On the Quaternion Transformation and Field Equations in Curved Space-Time

IF 0.8 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
B. C. Chanyal
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引用次数: 3

Abstract

In this paper, we use four-dimensional quaternionic algebra to describe space-time geodesics in curvature form. The transformation relations of a quaternionic variables are established with the help of basis-transformations of quaternion algebra. We deduce the quaternionic covariant derivative that explains how the quaternion components vary with scalar and vector fields. The quaternionic metric tensor and the geodesic equation are also discussed to describe the quaternionic line element in curved space-time. We examine a quaternionic metric tensor equation for the Riemannian Christoffel curvature tensor. We present the quaternionic Einstein’s field-like equation, which indicates that quaternionic matter and geometry are equivalent. Relevance of the work:In recent decades, hypercomplex algebra, viz., quaternion and octonions, has been widely used to explain various branches of physics. In this way, we have investigated quaternionic transformations and field equations in curved space-time. The present novel work will help to explain the characteristics of the curved space-time universe in terms of quaternion algebra. It can also be used to describe quaternionic gravitational waves, the black hole formulation, and so on.

弯曲时空中的四元数变换与场方程
本文利用四维四元数代数以曲率形式描述时空测地线。利用四元数代数的基变换,建立了四元数变量的变换关系。我们推导了四元数协变导数,解释了四元数成分如何随标量场和向量场变化。还讨论了四元数度量张量和测地线方程来描述弯曲时空中的四元数线素。我们研究了黎曼克里斯托费尔曲率张量的四元数度规张量方程。我们提出了四元数爱因斯坦类场方程,它表明四元数物质和几何是等价的。工作的相关性:近几十年来,超复杂代数,即四元数和八元数,已被广泛用于解释物理学的各个分支。用这种方法,我们研究了弯曲时空中的四元数变换和场方程。本文的新工作将有助于从四元数代数的角度解释弯曲时空宇宙的特征。它也可以用来描述四元数引力波,黑洞公式,等等。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.60
自引率
0.00%
发文量
37
审稿时长
>12 weeks
期刊介绍: To promote research in all the branches of Science & Technology; and disseminate the knowledge and advancements in Science & Technology
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