Chern-Simons Modification of General Relativity

TL;DR

This paper extends general relativity by incorporating a four-dimensional Chern-Simons term, leading to modified gravitational wave properties and hidden symmetry breaking, while preserving key solutions like Schwarzschild.

Contribution

It introduces a novel four-dimensional Chern-Simons modification of general relativity with a fixed embedding coordinate, revealing new gravitational wave features and hidden symmetry breaking.

Findings

Schwarzschild solution remains valid.

Gravitational waves have two polarizations traveling at light speed.

Gravitational wave intensities are affected by the modification.

Abstract

General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant in its time component. The theory is identical to one in which the embedding coordinate is itself a dynamical variable, rather than a fixed, external quantity. Consequently diffeomorphism symmetry breaking is hidden in the modified theory: the Schwarzschild metric is a solution; gravitational waves possess two polarizations, each traveling at the velocity of light; a conserved energy-momentum (pseudo-) tensor can be constructed. The modification is visible in the intensity of gravitational radiation: the two polarizations of a gravity wave carry intensities that are suppressed/enchanced by the extension.