Radiative Penrose process: Energy gain by a single radiating charged particle in the ergosphere of rotating black hole

We demonstrate an extraordinary effect of energy gain by a single radiating charged particle inside the ergosphere of a Kerr black hole in presence of magnetic field. We solve numerically the covariant form of the Lorentz-Dirac equation reduced from the DeWitt-Brehme equation and analyze energy evolution of the radiating charged particle inside the ergosphere, where the energy of emitted radiation can be negative with respect to a distant observer in dependence on the relative orientation of the magnetic field, black hole spin and the direction of the charged particle motion. Consequently, the charged particle can leave the ergosphere with energy greater than initial in expense of black hole’s rotational energy. In contrast to the original Penrose process and its various modification, the new process does not require the interactions (collisions or decay) with other particles and consequent restrictions on the relative velocities between fragments. We show that such a radiative Penrose effect is potentially observable and discuss its possible relevance in formation of relativistic jets and in similar high-energy astrophysical settings.

Figure 1

Radiating charged particle trajectories demonstrating the radiative Penrose process for three different orbits. We show projections of particle trajectory into $xy$, $xz$ planes, particle specific energy $\mathcal{E}$, radial coordinate $r$ and covariant component $u_t$, $u_{\varphi }$, as functions of proper time $\tau$. Change of the colors denotes the evolution with the proper time, gray disk denotes BH interior, and dotted curve shows the boundaries of the egrosphere. In the first row the particle has been located little bit off equatorial plane and we see that radiative Penrose process occurs only at the beginning of particle’s trajectory, when the particle is still in ergosphere and conditions for negative photon existence (14) are fulfilled. Particle is escaping ergoregion with increased energy, and during its escape from the BH along magnetic field line is losing its energy by radiating photons with positive energy. In the second row we can see that negative photon existence, Eq. (14), is really the condition for radiative Penrose process: counter-rotating particle $u_{\varphi }<0$ in equatorial plane is gaining energy inside ergosphere ($u_t>0$, radiating photons with negative energy), while losing energy when peek out of ergosphere ($u_t<0$, photons with positive energy). In the third row we can see counterrotating particle energy gain before its capture by rotating BH.