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Extended Klein-Gordon Action, Gravity and Non-Relativistic Fluid
High Energy Physics - Theory · Submitted 24 Nov 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider a scalar field action for which the Lagrangian density is a power of the massless Klein-Gordon Lagrangian. | contribution 0.78 | 0.56 | 0.04 | asserted 0.92 |
| s1 | The coupling of gravity to this matter action is considered. | contribution 0.79 | 0.72 | 0.04 | asserted 0.74 |
| s2 | 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. | result 0.99 | 0.94 | 0.48 | asserted 1.00 |
| s3 | These configurations in spite of being coupled to gravity do not affect the curvature of spacetime. | result 0.86 | 0.86 | 0.30 | asserted 1.00 |
| s4 | The properties of this particular matter action are also analyzed. | contribution 0.96 | 0.83 | 0.03 | unclear 0.66 |
| s5 | 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. | result 0.99 | 0.93 | 0.12 | asserted 1.00 |
| s6 | We also establish a correspondence between this action and a non-relativistic isentropic fluid in one fewer dimension. | result 0.76 | 0.93 | 0.12 | asserted 1.00 |
| s7 | This fluid can be identified with the (generalized) Chaplygin gas for a particular value of the power. | result 0.88 | 0.86 | 0.08 | asserted 0.99 |
| s8 | 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. | result 0.98 | 0.91 | 0.07 | asserted 1.00 |
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Original abstract
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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