  We present results of a set of three-dimensional, general relativistic
radiation magnetohydrodynamics simulations of thin accretion discs around a
non-rotating black hole to test their thermal stability. We consider two cases,
one that is initially radiation pressure dominated and expected to be thermally
unstable and another that is initially gas-pressure dominated and expected to
remain stable. Indeed, we find that cooling dominates over heating in the
radiation pressure dominated model, causing the disc to collapse vertically on
roughly the local cooling timescale. We also find that heating and cooling
within the disc have a different dependence on the mid-plane pressure, a
prerequisite of thermal instability. Comparison of our data with the relevant
thin-disc thermal equilibrium curve suggests that our disc may be headed for
the thermally stable, gas-pressure-dominated branch. However, because the disc
collapses to the point that we are no longer able to resolve it, we had to
terminate the simulation. On the other hand, the gas pressure dominated model,
which was run for twice as long as the radiation pressure dominated one,
remains stable, with heating and cooling roughly in balance. Finally, the
radiation pressure dominated simulation shows some evidence of viscous
instability. The strongest evidence is in plots of surface density, which show
the disc breaking up into rings.

High Energy Astrophysical Phenomena