Singularities in Horava–Lifshitz theory

Abstract

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 Kij , 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 Kij K ij are singular only at the center for the de Sitter Schwarzschild solution, but singular at both the center and r = (3M/|Λ|)for the anti-de Sitter Schwarzschild solution. The singularity at r = (3M/|Λ|) 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 = rs > 0, or r = r1 and r = r2 with r2 > r1 > 0, or r = rs > 0 and r = ∞, depending on the choice of the free parameter λ.PACS numbers: 98.80.Cq; 98.80.Bp

Lifshitz spacetimes, solitons, and generalized BTZ black holes in quantum gravity at a Lifshitz point

“…If it is forced to do so, the resulted solutions usually do not satisfy the corresponding HL field equations. Examples of this kind were provided in [99]. However, it can be shown that the current case is an exception.…”

Quantization of 2d Hořava gravity: Nonprojectable case

“…It should be noted that this identification is only in the action level, as the two theories have different gauge symmetries, and the 2d HL theory is only a gauge-fixed form of the 2d Einstein-aether one. Contrary examples can be found in [20,23].…”

Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory

“…Then, from Eq. (5.5), it can be seen that the spacetime is singular at r s ≡ (2m 2 ) 1/3 [46]. This is different from GR, in which the only singularity of the anti-de Sitter Schwarzschild solution is at r = 0.…”

“…Otherwise, the resulting solutions do not satisfy the field equations. Explicit examples of this kind were given in [46]. In [22], the isotropic coordinate ρ was introduced, 24) in terms of which the metric (4.6) takes the form, 25) which is non-singular for ρ > 0.…”