B. O. J. Tupper

Special conformal Killing vector space‐times and symmetry inheritance

Viscous heat‐conducting fluid and anisotropic fluid space‐times admitting a special conformal Killing vector (SCKV) are studied and some general theorems concerning the inheritance of the symmetry associated with the SCKV are proved. In particular, for viscous fluid space‐times it is shown that (i) if the SCKV maps fluid flow lines into fluid flow lines, then all physical components of the energy‐momentum tensor inherit the SCKV symmetry; or (ii) if the Lie derivative along a SCKV of the shear viscosity term ησab is zero then, again, we have symmetry inheritance. All space‐times admitting a SCKV and satisfying the dominant energy condition are found. Apart from the vacuum pp‐wave solutions, which are the only vacuum solutions that can admit a SCKV, the energy‐momentum tensor associated with these space‐times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid. No perfect fluid space‐times can admit a SCKV. These SCKV space‐t...

The equivalence of electromagnetic fields and viscous fluids in general relativity

It is shown that spacetimes satisfying the Einstein–Maxwell equations, either in vacuo or coupled with a perfect fluid, may also satisfy the field equations for a viscous fluid. The necessary conditions for this alternative interpretation are found and examples of Einstein–Maxwell solutions admitting, and also not admitting, the viscous fluid interpretation are given.

Two‐fluid cosmological models

Homogeneous and isotropic, relativistic two‐fluid cosmological models are investigated. In these models two separate fluids act as the source of the gravitational field, as represented by the FRW line element. The general theory of two‐fluid FRW models in which neither fluid need be comoving or perfect is developed. However, attention is focused on the physically interesting special class of flat FRW models in which one fluid is a comoving radiative perfect fluid and the second a noncomoving imperfect fluid. The first fluid is taken to model the cosmic microwave background and the second to model the observed material content of the universe. One of the motivations of the present work is to model the observed velocity of our galaxy relative to the cosmic microwave background that was recently discovered by G. F. Smoot, M. V. Gorenstein, and R. A. Muller [Phys. Rev. Lett. 39, 898 (1977)]. Several models within this special class are found and analyzed. The models obtained are theoretically satisfactory in ...

Conformally flat solutions of the Einstein−Maxwell equations for null electromagnetic fields

The spin coefficient formalism of Newman and Penrose is employed to obtain a direct derivation of the most general conformally flat solution of the source−free Einstein−Maxwell equations for null electromagnetic fields.

The uniqueness of the Bertotti‐Robinson electromagnetic universe

By employing the spin coefficient formalism of Newman and Penrose a direct proof is obtained that the Bertotti‐Robinson electromagnetic universe is the only conformally flat solution of the source‐free Einstein‐Maxwell equations for nonnull fields.

Affine conformal vectors in space‐time

All space‐times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space‐times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space‐time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space‐time decomposes further). Furthermore, it is proved that all space‐times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp‐wave space‐times) must have Ricci tensor of Segre type {2,(1,1)}. It follows that, among space‐times admitting proper ACV, the Einstein static universe is the only perfect fluid space‐time, there are no non‐null Einstein–Maxwell space‐times, and only the pp‐wave space‐times are representative of null Einstein–Maxwell solutions. Otherwise, the space‐times can represent anisotropic fluids and viscous heat‐conducting fluids, but only with restricted equations of state in each case.

Space‐times admitting special affine conformal vectors

Space‐times admitting a special affine conformal vector (SACV) are shown to be precisely the space‐times that admit a special conformal Killing vector. All possible SACV space‐times are listed together with the corresponding SACV’s and covariantly constant tensors.

Einstein--Maxwell metrics admitting a dual interpretation

Conditions are given under which the metric part of a solution of the source‐free Einstein–Maxwell equations may be interpreted as the metric part of a solution with sources. Examples are given of space–times which admit this dual interpretation and also of space–times admitting one interpretation only.

Conformally Ricci-flat viscous fluids

It is shown that if the gradient of the conformal scalar in a conformally Ricci‐flat space‐time is parallel to an eigenvector (timelike, spacelike, or null) of the stress‐energy tensor, then acceptable solutions, without restrictions on the physical and kinematical quantities, of the Einstein field equations for a viscous fluid with heat conduction may be found.

Conformal symmetry inheritance with cosmological constant

A study is made of space‐times satisfying the Einstein field equations with a nonzero cosmological constant and admitting a conformal Killing vector (CKV), ξa, which is such that the Lie derivative of the energy‐momentum tensor in the direction of ξa is zero. This condition is necessary, but not sufficient, to ensure that the physical quantities associated with the energy‐momentum tensor inherit the CKV symmetry. It is shown that this condition leads to two classes of space‐times, each of which may be regarded as generalizations of the de Sitter space‐times. The possible physical interpretations of these models are discussed.