English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

The intriguing superradiant amplification phenomenon allows an orbitingscalar field to extract rotational energy from a spinning Kerr black hole.Interestingly, the energy extraction rate can grow exponentially in time if theblack-hole-field system is placed inside a reflecting mirror which prevents thefield from radiating its energy to infinity. This composedKerr-black-hole-scalar-field-mirror system, first designed by Press andTeukolsky, has attracted the attention of physicists over the last fourdecades. Previous numerical studies of this spinning {\it black-hole bomb} haverevealed the interesting fact that the superradiant instability shuts down ifthe reflecting mirror is placed too close to the black-hole horizon. In thepresent study we use analytical techniques to explore the superradiantinstability regime of this composedKerr-black-hole-linearized-scalar-field-mirror system. In particular, it isproved that the lower bound ${{r_{\text{m}}}\over{r_+}}>{1\over2}\Big(\sqrt{1+{{8M}\over{r_-}}}-1\Big)$ provides a necessary condition for thedevelopment of the exponentially growing superradiant instabilities in thiscomposed physical system, where $r_{\text{m}}$ is the radius of the confiningmirror and $r_{\pm}$ are the horizon radii of the spinning Kerr black hole. Wefurther show that, in the linearized regime, this {\it analytically} derivedlower bound on the radius of the confining mirror agrees with direct {\itnumerical} computations of the superradiant instability spectrum whichcharacterizes the spinning black-hole-mirror bomb.

The spinning Kerr-black-hole-mirror bomb: A lower bound on the radius of the reflecting mirror