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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tensor–vector–scalar gravity ： ウィキペディア英語版 Tensor–vector–scalar gravity Tensor–vector–scalar gravity (TeVeS),〔 〕 developed by Jacob Bekenstein in 2004, is a relativistic generalization of Mordehai Milgrom's Modified Newtonian dynamics (MOND) paradigm.〔 〕 The main features of TeVeS can be summarized as follows: * As it is derived from the action principle, TeVeS respects conservation laws; * In the weak-field approximation of the spherically symmetric, static solution, TeVeS reproduces the MOND acceleration formula; * TeVeS avoids the problems of earlier attempts to generalize MOND, such as superluminal propagation; * As it is a relativistic theory it can accommodate gravitational lensing. The theory is based on the following ingredients: * A unit vector field; * A dynamical scalar field; * A nondynamical scalar field; * A matter Lagrangian constructed using an alternate metric; * An arbitrary dimensionless function. These components are combined into a relativistic Lagrangian density, which forms the basis of TeVeS theory. ==Details== MOND〔 is a phenomenological modification of the Newtonian acceleration law. In Newtonian gravity theory, the gravitational acceleration in the spherically symmetric, static field of a point mass $M$ at distance $r$ from the source can be written as $$ a = -\frac, where $G$ is Newton's constant of gravitation. The corresponding force acting on a test mass $m$ is $$ F=ma. To account for the anomalous rotation curves of spiral galaxies, Milgrom proposed a modification of this force law in the form $$ F=\mu(a/a_0)ma, where $\backslash mu(x)$ is an arbitrary function subject to the following conditions: $$ \mu(x)=1~\mathrm~|x|\gg 1, $$ \mu(x)=x~\mathrm~|x|\ll 1. In this form, MOND is not a complete theory: for instance, it violates the law of momentum conservation. However, such conservation laws are automatically satisfied for physical theories that are derived using an action principle. This led Bekenstein〔 to a first, nonrelativistic generalization of MOND. This theory, called AQUAL (for A QUAdratic Lagrangian) is based on the Lagrangian $$ =-\fracf\left(\frac\right)-\rho\Phi, where $\backslash Phi$ is the Newtonian gravitational potential, $\backslash rho$ is the mass density, and $f(y)$ is a dimensionless function. In the case of a spherically symmetric, static gravitational field, this Lagrangian reproduces the MOND acceleration law after the substitutions $a=-\backslash nabla\backslash Phi$ and $\backslash mu(\backslash sqrt)=df(y)/dy$ are made. Bekenstein further found that AQUAL can be obtained as the nonrelativistic limit of a relativistic field theory. This theory is written in terms of a Lagrangian that contains, in addition to the Einstein–Hilbert action for the metric field $g\_$, terms pertaining to a unit vector field $u^\backslash alpha$ and two scalar fields $\backslash sigma$ and $\backslash phi$, of which only $\backslash phi$ is dynamical. The TeVeS action, therefore, can be written as $$ S_\mathrm=\int\left(_g+_s+_v\right)d^4x. The terms in this action include the Einstein–Hilbert Lagrangian (using a metric signature $()$ and setting the speed of light, $c=1$): $$ _g=-\fracR\sqrt, where $R$ is the Ricci scalar and $g$ is the determinant of the metric tensor. The scalar field Lagrangian is $$ _s=-\frac\left()\sqrt, with $h^=g^-u^\backslash alpha\; u^\backslash beta$, $l$ is a constant length, $k$ is the dimensionless parameter and $F$ an unspecified dimensionless function; while the vector field Lagrangian is $$ _v=-\frac\left(u_\nu-1)\right )\sqrt where $B\_=\backslash partial\_\backslash alpha\; u\_\backslash beta-\backslash partial\_\backslash beta\; u\_\backslash alpha$, while $K$ is a dimensionless parameter. $k$ and $K$ are respectively called the scalar and vector coupling constants of the theory. The consistency between the Gravitoelectromagnetism of the TeVeS theory and that predicted and measured by the general relativity leads to $K=\backslash frac$ .〔 〕 In particular, $\_v$ incorporates a Lagrange multiplier term that guarantees that the vector field remains a unit vector field. The function $F$ in TeVeS is unspecified. TeVeS also introduces a "physical metric" in the form $$ ^=e^g^-2u^\alpha u^\beta\sinh(2\phi). The action of ordinary matter is defined using the physical metric: $$ S_m=\int(_,f^\alpha,f^\alpha_,...)\sqrt_ are denoted by $|$. TeVeS solves problems associated with earlier attempts to generalize MOND, such as superluminal propagation. In his paper, Bekenstein also investigated the consequences of TeVeS in relation to gravitational lensing and cosmology. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tensor–vector–scalar gravity」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.