Black holes and stars in Horava-Lifshitz theory with projectability
  condition
  We systematically study spherically symmetric static spacetimes filled with a
fluid in the Horava-Lifshitz theory of gravity with the projectability
condition, but without the detailed balance. We establish that when the
spacetime is spatially Ricci flat the unique vacuum solution is the de Sitter
Schwarzshcild solution, while when the spacetime has a nonzero constant
curvature, there exist two different vacuum solutions; one is an (Einstein)
static universe, and the other is a new spacetime. This latter spacetime is
maximally symmetric and not flat. We find all the perfect fluid solutions for
such spacetimes, in addition to a class of anisotropic fluid solutions of the
spatially Ricci flat spacetimes. To construct spacetimes that represent stars,
we investigate junction conditions across the surfaces of stars and obtain the
general matching conditions with or without the presence of infinitely thin
shells. It is remarkable that, in contrast to general relativity, the radial
pressure of a star does not necessarily vanish on its surface even without the
presence of a thin shell, due to the presence of high order derivative terms.
Applying the junction conditions to our explicit solutions, we show that it is
possible to match smoothly these solutions (all with nonzero radial pressures)
to vacuum spacetimes without the presence of thin matter shells on the surfaces
of stars.
