E. N. Glass

Exact spatially homogeneous cosmologies

We consider perfect fluid spatially homogeneous cosmological models. Starting with a new exact solution of Blanchi type VIII, we study generalizations which lead to new classes of exact solutions. These new solutions are discussed and classified in several ways. In the original type VIII solution, the ratio of matter shear to expansion is constant, and we present a theorem which delimits those space-times for which this condition holds.

Shear‐free gravitational collapse

Spherically symmetric perfect fluids are studied under the restriction of shear‐free motion. All solutions of the field equations are found by solving a single second order nonlinear equation containing an arbitrary function. It is shown that this arbitrary function is a geometric invariant, E, which measures the gravitational field energy, and it is shown that E=const generates all the homogeneous density solutions. An improved proof is given for the nonexistence of any one‐parameter equation of state. A number of exact solutions are presented and discussed.

The Weyl tensor and shear‐free perfect fluids

It is proved that a necessary and sufficient condition for a shear‐free perfect fluid to be irrotational is that the Weyl tensor be pure electric type. For shear‐free isentropic flow with unit tangent uα, we find the conservation law ∇α(n1/3iω uα) =0, where i is the relativistic specific enthalpy, n is the conserved particle number density, and ω is the vorticity scalar.

Two-fluid atmosphere for relativistic stars

We have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid. This paper expands our brief introduction to extensions of the Schwarzschild vacuum which appeared in 1998 Phys. Rev. D 57 R5945. Assuming diffusive transport for the string fluid, we find new analytic solutions of Einsteins field equations.

Relativistic spherical stars reformulated

The problem of finding static, spherically symmetric, solutions of Einstein’s equations for a perfect fluid is reformulated. A field equation connecting the pressure and density and free of metric components is obtained. Upon finding a solution of this field equation, the metric components are then obtained by quadrature. A solution‐generating technique is developed which yields physically valid pressure‐density configurations for adiabatically stable stars. Analytic solutions are obtained for the pressure, density, and metric components.

Adding twist to anisotropic fluids

We present a solution generating technique for anisotropic fluids which preserves specific Killing symmetries. Anisotropic matter distributions that can be used with the one parameter Ehlers–Geroch transform are discussed. Example space–times that support the appropriate anisotropic stress-energy are found and the transformation applied. The 3+1 black string solution is one of the space–times with the appropriate matter distribution. Use of the transform with a black string seed is discussed.

Radiating collapse solutions

Exact gravitational collapse solutions with shear and radial heat flow are obtained by integrating a field equation. Junction conditions which match the collapse solutions to an exterior Vaidya metric show that, at the boundary, the pressure is proportional to the magnitude of the heat flow vector.

Killing tensors and symmetries

A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvins magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.

Solutions of Penrose’s equation

The computational use of Killing potentials which satisfy Penrose’s equation is discussed. Penrose’s equation is presented as a conformal Killing–Yano equation and the class of possible solutions is analyzed. It is shown that solutions exist in space–times of Petrov type O, D, or N. In the particular case of the Kerr background, it is shown that there can be no Killing potential for the axial Killing vector.

Solution generating with perfect fluids

We apply a technique, due to Stephani, for generating solutions of the Einstein-perfect-fluid equations. This technique is similar to the vacuum solution generating techniques of Ehlers, Harrison, Geroch and others. We start with a “seed” solution of the Einstein-perfect-fluid equations with a Killing vector. The seed solution must either have (i) a spacelike Killing vector and equation of state P = ρ or (ii) a timelike Killing vector and equation of state ρ + 3P = 0. The new solution generated by this technique then has the same Killing vector and the same equation of state. We choose several simple seed solutions with these equations of state and where the Killing vector has no twist. The new solutions are twisting versions of the seed solutions.