# Spacetimes with continuous linear isotropies III: null rotations

@article{MacCallum2021SpacetimesWC, title={Spacetimes with continuous linear isotropies III: null rotations}, author={Malcolm A. H. MacCallum}, journal={General Relativity and Gravitation}, year={2021} }

It is shown that in many of the possible cases local null rotation invariance of the curvature and its first derivatives is sufficient to ensure that there is an isometry group $$G_r$$
G
r
with $$r\ge 3$$
r
≥
3
acting on (a neighbourhood of) the spacetime and containing a null rotation isotropy. The exceptions where invariance of the second derivatives is additionally required to ensure this conclusion are Petrov type N Einstein spacetimes, spacetimes containing “pure radiation… Expand

#### References

SHOWING 1-10 OF 26 REFERENCES

Symmetry classes ofpp-waves

- Physics
- 1986

The isometry groups admitted by plane-fronted gravitational waves with parallel rays are determined without use of any field equations. New groups with 5, 6, and 7 parameters arise which cannot occur… Expand

Algebraically independent nth derivatives of the Riemannian curvature spinor in a general spacetime

- Physics
- 1986

Explicit sets of spinor nth derivatives of the Riemann curvature spinor for a general spacetime are specified for each n so that they contain the minimal number of components enabling all derivatives… Expand

On space-times admitting a three-parameter isometry group with two-dimensional null orbits

- Mathematics
- 1979

Space-times admitting a three-parameter group of motions acting on two-dimensional null orbits are considered. A coordinate transformation relating the canonical form of the metrics as given by… Expand

Dynamics of Pressure‐Free Matter in General Relativity

- Physics
- 1967

An orthonormal tetrad system and associated coordinate system is obtained, which may be used to locally describe any dust‐filled space‐time. This is used to study dust‐filled spaces in which there… Expand

Investigations of space-times with four-parameter groups of motions acting on null hypersurfaces

- Physics
- 1977

An investigation of all metric having a four‐parameter group of symmetrics with null three‐dimensional orbits is made. An attempt to solve the Einstein field equations using various simple… Expand

Exact Solutions of Einstein's Field Equations

- Physics
- 2004

We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in Negi and Durgapal [Gravitation and Cosmology7, 37 (2001)] which should be… Expand

Symmetries of the nontwisting type‐N solutions with cosmological constant

- Physics
- 1983

The conformal, homothetic, and isometric symmetries of all nontwisting type‐N solutions are established. All solutions with λ allow at most the existence of two Killing vectors. All vacuum solutions,… Expand

Totally symmetrized spinors and null rotation invariance

- Physics
- 2020

In the existing implementations of the Cartan-Karlhede procedure for characterization and classification of spacetimes, a prominent role is played by multi-index two-component spinors symmetrized… Expand

Some remarks on wave solutions in general relativity theory

- Mathematics
- Arabian Journal of Mathematics
- 2019

This paper reviews the concept of pp-waves and plane waves in classical general relativity theory. The first four sections give discussions of some algebraic constructions and symmetry concepts which… Expand

Symmetries and Curvature Structure in General Relativity

- Mathematics
- 2004

Introduction topological spaces groups and linear algebra manifold theory transformation groups the Lorentz group general relativity theory space-time holonomy curvature structure in general… Expand