The accretion of relativistic and nonrelativistic fluids into a Reissner-Nordström black hole is revisited. The position of the critical point, the flow velocity at this point, and the accretion rate are only slightly affected with respect to the Schwarzschild case when the fluid is nonrelativistic. On the contrary, relativistic fluids cross the critical point always subsonically. In this case, the sonic point is located near the event horizon, which is crossed by the fluid with a velocity less than the light speed. The accretion rate of relativistic fluids by a Reissner-Nordström black hole is reduced with respect to those estimated for uncharged black holes, being about 60% less for the extreme case (charge-to-mass ratio equal to one).

The steady relativistic spherical flow of a perfect gas into a black hole has been intensely investigated in the past thirty years and a comprehensive review on the subject can be found, for instance, in [

Under adiabatic conditions (the cooling time is longer than the free-fall timescale), the gas is compressed as it approaches the horizon, its temperature increases, and X-rays are emitted from the inner accreting envelope. This emission preheats the infalling gas, reducing considerably the accretion rate and the radiative efficiency [

How the inflow properties are affected if the black hole has an electrical charge? Although the existence of charged black holes in the universe may be contested, some authors have hypothesized that such objects could play an important role in some astrophysical processes. For instance, the creation of positron-electron pairs in the “dyadosphere” of a Reissner-Nordström (RN) black hole was investigated in [

As mentioned above, the formation of a charged black hole during the gravitational collapse and, in particular, the formation of a “dyadosphere” present several difficulties whose discussion is beyond the scope of the present paper (see, however, criticisms by [

The metric describing an RN black hole is given by

We assume that a steady spherical inflow is set up inside the influence radius of the black hole, defined by the equality between the gravitational potential of the black hole and the mean kinetic energy of particles constituting the fluid far away from the horizon. Denoting by “

On the other hand, the integration of the space component of (

The critical point of the flow occurs when both bracketed factors in (

The conditions at the critical point (coordinate

For a baryonic nonrelativistic fluid with an equation of state

The accretion rate can now be computed from the conditions at the critical radius, that is,

In order to derive the radial velocity and the density profiles of the flow, let us define the dimensionless variables ^{−1}.

Radial velocity profiles for a nonrelativistic fluid being accreted by a Reissner-Nordström black hole for different charge-to-mass ratios. The radial coordinate is given in terms of the gravitational radius.

Figure ^{6}–10^{7} K near the horizon. It should be emphasized that these values correspond to an adiabatic flow and that radiative transfer effects may change appreciably these results.

Compression factor profiles for an inflow of a nonrelativistic gas as a function of the radial coordinate in units of the gravitational radius for different charge-to-mass ratios.

When

In the case of a relativistic fluid, the equation of state is simply given by

When

For the extreme case (

The radial velocity profile (left ordinate) for an accreting relativistic fluid as a function of the radial coordinate, in units of the gravitational radius, for an extreme RN black hole. The profile of the compression ratio (right ordinate) is also shown.

The accretion rate can be computed from the flow conditions at the critical point by following the same steps as before. In this case, one obtains

It can be easily verified that in this case the accretion efficiency decreases by almost 60% with respect to an uncharged black hole.

The steady and spherically symmetric accretion of nonrelativistic and relativistic fluids into a Reissner-Nordström black hole was revisited. A charged black hole modifies slightly the properties of the inflow of a nonrelativistic fluid since the critical radius, the radial velocity at the critical point, and the accretion rate are affected only by second-order terms in the charge-to-mass ratio.

The situation is rather different for the inflow of relativistic fluids. Firstly, the critical point occurs closer to the horizon, what is not the case for the inflow of nonrelativistic fluids. Secondly, the crossing of the critical point occurs always in a subsonic regime, even if the black hole is uncharged, contrary to what is usually stated in the literature. The sonic point is reached only very near the horizon and the fluid crosses the horizon with a velocity less than the light speed. In nonrelativistic flows, the ratio between the particle density near the horizon and at “infinity” may attain values of the order of

When