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Comoving Self-Gravitating Scalar Field in the Newman Penrose Formalism

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The Einstein field equation, coupled to the scalar field, is studied in a spherically symmetric comoving system. The problem is translated into the language of the Newman Penrose formalism that is based on the choice of a null tetrad frame. The corresponding (tabulated) Einstein field equation, Bianchi identities and scalar field equation are explicited in terms of the Weyl and Ricci scalars and discussed. Spherical symmetry reduces the difficulties but not so far to enable to integrate the scheme in general. The main result is that static self-gravitation is possible only for massless scalar field. The static solution is determined. It depends on an arbitrary function that can be interpreted as radial coordinate. The part of the space–time solution of the problem does not contain black holes. It is remarked that in the part of the space–time not solution of the problem, light rays cannot propagate radially but admit circular orbits.

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  1. Antonio Zecca

    Present address: Gruppo Nazionale par la Fisica Matematica, Milan, Italy

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  1. Dipartimento di Fisica dell’ Universita’ and INFN, Via Celoria 16, 20133, Milan, Italy

    Antonio Zecca

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  1. Antonio Zecca
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Correspondence to Antonio Zecca.

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Zecca, A. Comoving Self-Gravitating Scalar Field in the Newman Penrose Formalism. Int J Theor Phys 45, 375–383 (2006). https://doi.org/10.1007/s10773-006-9028-0

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  • DOI: https://doi.org/10.1007/s10773-006-9028-0

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