Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner-Sharp mass in the Oppenheimer-Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.Comment: 16 pages (single column), v3 (major revision): more discussion on a compact star included, a comparison with previous results given in the appendix, more references adde

Conserved charges in general relativity

We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved space–time with Killing vectors. This definition enables us to define energy and momentum for matter by the volume integral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner–Sharp mass in the Oppenheimer–Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold

Dynamics of Subcritical Bubbles in First Order Phase Transition

We derivate the Langevin and the Fokker-Planck equations for the radius of $O(3)$-symmetric subcritical bubbles as a phenomenological model to treat thermal fluctuation. The effect of thermal noise on subcritical bubbles is examined. We find that the fluctuation-dissipation relation holds and that in the high temperature phase the system settles down rapidly to the thermal equilibrium state even if it was in a nonequilibrium state initially. We then estimate the typical size of subcritical bubbles as well as the amplitude of fluctuations on that scale. We also discuss their implication to the electroweak phase transition.Comment: 13 pages, LaTex file, To appear in Progress of Theoretical Physic

Charge Conservation, Entropy Current, and Gravitation

We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.Comment: 14 pages, 2 figures, published versio

What does a quantum black hole look like?

We take a first step towards a holographic description of a black hole by means of a flow equation. We consider a free theory of multiple scalar fields at finite temperature and study its holographic geometry defined through a free flow of the scalar fields. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.Comment: 15 pages, 4 figures. v2: 16 pages, 4 figures, comment on entropy and a reference added, a figure and discussion improved. v3: published version in PL

A Similarity-Ranking Method on Semantic Computing for Providing Information-Services in Station-Concierge System

The prevalence of smartphones and wireless broadband networks have been progressing as a new Railway infomration environment.　According to the spread of such devices and information technology, various types of information can be obtained from databases connected to the Internet. One scenario of obtaining such a wide variety of information resources is in the phase of user’s transportation. This paper proposes an information provision system, named the Station Concierge System that matches the situation and intention of passengers. The purpose of this system is to estimate the needs of passengers like station staff or hotel concierge and to provide information resources that satisfy user’s expectations dynamically. The most important module of the system is constructed based on a new information ranking method for passenger intention prediction and service recommendation. This method has three main features, which are (1) projecting a user to semantic vector space by using her current context, (2) predicting the intention of a user based on selecting a semantic vector subspace, and (3) ranking the services by a descending order of relevant scores to the user’ intention. By comparing the predicted results of our method with those of two straightforward computation methods, the experimental studies show the effectiveness and efficiency of the proposed method. Using this system, users can obtain transit information and service map that dynamically matches their context

マトリックスメタロプロテアーゼと膵疾患

Matrix metalloproteinases (MMPs) is a family of collagenolytic enzymesand are associated with many pathological conditions. Especially, MMPs have a strong relation with tumor progression and invasion. In this review, we focused on association of MMPs and pancreatic diseases, and a potential treatment of MMPs inhibitors for pancreatic cancer.マトリックスメタロブロテアーゼ（MMP）は，コラーゲン分解能を有し，種々の疾患との関連性が示唆されている。とりわけ,癌の浸潤，転移には密接な関係があるとされている。また，MMP阻害剤を癌の治療に用いる試みもなされている。本稿ではMMPと膵疾患の関連性，MMP阻害剤の膵癌への応用の可能性について総説する