# Inverse approach to Einstein's equations for nonconducting fluids

@article{Ishak2003InverseAT, title={Inverse approach to Einstein's equations for nonconducting fluids}, author={Mustapha Ishak and Kayll Lake Princeton University and Queen's University and Kingston}, journal={Physical Review D}, year={2003}, volume={68}, pages={104031} }

We show that a flow (timelike congruence) in any type ${B}_{1}$ warped product spacetime is uniquely and algorithmically determined by the condition of zero flux. (Though restricted, these spaces include many cases of interest.) The flow is written out explicitly for canonical representations of the spacetimes. With the flow determined, we explore an inverse approach to Einstein's equations where a phenomenological fluid interpretation of a spacetime follows directly from the metric…

## 4 Citations

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## References

SHOWING 1-10 OF 20 REFERENCES

NONSTATIC ANALOGS OF SCHWARZSCHILD'S INTERIOR SOLUTION IN GENERAL RELATIVITY.

- Physics
- 1968

A class of nonstatic solutions of Einstein's field equations representing the gravitational field within a spherically symmetric distribution of matter, possessing the property that the…

Zero-Curvature Friedmann-Robertson-Walker Models as Exact Viscous Magnetohydrodynamic Cosmologies

- Physics
- 1983

It is shown that FRW cosmologies, in particular the zero-curvature models,do not necessarily represent perfect fluid solutions but also can be exact solutions of the field equations for a viscous…

The contraction of gravitating spheres

- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1964

Earlier ideas associating an invariant integral of the energy invariant with the number of nucleons in a gravitating body are shown to be fallacious, and thus do not provide a means of following…

Relativistic fluid spheres and noncomoving coordinates. I

- Mathematics
- 1977

Spherically symmetric relativistic spheres of perfect fluid are defined to be isotropic by Walker's (1935) isotropy condition. This condition permits the use of noncomoving coordinate systems, which,…

Adiabatic Models of the Cosmological Radiative Era

- Physics
- 2001

We consider a generalization of the Lemaitre-Tolman-Bondi (LTB) solutions by keeping the LTB metric but replacing its dust matter source by an imperfect fluid with anisotropic pressure Πab. Assuming…

A non-stationary generalised Robinson-Trautman solution

- Mathematics
- 1988

A non-stationary solution to Einstein's equations, describing a perfect fluid and depending on essentially one parameter, is presented. The metric is of Petrov type D and admits a group G3 on V2, the…

The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid

- Physics
- 1940

The considerations of the first paper of this series are modified so as to be consistent with the special theory of relativity. It is shown that the inertia of energy does not obviate the necessity…

All static spherically symmetric perfect-fluid solutions of Einstein’s equations

- Mathematics, Physics
- 2003

An algorithm based on the choice of a single monotone function (subject to boundary conditions) is presented which generates all regular static spherically symmetric perfect-fluid solutions of…

An online interactive geometric database including exact solutions of Einstein's field equations

- Computer Science, Physics
- 2001

A new interactive database of geometric objects in the general area of differential geometry designed for researchers (and teachers) in applied mathematics, physics and related fields, built using a modular and object-oriented design and using several Java technologies.