The 3+1 decomposition of Conformal Yano-Killing tensors and "momentary" charges for spin-2 field

TL;DR

This paper introduces a 3+1 decomposition approach to conformal Yano-Killing tensors, defining quasi-local gravitational charges for spin-2 fields, including a Coulomb-like solution, applicable to Schwarzschild-like spacetimes.

Contribution

It provides a novel 3+1 decomposition method for conformal Yano-Killing tensors to define momentary gravitational charges in spin-2 fields.

Findings

Presented a 'fully charged' Coulomb-like spin-2 solution.

Defined quasi-local gravitational charges using conformal Yano-Killing tensors.

Constructed momentary gravitational charges on initial surfaces for Schwarzschild-like spacetimes.

Abstract

The "fully charged" spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the "non-waving" part of the spin-2 field theory. Basic facts and definitions of the spin--2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3+1 decomposition leads to the construction of the momentary gravitational charges on initial surface which is applicable for Schwarzschild-like spacetimes.