Linear stability of Israel-Stewart theory in the presence of net-charge diffusion was investigated in [C. V. Brito and G. S. Denicol, Linear stability of Israel-Stewart theory in the presence of net-charge diffusion, Phys. Rev. D 102, 116009 (2020)] for the case of a massless, classical gas of noninteracting particles. However, in that work only a vanishing net-charge background was considered. In this work, we extend that study to the case of a nonvanishing background charge. We find that this effectively results in a change of the numeric value of the charge-diffusion coefficient, in a way that when the background charge goes to infinity, this coefficient can become at most four times its value at zero background charge. We also extend the analysis of Brito and Denicol [Linear stability of Israel-Stewart theory in the presence of net-charge diffusion, Phys. Rev. D 102, 116009 (2020)] by performing a systematic parameter study in the plane of charge-diffusion coefficient vs the coupling term between shear-stress and net-charge diffusion. In this plane, we identify regions where the solutions remain stable and causal and where they become acausal and/or unstable.

Germany

Julia Sammet

Markus Mayer

Dirk H. Rischke

Linear stability analysis of Israel-Stewart theory in the case of a nonzero background charge

The energy-momentum tensor (EMT) of the ’t Hooft-Polyakov monopole and the Julia-Zee dyon are studied. This tensor contains important information about the pressure and the shear force distributions which define mechanical properties of systems. Obtaining the violation of the local stability criterion for the magnetic monopole and dyon we decompose the EMTs into the long- and short-range parts. This decomposition depends on the Abelian field strength tensor which cannot be uniquely defined. We suggest to use the modified ’t Hooft definition for the tensor. Finally, the long- and short-range parts of the EMTs are computed and new equilibrium equations are obtained. Numerical values for masses, <math><mi>D</mi></math>-terms, and various mean square radii for the monopole and the dyon are also computed.