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 space-time. 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 nonrelativistic 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 nonrelativistic fluid admits, apart from the Galileo symmetry, an additional symmetry whose action is a rescaling of the time.
Skip Nav Destination
Article navigation
March 2006
Research Article|
March 21 2006
Extended Klein-Gordon action, gravity and nonrelativistic fluid
Mokhtar Hassaïne
Mokhtar Hassaïne
a)
Instituto de Matemática y Física,
Universidad de Talca
, Casilla 747, Talca, Chile and Centro de Estudios Científicos (CECS)
, Casilla 1469, Valdivia, Chile
Search for other works by this author on:
a)
Electronic mail: [email protected]
J. Math. Phys. 47, 033101 (2006)
Article history
Received:
January 26 2006
Accepted:
January 27 2006
Citation
Mokhtar Hassaïne; Extended Klein-Gordon action, gravity and nonrelativistic fluid. J. Math. Phys. 1 March 2006; 47 (3): 033101. https://doi.org/10.1063/1.2179050
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Cascades of scales: Applications and mathematical methodologies
Luigi Delle Site, Rupert Klein, et al.
Related Content
The pseudodifferential operator square root of the Klein–Gordon equation
J. Math. Phys. (September 1993)
Local Cauchy problem for the nonlinear Dirac and Dirac-Klein-Gordon equations on Kerr space–time
J. Math. Phys. (May 2006)
Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit
J. Math. Phys. (January 2018)
Accelerating universe from nonminimal derivative coupling in 5D universal extra dimension
AIP Conference Proceedings (May 2012)
A note on the Klein–Gordon equation in the background of a rotating black hole
J. Math. Phys. (January 2009)