arXiv 1001.01552010-01hep-thastro-ph.COgr-qchep-ph

Horava-Lifshitz理论中的奇点

Singularities in Horava-Lifshitz theory

Rong-Gen Cai, Anzhong Wang

备注：: Revtex4, six figures. Version to appear in Phys. Lett. B
发表信息：: Phys.Lett.B686:166-174,2010
DOI：: 10.1016/j.physletb.2010.02.053

摘要：

研究了$(3+1)$维Horava-Lifshitz（HL）引力理论的奇异性。这些奇点可以分为标量、非标量曲率和坐标奇点。由于该理论的叶理保持性，由非本征曲率张量$K_{ij}$、三维黎曼张量及其导数构造的标量的数目远大于由广义相对论（GR）中的四维黎曼张量及其导数构造的标量的数目.因此，即使对于同一时空，它在HL理论中也可能是奇异的，而在GR中则不是。本文研究了两类具有可投射条件的解，一类是（反）de Sitter Schwarzschild解，另一类是满足可投射条件的Lu-Mei-Pope（LMP）解--广义LMP解。（反）de Sitter Schwarzschild解是HL理论和GR的真空解，而具有可投射条件的LMP解满足与各向异性热流流体耦合的HL方程。发现标量$K$和$K_{ij}K^{ij}$对于de Sitter Schwarzschild解仅在中心奇异，而对于反de Sitter Schwarzschild解在中心和$ r = (3M/|Λ|)^{1/3}$都奇异.在$ r = (3M/|Λ|)^{1/3}$的奇异性是不存在的GR。此外，所有的广义LMP解决方案有两个标量曲率奇点，位于$r = 0$和$r=r_{s} > 0$，或$r=r_{1}$和$r= r_{2}$与$r_{2} > r_{1} > 0$，或$r=r_{s} > 0$和$r = \infty$，取决于自由参数$λ$的选择。

英文摘要：

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/|Λ|)^{1/3}$ 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 $r=r_{s} > 0$, 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 $λ$.

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摘要：

英文摘要：

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