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Black ring entropy from the weyl tensor

Frontiers of physics 2018年第5期13卷 221-230页

作者： Ze-Wei Zhao Chun-Kai Yu Nan Li Department of Physics College of Sciences Northeastern University Shenyang 110819 China Department of Modern Physics University of Science and Technology of China Hefei 230026 China

A black ring is an asymptotically fiat vacuum solution of the n-dimensional Einstein equations with an event horizon of topology S1× Sn-3. In this study, a connection between the black ring entropy and the weyl tensor Cμνλρ is explored by interpreting the weyl scalar invariant CμνλρCμνλρ as the entropy density in five-dimensional space-time. It is shown that the proper volume integral of CμνλρCμνλρfor a neutral black ring is proportional to the black ring entropy in the thin-ring limit. Similar calculations are extended to more general cases： a black string, a black ring with two angular momenta, and a black ring with a cosmological constant. The proportionality is also found to be valid for these complex black objects at the leading order.

关键词： black ring weyl tensor entropy Penrose conjecture

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Vanishing Results for the Cotton tensor on Gradient Quasi-Einstein Solitons

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Acta Mathematica Sinica,English Series 2021年第4期37卷 588-596页

作者： Lin Feng WANG School of Science Nantong UniversityNantong 226007P.R.China

In this paper we study on gradient quasi-Einstein solitons with a fourth-order vanishing condition on the weyl *** precisely,we show that for n≥4,the Cotton tensor of any ndimensional gradient quasi-Einstein soliton with fourth order f-divergence free weyl tensor is flat,if the manifold is compact,or noncompact but the potential function satisfies some growth *** corollaries,some local characterization results for the quasi-Einstein metrics are derived.

关键词： Gradient quasi-Einstein soliton Cotton tensor weyl tensor locally conformally flat

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A Global Rigidity Theorem for the Length of Concircular Curvature tensor on the Locally Conformally Symmetric Riemannian Manifold

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Journal of Mathematical Research with Applications 2020年第2期40卷 187-195页

作者： Shipei HU Department of Mathematics Jiaxing University

In this paper, we study the locally conformally symmetric closed Riemannian manifold, and establish a global rigidity theorem for the length of the concircular curvature vector.

关键词： conformally symmetric Riemannian curvature tensor concircular curvature vector weyl tensor Schouten tensor

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Airy, Beltrami, Maxwell, Einstein and Lanczos Potentials Revisited

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Journal of Modern Physics 2016年第7期7卷 699-728页

作者： J.-F. Pommaret CERMICS Ecole des Ponts ParisTech Marne-la-Vallée France

The purpose of this paper is to revisit the well known potentials, also called stress functions, needed in order to study the parametrizations of the stress equations, respectively provided by G.B. Airy (1863) for 2-dimensional elasticity, then by E. Beltrami (1892), J.C. Maxwell (1870) for 3-dimensional elasticity, finally by A. Einstein (1915) for 4-dimensional elasticity, both with a variational procedure introduced by C. Lanczos (1949, 1962) in order to relate potentials to Lagrange multipliers. Using the methods of Algebraic Analysis, namely mixing differential geometry with homological algebra and combining the double duality test involved with the Spencer cohomology, we shall be able to extend these results to an arbitrary situation with an arbitrary dimension n. We shall also explain why double duality is perfectly adapted to variational calculus with differential constraints as a way to eliminate the corresponding Lagrange multipliers. For example, the canonical parametrization of the stress equations is just described by the formal adjoint of the components of the linearized Riemann tensor considered as a linear second order differential operator but the minimum number of potentials needed is equal to for any minimal parametrization, the Einstein parametrization being “in between” with potentials. We provide all the above results without even using indices for writing down explicit formulas in the way it is done in any textbook today, but it could be strictly impossible to obtain them without using the above methods. We also revisit the possibility (Maxwell equations of electromagnetism) or the impossibility (Einstein equations of gravitation) to obtain canonical or minimal parametrizations for various equations of physics. It is nevertheless important to notice that, when n and the algorithms presented are known, most of the calculations can be achieved by using computers for the corresponding symbolic computations. Finally, though the paper is mathemati

关键词： Stress Equations Stress Functions Elasticity Theory Lagrange Multipliers Formal Adjoint Control Theory General Relativity Einstein Equations Lanczos Potentials Algebraic Analysis Riemann tensor weyl tensor

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