Quasinormal modes and hidden conformal symmetry in the Reissner-Nordstrom black hole

It is shown that the scalar wave equation in the near-horizon limit respects a hidden SL(2,R) invariance in the Reissner-Nordstrom (RN) black hole spacetimes. We use the SL(2,R) symmetry to determine algebraically the purely imaginary quasinormal frequencies of the RN black hole. We confirm that these are exactly quasinormal modes of scalar perturbation around the near-extremal black hole.Comment: 17 pages, 1 figure, version to appear in EPJ

Slowly rotating black holes in the Horava-Lifshitz gravity

We investigate slowly rotating black holes in the Ho\v{r}ava-Lifshitz (HL) gravity. For $\Lambda_W=0$ and $\lambda=1$, we find a slowly rotating black hole of the Kehagias-Sfetsos solution in asymptotically flat spacetimes. We discuss their thermodynamic properties by computing mass, temperature, angular momentum, and angular velocity on the horizon.Comment: 12 pages, no figures, version to appear in EPJ

Extremal black holes in the Ho\v{r}ava-Lifshitz gravity

We study the near-horizon geometry of extremal black holes in the $z=3$ Ho\v{r}ava-Lifshitz gravity with a flow parameter $\lambda$. For $\lambda>1/2$, near-horizon geometry of extremal black holes are AdS$_2 \times S^2$ with different radii, depending on the (modified) Ho\v{r}ava-Lifshitz gravity. For $1/3\le \lambda \le 1/2$, the radius $v_2$ of $S^2$ is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein-Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein-Hawking entropy of extremal black holes.Comment: 18 pages, v2:some points on Lifshitz black holes claified, v3: version to appear in EJP

Does the enhancement observed in γγ→DDˉ\gamma\gamma\to D\bar{D} contain two PP-wave higher charmonia?

Solved is a new puzzle raised by the observation of an enhancement structure Z(3930) in $\gamma\gamma\to D\bar{D}$. If categorizing Z(3930) as $\chi_{c2}(2P)$ suggested by Belle and BaBar, we must explain why $\chi_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the $D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930) enhancement structure may contain two $P$-wave higher charmonia {$\chi_{c0}(2P)$} and $\chi_{c2}(2P)$. We show that this assumption is supported by our analysis of the $D\bar{D}$ invariant mass spectrum and $\cos\theta^\ast$ distribution of $\gamma\gamma\to D\bar{D}$. This observation would not only provide valuable information of two P-wave higher charmonia $\chi_{c0}(2P)$ and $\chi_{c2}(2P)$, but also serve as the crucial test of our novel proposal to the observed enhancement structure Z(3930), especially at the forthcoming BelleII and the approved SuperB.Comment: 5 pages, 2 tables, 3 figures. More contents and discussions adde

The absence of the Kerr black hole in the Ho\v{r}ava-Lifshitz gravity

We show that the Kerr metric does not exist as a fully rotating black hole solution to the modified Ho\v{r}ava-Lifshitz (HL) gravity with $\Lambda_W=0$ and $\lambda=1$ case. We perform it by showing that the Kerr metric does not satisfy full equations derived from the modified HL gravity.Comment: 35 pages, no figure

Two charged strangeonium-like structures observable in the Y(2175)→ϕ(1020)π+π−Y(2175) \to \phi(1020)\pi^{+} \pi^{-} process

Via the Initial Single Pion Emission (ISPE) mechanism, we study the $\phi(1020)\pi^{+}$ invariant mass spectrum distribution of $Y(2175) \to \phi(1020)\pi^{+} \pi^{-}$. Our calculation indicates there exist a sharp peak structure ($Z_{s1}^+$) close to the $K\bar{K}^\ast$ threshold and a broad structure ($Z_{s2}^+$) near the $K^\ast\bar{K}^\ast$ threshold. In addition, we also investigate the $\phi(1680) \to \phi(1020)\pi^{+} \pi^{-}$ process due to the ISPE mechanism, where a sharp peak around the $K\bar{K}^\ast$ threshold appears in the $\phi(1020)\pi^{+}$ invariant mass spectrum distribution. We suggest to carry out the search for these charged strangeonium-like structures in future experiment, especially Belle II, Super-B and BESIII.Comment: 7 pages, 5 figures. Accepted by Eur. Phys. J.

Does entropic force always imply the Newtonian force law?

We study the entropic force by introducing a bound $S \le A^{3/4}$ between entropy and area which was derived by imposing the non-gravitational collapse condition. In this case, applying a modified entropic force to this system does not lead to the Newtonian force law.Comment: 11 pages, version to appear in EPJ

Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

Continuous Percolation Phase Transitions of Two-dimensional Lattice Networks under a Generalized Achlioptas Process

The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability $p$. At $p=0.5$, the GAP becomes the random growth model and leads to the minority product rule at $p=1$. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with $0.5 \le p \le 1$ are always continuous and their critical exponents depend on $p$. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter $p$ in addition.Comment: 7 pages, 14 figures, accepted for publication in Eur. Phys. J.

Caustic avoidance in Horava-Lifshitz gravity

There are at least four versions of Horava-Lishitz gravity in the literature. We consider the version without the detailed balance condition with the projectability condition and address one aspect of the theory: avoidance of caustics for constant time hypersurfaces. We show that there is no caustic with plane symmetry in the absence of matter source if \lambda\ne 1. If \lambda=1 is a stable IR fixed point of the renormalization group flow then \lambda is expected to deviate from 1 near would-be caustics, where the extrinsic curvature increases and high-energy corrections become important. Therefore, the absence of caustics with \lambda\ne 1 implies that caustics cannot form with this symmetry in the absence of matter source. We argue that inclusion of matter source will not change the conclusion. We also argue that caustics with codimension higher than one will not form because of repulsive gravity generated by nonlinear higher curvature terms. These arguments support our conjecture that there is no caustic for constant time hypersurfaces. Finally, we discuss implications to the recently proposed scenario of ``dark matter as integration constant''.Comment: 19 pages; extended to general z \geq 3, typos corrected (v2); version accepted for publication in JCAP (v3