Collisional Penrose process of extended test particles near an extremal Kerr black hole

We investigate the collisional Penrose process of extended test particles near extremal Kerr black holes using the pole-dipole-quadrupole approximation. We analyze the motion of the test particles and examine the dynamics and maximum efficiency of energy extraction in this process. Our results demonstrate that the maximum extracted energy in the collisional Penrose process is influenced by the spin s and quadrupolar parameter CES2 of the test particles. Specifically, we observe that, at a fixed collisional position, the energy extraction efficiency decreases as the spin increases for either the pole-dipole or the pole-dipole-quadrupole approximation case. Furthermore, for a fixed spin, the energy extraction efficiency is higher in the pole-dipole-quadrupole approximation compared to the pole-dipole approximation. These findings provide insight into the role of the internal structures of the test particles in the collisional Penrose process.Comment: 7 pages and 3 figure

Splitting the Echoes of Black Holes in Einstein-nonlinear Electrodynamic Theories

Black hole echo is an important observable that can help us better understand gravitational theories. We present that the non-linear electrodynamic black holes can admit the multi-peak effective potential for the scalar perturbations, which can give rise to the echoes. After choosing suitable parameters, the effective potential can exhibit a structure with more than two peaks. Putting the initial wave packet released outside the peaks, we find that the time-domain profile of the echo will split when the peaks of the effective potential change from two to three. This is a phenomenon of black hole echo and it might be possible to determine the geometric structure of the black hole according to this phenomenon through gravitational wave detection.Comment: 7 pages, 6 figures, and 1 table; reference added, title change

Collisional Penrose process of extended test particles near an extremal Kerr black hole

Abstract We investigate the collisional Penrose process of extended test particles near an extremal Kerr black hole using the pole-dipole-quadrupole approximation. We analyze the motion of the test particles and examine the dynamics and maximal efficiency of energy extraction in this process. Our results demonstrate that the maximal extracted energy in the collisional Penrose process is influenced by the spin s and quadrupolar parameter C of the test particles. Specifically, we observe that, at a fixed collisional position, the energy extraction efficiency decreases as the spin increases for either the pole-dipole or the pole-dipole-quadrupole approximation case. Furthermore, for a fixed spin, the energy extraction efficiency is higher in the pole-dipole-quadrupole approximation compared to the pole-dipole approximation. These findings provide insight into the role of the internal structures of the test particles in the collisional Penrose process