Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?. (arXiv:1811.04647v1 [gr-qc])

Does nonlocal gravity yield divergent gravitational energy-momentum fluxes?. (arXiv:1811.04647v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Chu_Y/0/1/0/all/0/1">Yi-Zen Chu</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Park_S/0/1/0/all/0/1">Sohyun Park</a>

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.

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.

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