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Solutions to the Einstein-scalar field constraint equations with a small TT-tensor

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Abstract

In this paper, we prove a far-from-CMC result similar to Holst et al. (Phys Rev Lett 100(16):161101, 4, 2008), Holst et al. (Commun Math Phys 288(2):547–613, 2009), Maxwell (Math Res Lett 16(4):627–645, 2009), Gicquaud and Ngô (Class Quantum Grav 31(19):195014 (20 pp), 2014) for the conformal Einstein-scalar field constraint equations on compact Riemannian manifolds with positive (modified) Yamabe invariant.

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Acknowledgments

We are grateful to Emmanuel Humbert for his support and his careful proofreading of a preliminary version of this article. We also warmly thank Laurent Véron for useful discussions. Last but not least, we are indebted to both referees for their remarks that led to improvements of the quality of the article.

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Authors and Affiliations

  1. Laboratoire de Mathématiques et de Physique Théorique, Université François Rabelais de Tours, Parc de Grandmont, 37200, Tours, France

    Romain Gicquaud & Cang Nguyen

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  1. Romain Gicquaud
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  2. Cang Nguyen
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Correspondence to Romain Gicquaud.

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Communicated by A. Neves.

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Gicquaud, R., Nguyen, C. Solutions to the Einstein-scalar field constraint equations with a small TT-tensor. Calc. Var. 55, 29 (2016). https://doi.org/10.1007/s00526-016-0963-1

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