Gravitational Instantons from Minimal Surfaces
نویسنده
چکیده
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 V II0, 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.
منابع مشابه
Gravitational Instantons Derived from Minimal Surfaces
The interest in instantons originates from the discovery of finite-action solutions of the classical Yang-Mills equations, instantons [1]-[3], which are localized in imaginary time. They provide the dominant contribution to the path-integral in the quantization of the Yang-Mills fields. The expectation that their gravitational counterparts should play a similar role in the path-integral approac...
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