An Interesting Form of the Einstein-Palatini Action with Cosmological Constant Λ

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2025-12-01 Epub Date: 2025-12-31 DOI:10.1016/S0034-4877(25)00079-5

Janusz Garecki

引用次数: 0

Abstract

We show in a new way that the general relativity (GR) action (and Lagrangian) in recent Einstein-Palatini (EP) formulation is equivalent in four dimensions to the action (and Lagrangian) of a gauge field.

Firstly, we present EP action with cosmological constant Λ ≢ 0 and derive Einstein field equations from it. Then, we consider this action in terms of the corrected curvature Ω_cor. We will see that in terms of Ω_cor the EP action takes the typical form for action of a gauge field. Finally, we give a geometrical interpretation of the corrected curvature Ω_cor.

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爱因斯坦-帕拉蒂尼作用与宇宙常数的有趣形式Λ

我们以一种新的方式证明了广义相对论（GR）作用（和拉格朗日量）在最近的爱因斯坦-帕拉蒂尼（EP）公式中与规范场的作用（和拉格朗日量）在四维上是等价的。首先，我们用宇宙学常数Λ 0表示EP作用，并由此推导出爱因斯坦场方程。然后，我们考虑这个作用的修正曲率Ωcor。我们将看到，在Ωcor中，EP动作采用规范场动作的典型形式。最后，我们给出了修正曲率的几何解释Ωcor。

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

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.