TL;DR
This paper explores the theoretical concept of anti-gravitating particles, defining their properties, equations of motion, and how they interact with regular matter within the framework of general relativity.
Contribution
It introduces a formalism for anti-gravitating fields, derives their equations of motion, and analyzes their impact on Einstein's field equations, highlighting their suppressed interaction at the Planck scale.
Findings
Anti-gravitating fields have positive kinetic energy.
They can contribute negatively to Einstein's equations.
Interaction between matter and anti-gravitating fields is Planck-scale suppressed.
Abstract
The possibility of a symmetry between gravitating and anti-gravitating particles is examined. The properties of the anti-gravitating fields are defined by their behavior under general diffeomorphisms. The equations of motion and the conserved canonical currents are derived, and it is shown that the kinetic energy remains positive whereas the new fields can make a negative contribution to the source term of Einstein's field equations. The interaction between the two types of fields is naturally suppressed by the Planck scale.
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