Riemann-Liouville Fractional Einstein Field Equations

Joakim Munkhammar

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arXiv · 1003.4981

Riemann-Liouville Fractional Einstein Field Equations

Joakim Munkhammar

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Abstract

In this paper we establish a fractional generalization of Einstein field equations based on the Riemann-Liouville fractional generalization of the ordinary differential operator $\partial_μ$. 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.

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Joakim Munkhammar. 2010-03-18. Riemann-Liouville Fractional Einstein Field Equations. https://arxiv.org/abs/1003.4981

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