Global structure and physical interpretation of the Fonarev solution for a scalar field with exponential potential

Understand

We discuss the physical interpretation of a dynamical and inhomogeneous spherically symmetric solution obtained by Fonarev for a scalar field with an exponential potential.

• There is a single parameter $w$ in the solution which can be set to $\pm1$ if it is non-zero, in addition to the steepness parameter $\lambda$ in the potential.
• The spacetime is conformally static and asymptotically flat Friedmann-Robertson-Walker spacetime.
• The solution reduces to the Friedmann-Robertson-Walker solution for $w=0$.