Hans Stephani

A note on Killing tensors

The connection between symmetric and skew-symmetric Killing tensors is studied. Some theorems on skew-symmetric Killing tensors are generalized, and it is shown that in all type-D vacuum metrics admitting a symmetric Killing tensor, this Killing tensor can be given in terms of a skew-symmetric Killing tensor.

Spherically symmetric perfect fluids in shear-free motion - the symmetry approach

In general relativity, the motion of expanding shear-free perfect fluids is governed by the ordinary differential equation , where F is an arbitrary function from which the equation of state can be computed. A complete symmetry analysis of this differential equation is given; its solutions are classified according to this scheme, and in particular the relation to Wymans Painleve analysis is clarified.

Letter: Some Remarks on Standing Gravitational Waves

An intuitive definition of standing gravitational waves is proposed. Some main classes of exact vacuum solutions are searched for standing gravitational waves, in most cases with a negative result. Only some Einstein–Rosen waves meet the conditions.

A note on the solutions of the diverging, twisting type N vacuum field equations

The field equations are linearized and solved. Some comments are made on the implications of the unavoidable occurrence of singularities in these solutions.

Algebraically special, diverging vacuum and pure radiation fields revisited

AbstractEinsteins field equations are reduced to two real differential equations for one complex potential

Perfect fluids with 4-velocity spanned by two commuting Killing vectors

\phi (\zeta , \bar \zeta , u)

Comment on 'A new solution for a rotating perfect fluid in general relativity'

. The known classes of vacuum solutions are invariantly characterized in terms of this potential, and a new representation of the Kerr-Schild class of solutions is given.

Algebraically special, shearfree, diverging, and twisting Einstein-Maxwell fields

Metrics of the formds2=dx2+dy2−dt2+N2dz2 are considered and found to contain rotating dust solutions as well as pure radiation fields.