Gravitational instantons from minimal surfaces

Aliev A., Hortacsu M., Kalayci J., Nutku Y.

CLASSICAL AND QUANTUM GRAVITY, vol.16, no.2, pp.631-642, 1999 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 1999
  • Doi Number: 10.1088/0264-9381/16/2/024
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.631-642
  • Istanbul Technical University Affiliated: No


Physical properties of gravitational instantons which are derivable from minimal surfaces in three-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 V11(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.