Holographic description of three dimensional Godel black hole

Three dimensional G\"{o}del black hole is a solution to Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We have studied the hidden conformal symmetry for massive scalar field without any additional condition in the background of three dimensional non-extremal and extremal G\"{o}del black holes. This conformal symmetry is uncovered by the observation that the radial wave equations in both cases can all be rewritten in the form of $SL(2, R)$ Casimir operators through introducing two sets of conformal coordinates to write the $SL(2, R)$ generators. At last, we give the holographic dual descriptions of Bekenstein-Hawking entropies of non-extremal and extremal black holes from Cardy formula of conformal field theory.Comment: 7 pages, no figur

Superradiant instability of the charged scalar field in stringy black hole mirror system

It has been shown that the mass of the scalar field in the charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against the massive charged scalar perturbation. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the unstable superradiant modes is derived by using the asymptotic matching method. It is also pointed out that the black hole mirror system becomes extremely unstable for a large charge $q$ of scalar field and the small mirror radius $r_m$.Comment: 5 pages, no figure, published versio

On The Memory Scalability of Spectral Clustering Algorithms

Spectral clustering has lots of advantages compared to previous more traditional clustering methods, such as k-means and Gaussian Mixture Models (GMM), and is popular since it was introduced. However, there are two major challenges, speed scalability and memory scalability, that impede the wide applications of spectral clustering. The first challenge has been addressed recently by Chen [1] [2] in the special setting of sparse or low dimensional data sets. In this work, we will first review the recent study by Chen that speeds up spectral clustering. Then we will propose three new computational methods for the same special setting of sparse or low dimensional data to address the memory challenge when the data sets are too large to be fully loaded into computer memory and when the data sets are collected sequentially. Numerical experiment results will be presented to demonstrate the improvements from these methods. Based on the experiments, the proposed methods show effective results on both simulated and real-world data