A very common feature of active black holes in the radio regime is the compact radio core with its characteristic, flat spectrum. In luminous quasars the cores have been known for many years. Studying these radio cores with VLBI has allowed us to make the most detailed images of the physics and environment of black holes (Zensus 1997). Such flat-spectrum radio cores have also been found in many nearby galaxies which show signs of nuclear activity (Wrobel and Heeschen 1984, Nagar et al 2000, Falcke et al 2000). A well-studied example is M81*, the compact core in the nearby galaxy M81, which shares many characteristics with Sgr A^* (Reuter and Lesch 1996, Bietenholz et al 2000, Brunthaler et al 2001). In essentially all cases these cores are related to relativistic outflows or jets. For this reason, we start with the simplest assumption, namely that Sgr A^* is not very different from these, and we will discuss in the following how to obtain the

Figure 1.1. The average fractional circular polarization of Sgr A^* and upper limits to the linear polarization from Bower et al (2002; and references therein). In the top right-hand corner we show the linear polarization values given in Aitken et al (2000) from single-dish values. The error bars are 1σ errors.

observed radio spectra within the context of jet physics.