The fundamental physical importance of generic off-diagonal solutions and Grigori Perelman entropy in the Einstein gravity theory

IF 2.8 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
Sergiu I. Vacaru, Elşen Veli Veliev
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引用次数: 0

Abstract

The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric task. Physically important solutions in GR were constructed using diagonal ansatz for metrics with maximum 4 independent coefficients. The Einstein equations can be solved in exact or parametric forms determined by some integration constants for corresponding assumptions on spherical or cylindric spacetime symmetries. The anholonomic frame and connection deformation method allows us to construct generic off-diagonal solutions described by 6 independent coefficients of metrics depending, in general, on all spacetime coordinates. New types of exact and parametric solutions are determined by generating and integration functions and (effective) generating sources. They may describe vacuum gravitational and matter fields solitonic hierarchies; locally anisotropic polarizations of physical constants for black holes, wormholes, black toruses, or cosmological solutions; various types of off-diagonal deformations of horizons etc. The additional degrees of freedom (related to off-diagonal coefficients) can be used to describe dark energy and dark matter configurations and elaborate locally anisotropic cosmological scenarios. In general, the generic off-diagonal solutions do not involve certain hypersurface or holographic configurations and can’t be described in the framework of the Bekenstein-Hawking thermodynamic paradigm. We argue that generalizing the concept of G. Perelman’s entropy for relativistic Ricci flows allows us to define and compute geometric thermodynamic variables for all possible classes of solutions in GR.

爱因斯坦引力理论中一般非对角解和Grigori Perelman熵的基本物理重要性
广义相对论中的引力场方程由一个复杂的非线性偏微分方程组组成。以非对角线形式求解这类方程通常是一项困难的解析或数值任务。利用最大4个独立系数度量的对角方差构造了GR的物理重要解。爱因斯坦方程可以用精确形式或参数形式求解,由相应的球面或圆柱时空对称性假设的积分常数决定。非完整框架和连接变形方法允许我们构造由6个独立度量系数描述的一般非对角线解,通常依赖于所有时空坐标。通过生成和积分函数和(有效的)生成源,确定了新型的精确和参数解。它们可以描述真空引力场和物质场的孤子层次;黑洞、虫洞、黑环体或宇宙学解的物理常数的局部各向异性极化各种类型的视界非对角线变形等。额外的自由度(与非对角线系数有关)可以用来描述暗能量和暗物质的构型,并详细说明局部各向异性的宇宙学情景。一般来说,一般非对角线解不涉及某些超曲面或全息构型,不能在贝肯斯坦-霍金热力学范式的框架内描述。我们认为推广相对论里奇流的G. Perelman熵的概念使我们能够定义和计算广义相对论中所有可能解的几何热力学变量。
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来源期刊
General Relativity and Gravitation
General Relativity and Gravitation 物理-天文与天体物理
CiteScore
4.60
自引率
3.60%
发文量
136
审稿时长
3 months
期刊介绍: General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation. It welcomes in particular original articles on the following topics of current research: Analytical general relativity, including its interface with geometrical analysis Numerical relativity Theoretical and observational cosmology Relativistic astrophysics Gravitational waves: data analysis, astrophysical sources and detector science Extensions of general relativity Supergravity Gravitational aspects of string theory and its extensions Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations Quantum field theory in curved spacetime Non-commutative geometry and gravitation Experimental gravity, in particular tests of general relativity The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.
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