geometría y Topología, Facultad de Ciencias & IMAG (Centro de Excelencia María de Maeztu), Universidad de Granada, Spain
Revista:
Advances in Theoretical and Mathematical Physics

ISSN: 1095-0761,  1095-0753

Any de publicació: 2022

Volum: 26

Número: 10

Pàgines: 3563-3631

Tipus: Article

DOI: 10.4310/ATMP.2022.V26.N10.A5 GOOGLE SCHOLAR

Altres publicacions en: Advances in Theoretical and Mathematical Physics

Resum

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 affine and metric equations for (N, L) are obtained. In Lorentzian signature with vanishing mean Landsberg tensor Lani , both the Finslerian Hilbertmetric equation and the classical Palatini conclusions are recovered by means of a combination of techniques involving the (Riemannian) maximum principle and an original argument about divisibility and fiberwise analyticity. Some of these findings are also extended to classical Riemannian solutions by using the eigenvalues of a Laplacian. When Lani ̸= 0, the Palatini conclusions fail necessarily, however, a good number of properties of the solutionsremain. The framework and proofs are built up in detail.