Gravitational Instantons from Minimal Surfaces

Details Gravitational Instantons from Minimal Surfaces Gravitational Instantons from Minimal Surfaces

1998-12-02

arxiv.org/abs/gr-qc/9812007v2

Class.Quant.Grav. 16 (1999) 631-642

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

One figure available by fax upon request. Abstract missing in original submission. Submitted to Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/16/2/024

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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