Scalar superradiance in the charged black-bounce spacetimes
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Zhiming Shuai, Xiangdong Zhang, Gui-Rong Liang
A black hole can act like a cosmic energy booster, making incoming waves leave stronger than they arrived. This study finds that a quantum-scale change to the black hole’s shape turns that booster down.
We numerically investigate the superradiant amplification effect of a charged scalar field in the scattering experiment and the black hole bomb model in a charged black-bounce spacetime. Due to the shallowing effect on the effective potential by the introduced quantum parameter λ, superradiance in both the above cases is verified to be weakened. In a scattering experiment, the quantum parameter and the field mass suppress the amplification in all frequency ranges, while the black hole and field charge suppress the amplification at low frequencies but enhance it at high frequencies. In a Type I black hole bomb model, where the reflective mirror is placed outside the ergo-region, we find a new distinct eigen-mode for the scalar field evolution in a high λ value, which is however absent in the light-particle sub-case of the Type II black hole bomb where the mirror is set inside the ergo-region. Moreover, we investigate the heavy field mass scenario in a Type II black hole bomb, in which an additional eigenfrequency emerges at the same high λ value but is not superradiantly amplified.
Transcript
A black hole can act like a cosmic energy booster, making incoming waves leave stronger than they arrived. This study finds that a quantum-scale change to the black hole’s shape turns that booster down. Superradiance is wave amplification that comes with energy loss from the system.
Around a black hole, the event horizon acts like a one-way membrane, creating a region where particles can have negative energy for distant observers. When an incoming wave interacts with that region, energy can be extracted from the black hole, in both rotating and charged, nonrotating settings.
The setting here is a charged black-bounce spacetime: a smooth model that can describe either a regular black hole or a wormhole as one parameter is changed. The geometry can be tuned smoothly between regular black-hole and wormhole solutions, with a quantum length scale deforming the classical Reissner–Nordström metric into a black-bounce geometry.
To track amplification, the study examines an effective potential, a landscape that depends on the black hole and field properties. Setting the quantum parameter to zero recovers the usual charged-black-hole landscape. That landscape is tied to the region where superradiance can occur, so changing its shape changes how strongly waves are amplified.
As the quantum parameter increases, the amplification factor decreases across a wide range of frequencies, and the decrease becomes progressively faster as the parameter keeps increasing. Increasing the field mass also gradually decreases amplification across all frequencies, while the critical frequency stays unchanged by either the quantum parameter or the field mass.
The wave can be strongly amplified only within a particular frequency range, then the effect abruptly disappears near a critical frequency. Increasing the field’s mass sharply reduces that amplification, while changing the coupling mainly reshapes its peak. Across the full frequency range, the quantum parameter reduces amplification, so the black-bounce black hole amplifies waves more weakly than the usual charged black hole.
A larger field mass also suppresses amplification at every frequency. By contrast, the black-hole and field charges raise the critical frequency, strengthening amplification at high frequencies while suppressing it at low frequencies. The study then places a reflective boundary around the black hole.
Waves trapped between the horizon and that boundary can be repeatedly amplified, allowing energy to accumulate. That buildup can eventually break the mirror, creating the proposed black hole bomb effect. In the second mirror arrangement, increasing the quantum parameter makes the field amplitudes, energy fluxes, and growth parts of the wave frequencies all decrease.
Unlike Type I, this case has only two eigenmodes, with no new mode appearing at the high parameter value of one point two. A possible explanation is that the extra left mirror makes the effective potential well shallower, leaving it able to support fewer eigenstates than the mirror-free arrangement.
The conclusions apply only to a spherically symmetric charged black-bounce black hole; the effects of the quantum parameter in nonsingular rotating black holes remain unstudied. The reflective boundary is artificially imposed, although nonlinear interactions could provide another way to confine the field.
The study also follows the field alone, leaving changes in the black hole’s mass and charge for future work. The charged black-bounce spacetime weakens wave amplification, and reflective boundaries can change which wave patterns survive. That matters for understanding how energy might escape or build up around altered black holes.
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