Interior Weyl-type solutions to the Einstein-Maxwell field equations.

*(English)*Zbl 1081.83510Summary: Static solutions of the electro-gravitationalfield equations exhibiting a functional relationship between the electric and gravitational potentials arestudied. General results for these metrics are presented which extend previous work of Majumdar. Inparticular it is shown that for any solution of the field equations exhibiting such a Weyl-typerelationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstrom solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.

##### MSC:

83C22 | Einstein-Maxwell equations |

83C15 | Exact solutions to problems in general relativity and gravitational theory |

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\textit{B. S. Guifoyle}, Gen. Relativ. Gravitation 31, No. 11, 1645--1673 (1999; Zbl 1081.83510)

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##### References:

[1] | Bohra, M. L. and Mehra, A. L. · Zbl 0436.35073 |

[2] | Bonnor, W. B. (1954). · Zbl 0055.20903 |

[3] | Buchdahl, · Zbl 0092.20802 |

[4] | Buchdahl, H. A., and Land, W. J. (196 |

[5] | Cooperstock, F. I., and De La Cruz, V. |

[6] | Das, A. (1962). · Zbl 0103.21403 |

[7] | Ehlers, J. (1967). Relativity Theory and Astrophysics, (A.M.S., Rhode Island), vol. 1. · Zbl 0203.28304 |

[8] | Florides, P. |

[9] | Florides, · Zbl 0555.70013 |

[10] | Gautreau, R., and Hoffman, R. B. |

[11] | Gürses, |

[12] | Gürses, M. (1998). In Proc. 1998 International Seminar on Mathematical Cosmology (Potsdam, Germany), M. Rainer and H.-J. Schmidt, eds. (World Scientific, Singapore), p.425. |

[13] | Kle |

[14] | Majumdar, S. D. (1947). Phys. Rev. 72, 390. |

[15] | Mehra, A. L. · Zbl 0444.76103 |

[16] | Mehra, A. |

[17] | Papapetrou, A. (1947). |

[18] | Papapetrou, A. (1974). Lectures on General Relativity (Reidel, Dordrecht). · Zbl 0299.53013 |

[19] | Patel, L. K. and Tikekar, R. (1992). Jour. |

[20] | Raychaudhuri, A. K. (1975). Ann. |

[21] | Schwarzschild, K. (1916). Sitzber. Preuss. Akad. Wiss., Phys.-Math. Kl. 424. |

[22] | Synge, J. L. (1966). Relativity: The General Theory (North-Holland, Amsterdam). · Zbl 0090.18504 |

[23] | Synge, J. L., and O’Brien, S. (1952). Jump Conditions at Discontinuities in General Relativity (Dublin Institute of Advanced Physics, 9A, Dublin, Ireland). · Zbl 0047.20802 |

[24] | Tolman, · Zbl 0020.28407 |

[25] | Wald, R. M. (1984). General Relativity (University of Chicago Press, Chicago). · Zbl 0549.53001 |

[26] | Weyl, H. ( · JFM 46.1303.01 |

[27] | Whittaker, J. M. (1968). · Zbl 0162.59204 |

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