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Nonlocal classical theory of gravity: massiveness of nonlocality and mass shielding by nonlocality

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Abstract

Nonlocal generalization of classical (Newtonian) gravity field theory is proposed by using the general fractional calculus in the Luchko form. Nonlocal analogs of the standard Gauss’s law and the “local” potentiality of gravitational field are suggested in integral and differential forms. Nonlocality is described by the pairs of Sonin kernels that belong to the Luchko set. The general fractional vector calculus, which can be considered as nonlocal vector calculus, is used as a mathematical tool for formulation of nonlocal field theory. General fractional (GF) vector operators, such as GF flux, GF circulation, GF divergence, GF curl operators and GF gradient are defined to describe nonlocalities in space. Examples of using the general nonlocal Gauss’s law to calculate gravity fields are proposed for the case of spherically symmetric nonlocality and mass distribution. The nonlocal effects caused by nonlocality in space are discussed. Among such effects, the following effects are described: effects of mass shielding by nonlocality, violation of local potentiality by nonlocality, and violation of local solenoidality by nonlocality (massiveness of nonlocality). A possibility of using the nonlocal theory of gravity to explain some nonstandard properties of dark matter and dark energy through the properties of nonlocality is discussed.

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  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia, 119991

    Vasily E. Tarasov

  2. Department of Physics, 915, Moscow Aviation Institute (National Research University), Moscow, Russia, 125993

    Vasily E. Tarasov

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Tarasov, V.E. Nonlocal classical theory of gravity: massiveness of nonlocality and mass shielding by nonlocality. Eur. Phys. J. Plus 137, 1336 (2022). https://doi.org/10.1140/epjp/s13360-022-03512-x

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