Spherically symmetric spacetimes in massive gravity

Abstract

We explore spherically symmetric stationary solutions, generated by "stars" with regular interiors, in purely massive gravity. We reexamine the claim that the resummation of non-linear effects can cure, in a domain near the source, the discontinuity exhibited by the linearized theory as the mass m of the graviton tends to zero. First, we find analytical difficulties with this claim, which appears not to be robust under slight changes in the form of the mass term. Second, by numerically exploring the inward continuation of the class of asymptotically flat solutions, we find that, when m is "small", they all end up in a singularity at a finite radius, well outside the source, instead of joining some conjectured "continuous" solution near the source. We reopen, however, the possibility of reconciling massive gravity with phenomenology by exhibiting a special class of solutions, with "spontaneous symmetry breaking" features, which are close, near the source, to general relativistic solutions and asymptote, for large radii, a de Sitter solution of curvature ∼ m 2 .

Galileon hairs of Dyson spheres, Vainshtein’s coiffure and hirsute bubbles

“…Substituting this in the junction conditions (12), and subtracting the second from the third of (12), yields the derivatives just outside,…”

“…Here we complete the discussion by showing how to construct the realistic fields of Dyson spheres by using the junction conditions (12) to connect the interior and the exterior into the complete configuration. After we take the interior of the Dyson sphere to be a ball of Minkowski space, we must pick the same coordinate gauge as the exterior metric, and further ensure that in this gauge the Dyson sphere sits at the same coordinate location r 0 as measured from the outside.…”

“…There were attempts to integrate background equations in purported nonlinear extensions of FierzPauli theory [12,13], but they have conflicting outcomes. In [12], it was noted that the solutions which are flat at infinity do not connect onto the smooth interiors near sources, but become singular in between the desired asymptotic regions.…”

“…There were attempts to integrate background equations in purported nonlinear extensions of FierzPauli theory [12,13], but they have conflicting outcomes. In [12], it was noted that the solutions which are flat at infinity do not connect onto the smooth interiors near sources, but become singular in between the desired asymptotic regions. More recently, in [13], numerical exploration suggested otherwise, and those authors claimed that the solutions which extrapolate smoothly between mass sources and asymptotic infinity do exist.…”

Light bending as a probe of the nature of dark energy

“…This parametrization covers SSS metrics of well studied gDE models: [12] corresponds to the non-perturbative solution found by Vainshtein (V) for a massive graviton [13] with mass m g . Massive gravity (MG) is an alternative to a cosmological constant [3];…”