Aspects of Boundary Conditions for Nonabelian Gauge Theories

The boundary values of the time-component of the gauge potential form externally specifiable data characterizing a gauge theory. We point out some consequences such as reduced symmetries, bulk currents for manifolds with disjoint boundaries and some nuances of how the charge algebra is realized.Comment: 15 page

Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation

An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Here, we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation as well as temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation- equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes.We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice-versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS.The first one employs root-finder methods and it is best suited for EoS in analytical form. The second one leans on lookup table and interpolation and results in a more computationally efficient approach although care must be taken to ensure thermodynamic consistency. A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is $500-10^4$ K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although using lookup table methods can significantly reduce the overhead by a factor $3\sim 4$.Comment: 17 pages, 10 figures, Accepted for publication in A&

A radiating dyon solution

We give a non-static exact solution of the Einstein-Maxwell equations (with null fluid), which is a non-static magnetic charge generalization to the Bonnor-Vaidya solution and describes the gravitational and electromagnetic fields of a nonrotating massive radiating dyon. In addition, using the energy-momentum pseudotensors of Einstein and Landau and Lifshitz we obtain the energy, momentum, and power output of the radiating dyon and find that both prescriptions give the same result.Comment: 9 pages, LaTe