  In the 60s and 70s super-massive central objects (from now onwards SMOs) were
thought to be the main source of active galactic nuclei (AGNs) characteristics
(luminosities of $L \approx 10^{12} L_{\odot}$). The release of gravitational
binding energy by the accretion of material on to an SMO in the range of $10^7
- 10^9 M_{\odot}$ has been suggested to be the primary powerhouse (Lynden-Bell
1969).
  That rather exotic idea in early time has become common sense nowadays. Not
only our own galaxy harbours a few million-solar mass black hole (Genzel 2001)
but also many of other non-active galaxies show kinematic and gas-dynamic
evidence of these objects (Magorrian et al. 1998) The concept of central
super-massive stars (SMSs henceforth) (${\cal M} \ge 5 \times 10^4 M_{\odot}$,
where ${\cal M}$ is the mass of the SMS) embedded in dense stellar systems was
suggested as a possible explanation for high- energy emissions phenomena
occurring in AGNs and quasars (Vilkoviski 1976, Hara 1978), such as X-ray
emissions (Bahcall and Ostriker, 1975). SMSs and super-massive black holes
(SMBHs) are two possibilities to explain the nature of SMOs, and SMSs may be an
intermediate step towards the formation of SMBHs (Rees 1984). In this paper we
give the equations that describe the dynamics of such a dense star-gas system
which are the basis for the code that will be used in a prochain future to
simulate this scenario. We also briefly draw the mathematical fundamentals of
the code
