Schwarzschild black hole spacetimes with viscous hot unmagnetized plasma Milky Way optically thin disc

The Schwarzschild spacetimes with hot viscous rarefied unmagnetized plasma are investigated under adiabatic perturbations of the 4-velocity of the plasma of the slim disc. The r-component of the 4-velocity and the ϕ-component of the 4-velocity are analytically written. The ϕ component of the 4-velocity is found not to depend on the 4-position. Indeed, the functional dependence of the canonical energy of the perturbation on the component uϕ of the 4-velocity is studied: it is defined to be unvaried for a vanishing value of uϕ and for a constant non-vanishing value of uϕ; differently, it varies with different characterizations of uϕ. The results are a comparison with the current understanding of the central region of the Milky Way and of the further regions. The position of the outer boundary conditions is newly discussed. The speed of sound in the disc is newly found to be dependent on the radial position, the accretion rate of the black hole object and the variation of the gravitational potential of the gravitating disc. The position of the outer boundary conditions is therefore newly discussed according to the transonic behavior of the disc and to the determination of the sonic points.