# Global structure and physical interpretation of the Fonarev solution for a scalar field with exponential potential - General Relativity and Quantum Cosmology

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Abstract: We discuss the physical interpretation of a dynamical and inhomogeneousspherically symmetric solution obtained by Fonarev for a scalar field with anexponential potential. There is a single parameter $w$ in the solution whichcan be set to $\pm1$ if it is non-zero, in addition to the steepness parameter$\lambda$ in the potential. The spacetime is conformally static andasymptotically flat Friedmann-Robertson-Walker spacetime. The solution reducesto the Friedmann-Robertson-Walker solution for $w=0$. There are two curvaturesingularities, of which one is a timelike central singularity and the other isa big-bang or big-crunch type singularity. Depending on the parameters, thespacetime can possess a future outer trapping horizon in the collapsing case.Then the solution represents a dynamical black hole in the sense of Haywardalthough there is a locally naked singularity at the center and no black-holeevent horizon. This demonstrates a weak point of the local definition of ablack hole in terms of a trapping horizon.

Autor: Hideki Maeda

Fuente: https://arxiv.org/