1 Introduction

There is much evidence that most GRBs have cosmological origin (see [17, Piran 1998] for a recent review). Observations give total isotropic energy fluences of these events in the range 10⁵¹ - 10⁵⁴ erg during several seconds. From BATSE observations, the GRBs rate is one burst per million years per galaxy. The energy release and rate can be reduced, of course, by several orders of magnitude if the GRBs are beamed with a factor of about of 10^-4 - 10^-5. The central point in the GRBs scenario is the origin of the "inner engine" that we do not detect directly. A significant difficulty with many proposed parent bodies of GRBs is that only a small amount of baryons ($< 10^{-5}\,M_\odot$) can be involved if a required relativistic expansion is to be produced [21, (Shemi & Piran 1990).] Scenarios using coalescence of two neutron stars [15, (Narayan et al. 1992)] or special types of supernovae [16, (Paczynski 1998)] involve potentially large amounts of "contaminating" baryons. A baryon-poor mechanism is based on the possibility to convert rotational energy of neutron stars due to strong magnetic field (10¹⁵ G) to a Poynting flux and then, to kinetic energy of particles (see e.g. [22, Usov 1992).] We proposed as similar sources of magnetic energy, the inhomogeneities in the magnetospheres of Single Black Holes (SBH) of $(10 - 10^{3})M_\odot$ [4, (Beskin et al. 1998).] These objects can be parent bodies of both galactic and cosmological GRBs.

In this paper we discuss in detail a possible connection between cosmological GRBs and SBHs.