A charged particle moving in the electromagnetic field can feel Landau–Lifshitz radiation reaction force due to synchrotron radiation, thus modifying the motion of the charged particle significantly when taking into account the radiation reaction force. Recent observations have demonstrated that there is strong evidence that a magnetic field of several hundred Gauss exists in the vicinity of the supermassive black hole at the center of the Milky Way (Eatough et al. 2013). A dynamo mechanism from an accretion disk around a black hole accounts for the appearance of such a magnetic field (Punsly 2001; Brandenburg et al. 1995; Hawley et al. 1996). There is also clear evidence that the magnetic field on the surface of the neutron star can be up to 1014 G (Duncan & Thompson 1992; Paczyński 1992; Usov 1992; Thompson & Duncan 1995, 1996; Vasisht & Gotthelf 1997). The Landau–Lifshitz radiation reaction has been investigated in detail in Landau & Lifshitz (1975) in flat space, while, in curved space, the radiation reaction is described in Sokolov et al. (1978, 1983), DeWitt & Brehme (1960), and Tursunov et al. (2018). Thus, the radiation reaction force can affect the charged particles from the accretion disk around the black hole and the neutron star significantly. Radiation reactions have been an important element of pair creation scenarios in positron–electron plasma just above the pole of the event horizon (Hirotani & Pu 2016). Curvature radiation in black hole magnetosphere pair creation schemes is radiation resistance limited (Broderick & Tchekhovskoy 2015). Recently, a radiation reaction has also been applied to protonic acceleration in the vortex above the pole of the black hole (Ruffini et al. 2018). Radiation reactions are of fundamental importance in the evacuated vortex of black hole magnetospheres (Punsly 2001). In particular, if the field line angular velocity is set much less than the horizon angular velocity by distant plasma and a very tenuous plasma exists in the event horizon magnetosphere, then radiation resistance will determine the flow dynamics of accretion as well as the rotational energy extraction by a putative jet (Punsly 2001, 1991). The dynamics mentioned above cannot be revealed by MHD simulations with mass floors. The ad hoc injection of mass will damp any large waves that can break ideal MHD and prevent the associated large local electromagnetic forces from being achieved. Therefore, all existing numerical simulations of the black hole magnetosphere bypass the radiation reaction dominated dynamics as a consequence of numerical dissipation of waves and numerical diffusion in the MHD system in the evacuated vortex above the event horizon. Thus, a proper treatment of radiation reaction is critical for assessing the time evolution of these types of astrophysical systems. Numerical simulations using general relativistic magnetohydrodynamics (GRMHDs) are applied to investigate the physical process in accretion disks around neutron stars, as well as in microquasars (μQSOs), gamma-ray bursts, and active galactic nuclei. In curved spacetime, the dynamical evolution of the high energy disks made of ion–electron plasma in simulated GRMHD is usually performed without the contribution from Landau–Lifshitz radiation reaction force, which may play a crucial role. The method of particle-in-cell (Chen & Beloborodov 2014; Philippov & Spitkovsky 2014; Belyaev 2015; Cerutti et al. 2015, 2016; Philippov et al. 2015b) containing the radiation reaction forces has been investigated in flat space, while, in curved space, the same method with a radiation reaction has been achieved in Philippov et al. (2015a). Incorporating the radiation reaction into the relativistic magnetohydrodynamic equations governing the dynamics of plasma has been studied by Tam & Kiang (1979) and Berezhiani et al. (2004, 2008). In a recent study, Liu et al. (2018) achieved the one-fluid relativistic magnetohydrodynamics description of two-fluid plasma in which the Landau–Lifshitz radiation reaction is incorporated. However, numerical simulation with the radiation reaction from Liu et al. (2018) is not practical due to its highly nonlinear form at present, we expect that analytical investigations are essential and provide more motivation for future work. Thus, in this work, similar to Liu et al. (2018), we get the GRMHD equation for the one-fluid description of two-fluid plasma containing a Landau–Lifshitz radiation reaction in curved space, and these results could be applied to both positron–electron and proton–electron plasma.
Citation: Punsly; 1991
Citation function: Background