Lemaitre-Tolman-Bondi Static Universe in Rastall-like Gravity
  In this work, we try to obtain a stable Lemaitre-Tolman-Bondi (LTB) static
universe, which is spherically symmetric and radially inhomogeneous. However,
this is not an easy task, and fails in general relativity (GR) and various
modified gravity theories, because the corresponding LTB static universes must
reduce to the Friedmann-Robertson-Walker (FRW) static universes. We find a way
out in a new type of modified gravity theory, in which the conservation of
energy and momentum is broken. In this work, we have proposed a novel
modification to the original Rastall gravity. In some sense, our Rastall-like
gravity is essentially different from GR and the original Rastall gravity. In
this Rastall-like gravity, LTB static solutions have been found. The stability
of LTB static universe against both the homogeneous and the inhomogeneous
scalar perturbations is also discussed in details. We show that a LTB static
universe can be stable in this Rastall-like gravity.
