2010/03/18 by Munkhammar, Joakim
#FOS: Physical sciences #General Physics (physics.gen-ph) #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.1003.4981
In this paper we establish a fractional generalization of Einstein field equations based on the Riemann-Liouville fractional generalization of the ordinary differential operator ∂μ. We show some elementary properties and prove that the field equations correspond to the regular Einstein field equations for the fractional order α= 1. In addition to this we show that the field theory is inherently non-local in this approach. We also derive the linear field equations and show that they are a generalized version of the time fractional diffusion-wave equation. We show that in the Newtonian limit a fractional version of Poisson's equation for gravity arises. Finally we conclude open problems such as the relation of the non-locality of this theory to quantum field theories and the possible relation to fractional mechanics.