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One of the stiffest equations of state for matter in a compact star isconstant energy density and this generates the interior Schwarzschild radius tomass relation and the Misner maximum mass for relativistic compact stars. Ifdark matter populates the interior of stars, and this matter is supersymmetricor of some other type, some of it possessing a tiny electric charge, there isthe possibility that highly compact stars can trap a small but non-negligibleelectric charge. In this case the radius to mass relation for such compactstars should get modifications. We use an analytical scheme to investigate thelimiting radius to mass relation and the maximum mass of relativistic starsmade of an incompressible fluid with a small electric charge. The investigationis carried out by using the hydrostatic equilibrium equation, i.e., theTolman-Oppenheimer-Volkoff (TOV) equation, together with the other equations ofstructure, with the further hypothesis that the charge distribution isproportional to the energy density. The approach relies on Volkoff and Misner'smethod to solve the TOV equation. For zero charge one gets the interiorSchwarzschild limit, and supposing incompressible boson or fermion matter withconstituents with masses of the order of the neutron mass one gets that themaximum mass is the Misner mass. For a small electric charge, our analyticalapproximating scheme valid in first order in the star's electric charge, showsthat the maximum mass increases relatively to the uncharged case, whereas theminimum possible radius decreases, an expected effect since the new field isrepulsive aiding the pressure to sustain the star against gravitationalcollapse.

Compact stars with a small electric charge: the limiting radius to mass relation and the maximum mass for incompressible matter