Levi-Civita cylinders with fractional angular deficit
J.P. Krisch, E.N. Glass
TL;DR
This paper introduces a fractional parameter into the Levi-Civita metric using Riemann-Liouville fractional integrals, revealing new behaviors in cylindrical solutions of general relativity.
Contribution
It extends the Levi-Civita solution by incorporating fractional calculus, providing a novel parameter that influences the geometry of relativistic cylinders.
Findings
New behavior in Gott-Hiscock cylinder
Novel features in Israel shell
Fractional index affects spacetime structure
Abstract
The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Nonlinear Dynamics and Pattern Formation · Fractional Differential Equations Solutions