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arXiv 2406.19147gr-qchep-thmath-phmath.MP
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二次引力中的一类新的非爱因斯坦 pp-波解

New class of non-Einstein pp-wave solutions to quadratic gravity

Sjors Heefer, Lorens F. Niehof, Andrea Fuster

AI总结:

本文在二次引力中构造了一族具有任意常曲率波面的新 pp-波精确真空解,其中非平坦波面情形为非爱因斯坦解,并证明场方程可化为线性双调和方程,从而给出通解及显式例子。

摘要:

我们得到了二次引力中一族新的精确真空解,这些解描述具有二维波面的 pp-波,且波面可以具有任意给定的常曲率。当波面为平坦时,我们恢复了由 Madsen 得到的 Peres 波,其中一部分恰好构成广义相对论的真空 pp-波。另一方面,如果波面具有非零常曲率,则我们所有的解都是非爱因斯坦的(即它们不满足爱因斯坦真空方程,无论是否带有宇宙学常数),并且我们发现曲率与宇宙学常数的值线性相关。我们证明了真空场方程可简化为弯曲波面上的一个简单的线性双调和方程,因此,通解可以明确写出。我们还提供了一些简单的显式例子。

英文摘要:

We obtain a new family of exact vacuum solutions to quadratic gravity that describe pp-waves with two-dimensional wave surfaces that can have any prescribed constant curvature. When the wave surfaces are flat we recover the Peres waves obtained by Madsen, a subset of which forms precisely the vacuum pp-waves of general relativity. If, on the other hand, the wave surfaces have non-vanishing constant curvature then all our solutions are non-Einstein (i.e. they do not solve Einstein's equations in vacuum, with or without cosmological constant) and we find that the curvature is linearly related to the value of the cosmological constant. We show that the vacuum field equations reduce to a simple linear biharmonic equation on the curved wave surfaces, and as consequence, the general solution can be written down. We also provide some simple explicit examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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