Draining Without Emptying a Stringy Black Hole: Repetitive Electric Penrose Process

Abstract

This paper studies the repetitive electric Penrose process in the Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) black hole under the optimal condition for maximum energy extraction. Unlike the Reissner-Nordström (RN) black hole, the effective potential curve of the incident particle in the GMGHS black hole remains unchanged during the iterations. The iteration termination conditions are determined by two aspects: the escape condition requires that particle 0 can overcome the effective potential peak and escape to infinity, and this condition is independent of the black hole charge; the existence condition for negative-energy particle 1 requires the black hole charge to be sufficiently large, indicating that the repetitive process cannot completely consume the charge of the GMGHS black hole to zero. Numerical simulations show that the return on investment of energy extraction can exceed $100\%$, but the energy utilization efficiency does not exceed $50\%$, and most of the extractable energy is converted into an increase in the irreducible mass of the black hole. In addition, a smaller decay radius and a larger absolute value of the charge-to-mass ratio of particle 1 can improve the return on investment and energy utilization efficiency of energy extraction; the larger the specific energy of the incident particle, the smaller the return on investment of energy extraction, while the energy utilization efficiency remains unchanged; for an initially non-extremal black hole, as the initial charge increases, the return on investment of energy extraction increases monotonically, while the energy utilization efficiency first increases and then decreases. After the iterations end, the black hole still retains extractable energy, and neither the charge nor the mass vanishes.