A family of relativistic charged thin disks with an inner edge

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Gutiérrez-Piñeres, Antonio C.
González, Guillermo A.
Viña-Cervantes, Viviana M.
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Universidad Industrial de Santander
Abstract
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A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.   
A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.   
Keywords
Classical General Relativity, exact solutions, self-gravitating system, Einstein equations, Classical General Relativity, exact solutions, self-gravitating system, Einstein equations
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