Conserving Integrals in [Non-]Metric Theories of Gravitation

TL;DR

This paper explores conserved quantities in metric and non-metric gravitational theories, proposing an alternative spinorial approach to construct conserved integrals like energy-momentum, building on Geroch's foundational work.

Contribution

It introduces a novel spinorial method for constructing conserved integrals in gravitational theories, extending Geroch's approach to include non-metric frameworks.

Findings

Conserved quantities can be derived from Killing vectors and symmetric tensors.

Spinorial fields provide an alternative way to construct conserved integrals.

The approach broadens the understanding of conservation laws in gravitational theories.

Abstract

In this work I present location to first mentioning to result of Robert Geroch Preprint deals with conserving quantities of metric gravitational theories They are constructed from Killing vector fields (if any exists) and symmetric tensors of arbitrary rank with vanishing divergence I also suggest alternative approach by introducing spinorial fields allowing to construct conserved integrals of energy-momentum etc