Singularities in Horava-Lifshitz theory
  Singularities in $(3+1)$-dimensional Horava-Lifshitz (HL) theory of gravity
are studied. These singularities can be divided into scalar, non-scalar
curvature, and coordinate singularities. Because of the foliation-preserving
diffeomorphisms of the theory, the number of scalars that can be constructed
from the extrinsic curvature tensor $K_{ij}$, the 3-dimensional Riemann tensor
and their derivatives is much large than that constructed from the
4-dimesnional Riemann tensor and its derivatives in general relativity (GR). As
a result, even for the same spacetime, it may be singular in the HL theory but
not in GR. Two representative families of solutions with projectability
condition are studied, one is the (anti-) de Sitter Schwarzschild solutions,
and the other is the Lu-Mei-Pope (LMP) solutions written in a form satisfying
the projectability condition - the generalized LMP solutions. The (anti-) de
Sitter Schwarzschild solutions are vacuum solutions of both HL theory and GR,
while the LMP solutions with projectability condition satisfy the HL equations
coupled with an anisotropic fluid with heat flow. It is found that the scalars
$K$ and $K_{ij}K^{ij}$ are singular only at the center for the de Sitter
Schwarzschild solution, but singular at both the center and $ r =
(3M/|\Lambda|)^{1/3}$ for the anti-de Sitter Schwarzschild solution. The
singularity at $ r = (3M/|\Lambda|)^{1/3}$ is absent in GR. In addition, all
the generalized LMP solutions have two scalar curvature singularities, located
at either $r = 0$ and $r=r_{s} > 0$, or $r=r_{1}$ and $r= r_{2}$ with $r_{2} >
r_{1} > 0$, or $r=r_{s} > 0$ and $r = \infty$, depending on the choice of the
free parameter $\lambda$.
