New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

Abstract

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.

7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Grav

References in corpus (2)

• An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'
• Integration in the GHP formalism II: An operator approach for spacetimes with killing vectors, with applications to twisting type n spaces

Cited by in corpus (3)

• Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries
• Lower-order ODEs to determine new twisting type N Einstein spaces via CR geometry
• Twisting type-N vacuum fields with a group $H_2$