2015/01/25 by Hemza Azri, Hemza Azrı · 2 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Einstein tensor #Exact solutions in general relativity #Geometry #Gravitation #Gravitational field #Lanczos tensor #Linearized gravity #Mathematical physics #Mathematics of general relativity #Maxwell's equations in curved spacetime #Numerical relativity #Physics #Quantum mechanics #Ricci curvature #Riemann curvature tensor #Spacetime #Stress–energy tensor #Tensor density #Tensor field #Weyl tensor #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1088/0264-9381/32/6/065009
published as Class.Quant.Grav. 32, 065009 (2015)
arxiv created 2015/01/25 · openalex publication_date 2015/02/26 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formulate Eddington's affine gravity in a spacetime that is immersed in a larger eight-dimensional space endowed with a hypercomplex structure. The dynamical equation of the first immersed Ricci-type tensor leads to gravitational field equations which include matter. We also study the dynamical effects of the second Ricci-type tensor when added to the Lagrangian density. A simple Lagrangian density constructed from a combination of the standard Ricci tensor and a new tensor field that appears due to the immersion, leads to gravitational equations in which the vacuum energy gravitates with a different cosmological strength as in Demir (2014 Phys. Rev. D 90 064017 ), rather than with Newton's constant. As a result, the tiny observed curvature is reproduced due to large hierarchies rather than fine tuning.