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Previous theorems concerning Weyl type systems, including Majumdar-Papapetrousystems, are generalized in two ways, namely, we take these theorems into dspacetime dimensions (${\rm d}\geq4$), and we also consider the veryinteresting Weyl-Guilfoyle systems, i.e., general relativistic charged fluidswith nonzero pressure. In particular within Newton-Coulomb theory of chargedgravitating fluids, a theorem by Bonnor (1980) in three-dimensional space isgeneralized to arbitrary $({\rm d}-1)>3$ space dimensions. Then, we prove a newtheorem for charged gravitating fluid systems in which we find the conditionthat the charge density and the matter density should obey. Within generalrelativity coupled to charged dust fluids, a theorem by De and Raychaudhuri(1968) in four-dimensional spacetimes in rendered into arbitrary ${\rm d}>4$dimensions. Then a theorem, new in ${\rm d}=4$ and ${\rm d}>4$ dimensions, forWeyl-Guilfoyle systems, is stated and proved, in which we find the conditionthat the charge density, the matter density, the pressure, and theelectromagnetic energy density should obey. This theorem comprises, asparticular cases, a theorem by Gautreau and Hoffman (1973) and results in fourdimensions by Guilfoyle (1999). Upon connection of an interior charged solutionto an exterior Tangherlini solution (i.e., a Reissner-Nordstr\"om solution ind-dimensions), one is able to give a general definition for gravitational massfor this kind of relativistic systems and find a mass relation with the severalquantities of the interior solution. It is also shown that for sources offinite extent the mass is identical to the Tolman mass.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Electrically charged fluids with pressure in Newtonian gravitation and  general relativity in d spacetime dimensions: theorems and results for Weyl  type systems