Rotating and counterrotating relativistic thin disks as sources of stationary electrovacuum spacetimes

Abstract

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.

Conformastatic disk-haloes in Einstein-Maxwell gravity

“…Furthermore, the stability of thin disks models has been investigated using a first order perturbation of the energy-momentum tensor in [31]. On the other hand, thin disks have been discussed as sources for Kerr-Newman fields [32,33], magnetostatic axisymmetric fields [34,35], and conformastatic and conformastationary metrics [36][37][38]. Also, models of electrovacuum static counterrotating dust disks were presented in [39], charged perfect fluid disks were studied in [40], and charged perfect fluid disks as sources of static and Taub-NUT-type spacetimes in [41,42].…”

Rotating Relativistic Thin Disks as Sources of Charged and Magnetized Kerr–nut Space–times

“…Since α(α ∓ 1) + 2 > 0 for any α, from (57) follows that D always is a positive quantity for Kerr-Newman fields and therefore the eigenvalues of the energy-momentum tensor are always real quantities. So we conclude that these disks can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure and without heat flow [18]. In order to study the behavior of D when b 2 = 0 and of the other physical quantities associated with the disks, we shall perform a graphical analysis of them for charged and magnetized Kerr-NUT disks with b 1 = 0.2, b 2 = 0.9, charged and magnetized Taub-NUT disks with b 2 = 0.9, and KerrNewman disks with b 1 = 0.2, for α = 2 and c = 1.0, 1.5, 2.0, 2.5, 3.0, as functions ofr.…”

Modelos relativistas de discos de polvo magnetizados en un espaciotiempo conformestático axialmente simétrico

“…De a cuerdo con esto, esta clase de configuraciones se han estudiado extensivamente en la literatura, tanto desde el contexto puramente astrofísico como en relatividad general. Sin embargo, existen muy pocas soluciones exactas de las ecuaciones de Einstein-Maxwell correspondientes a esta clase de fuentes [19][20][21][22][23][24][25]. Ahora bien, una característica principal de las soluciones anteriormente mencionadas es el hecho de que el tensor de momentum-energía de la fuente describe un fluido anisótropo.…”