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THE stress-energy tensor AND POHOZAEV'S IDENTITY FOR SYSTEMS

Acta Mathematica Scientia 2012年第1期32卷 433-439页

作者： N.D.Alikakos A.C.Faliagas Department of Mathematics University of Athens

Utilizing stress-energy tensors which allow for a divergence-free formulation, we establish Pohozaev＇s identity for certain classes of quasilinear systems with variational structure.

关键词： calculus of variations stress-energy tensor p-Lapacian minimal surface

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Monotonicity Formulas of EF-Critical Maps with Potential

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Journal of Mathematical Research with Applications 2015年第6期35卷 681-691页

作者： Yingbo HAN College of Mathematics and Information Science Xinyang Normal University

In this paper, we introduce the notion of EF-critical map with potential with respect to the functional EF,H(u). By using the stress-energy tensor, we obtain some monotonicity formulas and vanishing results for these ... 详细信息

关键词： EF-critical map with potential stress-energy tensor monotonicity formula

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A Re-Interpretation of Quasi-Local Mass

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Journal of Modern Physics 2022年第4期13卷 347-367页

作者： Edwin Eugene Klingman Cybernetic Micro Systems Inc. San Gregorio CA USA

Because the equivalence principle forbids local mass density, we cannot formulate general relativistic mass as an integral over mass density as in Newtonian gravity. This century-old problem was addressed forty years ago by Penrose, and many papers have since extended the concept. Currently there is no satisfactory physical understanding of the nature of quasi-local mass. In this paper I review the key issues, the current status, and propose an alternative interpretation of the problem of local mass and energy density for gravity systems from an information perspective.

关键词： Quasi-Local Mass Curved Space-Time Gravitational energy stress-energy tensor Encoding Information in Geometry Schwarzschild Metric

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Encoding energy-Density as Geometry

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Journal of Modern Physics 2021年第9期12卷 1190-1209页

作者： Edwin Eugene Klingman Cybernetic Micro Systems Inc. San Gregorio CA USA

Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time. Relativistic experiments support the “time-dilation” interpretation and others support “curved space-time” interpretation. In this, and related work, we investigate the key issues in terms of the intuitive space-time frame. In particular, we provide alternative approaches to explain “time dilation” and to explain the energy density for gravity systems. We approach the latter problem from an information perspective.

关键词： Curved Space-Time Gravitational energy stress-energy tensor Encoding Information in Geometry Time Dilation Equivalence Principle Minkowski Relation Schwarzschild Metric Linearized General Relativity Cosmology

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The Inverse Gravity Inflationary Theory of Cosmology

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Journal of Modern Physics 2016年第13期7卷 1762-1776页

作者： Edward A. Walker Mathematics Department Florida Memorial University Miami Gardens FL USA

Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expansion takes prominence over gravity. This assertion is referred to as the inverse gravity inflationary assertion. Thus, a correction to Newtonian gravitational force is introduced where a parameterized inverse gravity force term is incorporated into the classical Newtonian gravitational force equation where the inverse force term is negligible for distances less than the distance to which cosmological expansion takes prominence over gravity. Conversely, at distances greater than the distance to which cosmological expansion takes prominence over gravity. The inverse gravity term is shown to be dominant generating universal inflation. Gravitational potential energy is thence defined by the integral of the difference (or subtraction) between the conventional Newtonian gravitational force term and the inverse gravity term with respect to radius (r) which allows the formulation, incorporation, and mathematical description to and of gravitational redshift, the Walker-Robertson scale factor, the Robinson-Walker metric, the Klein-Gordon lagrangian, and dark energy and its relationship to the energy of the big bang in terms of the Inverse gravity inflationary assertion. Moreover, the dynamic pressure of the expansion of a cosmological fluid in a homogeneous isotropic universe is mathematically described in terms of the inverse gravity inflationary assertion using the stress-energy tensor for a perfect fluid. Lastly, Einstein’s field equations for the description of an isotropic and homogeneous universe are derived incorporating the mathematics of the inverse gravity inflationary assertion to fully show that the theoretical concept is potentially interwoven into the cosmological structure of the universe.

关键词： Isotropic and Homogeneous Universe Inverse Gravity Cosmological Inflation Gravitational Redshift Robertson-Walker Scale Factor Klein-Gordon Lagrangian Dark energy stress-energy tensor Friedman-Walker-Robertson Metric Photon

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