No Ghost State in the Brane World

We discuss the role of the trace part of metric fluctuations $h_{MN}$ in the Randall-Sundrum scenario of gravity. Without the matter, this field ($h=\eta^{MN}h_{MN}$) is a gauge-dependent term, and thus it can be gauged away. But, including the uniform source $\tilde{T}_{MN}$, this field satisfies the linearized equation $\Box_4 h =16\pi G_5 T^{\mu}_{\mu}$. This may correspond to the scalar $\xi^5$ in the bending of the brane due to the localized source. Considering the case of longitudinal perturbations ($h_{5\mu} =h_{55}=0$), one finds the source relation $\tilde{T}^{\mu}_{\mu}=2\tilde{T}_{55}$, which leads to the ghost states in the massive modes. In addition, if one requires $T_{44}=2(T_{22}+T_{33})$, it is found that in the limit of $m^2_h \to 0$ we have the massless spin-2 propagation without the ghost state. This exactly corresponds to the same situation as in the intermediate scales of Gregory-Rubakov-Sibiryakov (GRS) model.Comment: 7 pages, no figure, the version to appear in PLB, comments on the matter source and references added, main results unchange

Phase transitions for the topological de Sitter spaces and Schwarzschild-de Sitter black hole

We study whether the Hawking-Page phase transition may occur in topological de Sitter spaces (TdS) and Schwarzschild-de Sitter black hole (SdS). We show that at the critical temperature $T=T_1$, TdS with hyperbolic cosmological horizon can make the Hawking-Page transition from the zero mass de Sitter space to TdS. It is also shown that there is no Hawking-Page transition for TdS with Ricci-flat and spherical horizons, when the zero mass de Sitter space is taken as the thermal background. Also we find that the SdS undergoes a different phase transition at T=0 which the Nariai black hole is formed. Finally we connect our results to the dS/CFT correspondence.Comment: 17 pages, 9 eps figures, title slightly changed version to appear in PL

Chiral gravitational waves from z=2 Ho\v{r}ava-Lifshitz gravity

We construct the chiral gravitational waves from the $z=2$ Ho\v{r}ava-Lifshitz gravity with gravitational Chern-Simons term in the de Sitter and Minkowski backgrounds. These gravitational waves which show a feature of the Ho\v{r}ava-Lifshitz gravity may be related to the generalized uncertainty principle. In addition, we find the classical and quantum IR-UV transition rules in the $z=2$ Ho\v{r}ava-Lifshitz gravity.Comment: 14 pages, version to appear in PL

ADM mass and quasilocal energy of black hole in the deformed Ho\v{r}ava-Lifshitz gravity

Inspired by the Einstein-Born-Infeld black hole, we introduce the isolated horizon to study the Kehagias-Sfetsos (KS) black hole in the deformed Ho\v{r}ava-Lifshitz gravity. This is because the KS black hole is more close to the Einstein-Born-Infeld black hole than the Reissner-Nordstr\"om black hole. We find the horizon and ADM masses by using the first law of thermodynamics and the area-law entropy. The mass parameter $m$ is identified with the quasilocal energy at infinity. Accordingly, we discuss the phase transition between the KS and Schwarzschild black holes by considering the heat capacity and free energy.Comment: 17 pages, 2 figure