Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

Understand

We study the fractional gravity for spacetimes with non-integer dimensions.

• Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions.
• This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions.
• Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables.