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arXiv · gr-qc/9812007

Gravitational Instantons from Minimal Surfaces

A. N. Aliev·M. Hortacsu·J. Kalayci·Y. Nutku
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Abstract

Physical properties of gravitational instantons which are derivable from minimal surfaces in 3-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi Type $VII_0$, or E(2) which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

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A. N. Aliev, M. Hortacsu, J. Kalayci, Y. Nutku. 1998-12-09. Gravitational Instantons from Minimal Surfaces. https://doi.org/10.1088/0264-9381%2F16%2F2%2F024

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