  Electrospheres are environments with the same origin as pulsars; a highly
magnetized rotating neutron star. In pulsars, a cascade of electron-positron
pair creation enriches the plasma. The plasma surrounding an electrosphere
consists only of particles that have escaped from the neutron star's surface.
Electrospheres with a magnetic axis aligned with the rotation axis have been
well described for decades. Models of electrospheres with an oblique magnetic
axis relative to the rotation axis have resisted most theoretical
investigations. Some electrospheres and pulsars have been simulated using
particle-in-cell codes, but the numerical constraints did not allow the use of
realistic neutron star parameters. We aimed to develop a numerical simulation
code optimized for understanding the physics of electrospheres and pulsars,
with realistic neutron star parameters. As a first step, presented in this
paper, we focused on the simulation of oblique electrospheres with realistic
physical parameters. A specific code was developed for the computation of
stationary solutions. The resolution of Maxwell's equations was based on
spectral methods. Particle motions included their finite inertia. No hypothesis
was made in relation to the force-free behavior of the electrospheric plasma.
The numerical code is called Pulsar ARoMa (pulsar asymmetric rotating
magnetosphere). Various numerical simulations were conducted using realistic
neutron star parameters. We find that oblique electrospheres possess the same
global structure as aligned force-free electrospheres, with two domes of
electrons and a torus of positively charged particles. The domes are not
centered on the magnetic axis; nor are they symmetric. Yet, the solutions do
not exhibit a force-free behavior. The simulations performed with the Pulsar
ARoMa code require modest resources and little computing time. This code will
be upgraded for more ambitious investigations into pulsar physics.
