Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?

• Published in: arXiv.org
• Main Authors: Yi-Zen Chu, Park, Sohyun
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.01.2019
• Subjects: Energy conservation; Fluxes; Gravitation; Gravitational waves; Momentum; Physics - Cosmology and Nongalactic Astrophysics; Physics - General Relativity and Quantum Cosmology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1811.04647

Energy-momentum conservation requires the associated gravitational fluxes on an asymptotically flat spacetime to scale as \(1/r^2\), as \(r \to \infty\), where \(r\) is the distance between the observer and the source of the gravitational waves. We expand the equations-of-motion for the Deser-Woodard nonlocal gravity model up to quadratic order in metric perturbations, to compute its gravitational energy-momentum flux due to an isolated system. The contributions from the nonlocal sector contains \(1/r\) terms proportional to the acceleration of the Newtonian energy of the system, indicating such nonlocal gravity models may not yield well-defined energy fluxes at infinity. In the case of the Deser-Woodard model, this divergent flux can be avoided by requiring the first and second derivatives of the nonlocal distortion function \(f[X]\) at \(X=0\) to be zero, i.e., \(f'[0] = 0 = f''[0]\). It would be interesting to investigate whether other classes of nonlocal models not involving such an arbitrary function can avoid divergent fluxes.