We study a recursive Penrose process and the corresponding energy extraction for the decay of electrically charged particles in a Reissner–Nordström black hole spacetime with anti-de Sitter (AdS) asymptotics, incorporating the backreaction on the black hole’s mass and electric charge. A recursive process requires that the decay products remain confined within a finite spatial region so that the emitted particles bounce back and undergo further decay at some location, possibly the same location as the initial decay. In asymptotically AdS spacetimes, the confining property arises naturally. Outgoing particles encounter an outer turning point and are reflected inward. Alternatively, one may impose a reflecting mirror at a finite radius but in AdS backreaction makes these two confinement methods exactly equivalent. Let $Q_n$ denote the black hole charge after $n$ decays and define the index $n_{\mathrm{c}}$ as the value for which the black hole’s charge is zero, $Q_{n_{\mathrm{c}}}=0$. For $n_{\mathrm{c}}$ integer, which can be achieved for a specific choice of initial conditions, the black hole’s charge decreases step by step and reaches exactly zero, at least momentarily, after a finite number of decays, thereby terminating the recursive process. However, the last particle emitted turns back and, encountering zero charge, falls straight into the black hole. The final state is thus a charged black hole whose charge equals the sum of the original black hole charge with the initial particle charge. There is a fine-tuned possibility in which the process finishes with an uncharged black hole accompanied by a charged particle at rest precisely at the original decay position, which is an unstable configuration. For $n_{\mathrm{c}}$ noninteger, the black hole charge decreases and can be made arbitrarily small, but it never reaches zero. The last physically allowed decay occurs at $n=n_c^{-}$, where $n=n_c^{-}$ is the greatest integer less than $n_{\mathrm{c}}$. Any further decay would invalidate the approximations; one of the particles would carry a charge comparable to the black hole mass, transforming the problem into an uncontrolled two-body interaction. The would-be subsequent decay would moreover violate cosmic censorship, preventing it entirely. Therefore the process is terminated before any inconsistency arises. In both the integer and noninteger cases, the system yields a finite energy gain. Backreaction ensures that the process has a finite duration and extracts only a finite amount of energy. No black hole bomb occurs; the system can at most work as an energy factory. In short, we show that accounting for backreaction renders the black hole bomb impossible.

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• Classical black holes