Static charged fluid around a massive magnetic dipole

Abstract

An analytical solution of Einstein-Maxwell equations with a static fluid as a source is presented. The spacetime is represented by the axially symmetric Weyl metric and the energy-momentum tensor describes a coupling of a fluid with an electromagnetic field. When appropriate limits are performed we recover the well-known solutions of Gutsunaev-Manko and Schwarzschild. Also, using Eckart's thermodynamics, we calculated the temperature, the mechanical pressure, the charge density and the energy density of the system. The analysis of thermodynamic quantities suggests that the solution can be used to represent a magnetized compact stellar object surrounded by a charged fluid.

General magnetized Weyl solutions: disks and motion of charged particles

“…Analytical models that describe these astrophysical objects are often associated with solutions of Einsteins equations [17][18][19][20][21][22]. In the search for more realistic models for compact stellar systems, the energy-momentum tensor, the source of Einsteins equations, is modified by introducing more complex terms that take into account additional physical properties as, for example, electromagnetic fields [23].…”