Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-11-24
J.Math.Phys.47:033101,2006
Physics
High Energy Physics
High Energy Physics - Theory
7 pages, two columns. Minor changes
Scientific paper
10.1063/1.2179050
We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter action is considered. In this case, we show the existence of nontrivial scalar field configurations with vanishing energy-momentum tensor on any static, spherically symmetric vacuum solutions of the Einstein equations. These configurations in spite of being coupled to gravity do not affect the curvature of spacetime. The properties of this particular matter action are also analyzed. For a particular value of the exponent, the extended Klein-Gordon action is shown to exhibit a conformal invariance without requiring the introduction of a nonminimal coupling. We also establish a correspondence between this action and a non-relativistic isentropic fluid in one fewer dimension. This fluid can be identified with the (generalized) Chaplygin gas for a particular value of the power. It is also shown that the non-relativistic fluid admits, apart from the Galileo symmetry, an additional symmetry whose action is a rescaling of the time.
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