Abstract
In this paper, we will analyze the energy dependent deformation of massive gravity using the formalism of massive gravity's rainbow. So, we will use the Vainshtein mechanism and the dRGT mechanism for the energy dependent massive gravity, and thus analyze a ghost free theory of massive gravity's rainbow. We study the energy dependence of a time-dependent geometry, by analyzing the radiating Vaidya solution in this theory of massive gravity's rainbow. The energy dependent deformation of this Vaidya metric will be performed using suitable rainbow functions.
Highlights
It is expected that the usual energy-momentum dispersion relation will get deformed in the UV limit due to quantum gravitational effects
As the usual energy-momentum dispersion relation is fixed by Lorentz symmetry, the deformation of the usual energy-momentum dispersion relation in the UV limit seems to indicate a breaking of Lorentz symmetry in the UV limit
It may be noted that the threshold anomalies are only predicted by deformations where the usual energy-momentum dispersion relation is deformed by a preferred reference frame, and they do not occur in deformation where no such preferred reference frame exists [10]
Summary
It is expected that the usual energy-momentum dispersion relation will get deformed in the UV limit due to quantum gravitational effects. As Vaidya soltion is important in string theory, and string theory can be used to motivate a rainbow deformation of massive gravity, we we will study the the Vaidya spacetime, massive gravity’s rainbow. It may be noted even though Vaidya solution has been studied in gravity’s rainbow [84] it has not been studied in massive gravity’s rainbow, and so such it is interesting to analyze the Vaidya solution in massive gravity’s rainbow
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