Twisting type-N vacuum fields with a group $H_2$

Abstract

We derive the equations corresponding to twisting type-N vacuum gravitational fields with one Killing vector and one homothetic Killing vector by using the same approach as that developed by one of us in order to treat the case with two non-commuting Killing vectors. We study the case when the homothetic parameter $\varphi$ takes the value -1, which is shown to admit a reduction to a third-order real ordinary differential equation for this problem, similar to that previously obtained by one of us when two Killing vectors are present.

LaTeX, 11 pages. To be published in Classical and Quantum Gravity

References in corpus (2)

• An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'
• New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

Cited by in corpus (2)

• Gravitational wave solutions of quadratic curvature gravity using a null coframe formulation
• On twisting type $[\text{N}]\otimes [\text{N}]$ Ricci flat complex spacetimes with two homothetic symmetries