<p>Ultralight vector particles can form evolving condensates around a Kerr black hole (BH) due to superradiant instability. We study the effect of near-horizon reflection on the evolution of this system: by matching three pieces of asymptotic expansions of the Proca equation in Kerr metric and considering the leading order in the electric mode, we present explicit analytical expressions for the corrected spectrum and the superradiant instability rates. Particularly, in high-spin BH cases, we identify an anomalous situation where the superradiance rate is temporarily increased by the reflection parameter <i>ℛ</i>, which also occurs in the scalar scenario, but is largely magnified in vector condensates due to a faster growth rate in dominant mode. We point out that the condition for the growth anomaly in the adiabatic case is that information carried per particle exceeds a certain value <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11433_2024_2602_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="245" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta I/\delta N >2\pi k_{\mathrm{B}}\sqrt{(1+\mathcal{R})/(1-\mathcal{R})}$</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>δ</mi> <mi>I</mi> <mrow> <mo>/</mo> </mrow> <mi>δ</mi> <mi>N</mi> <mo>></mo> <mn>2</mn> <mi>π</mi> <msub> <mi>k</mi> <mrow> <mrow> <mi mathvariant="normal">B</mi> </mrow> </mrow> </msub> <msqrt> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mrow> <mi mathvariant="script">R</mi> </mrow> <mo stretchy="false">)</mo> <mrow> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <mrow> <mi mathvariant="script">R</mi> </mrow> <mo stretchy="false">)</mo> </msqrt> </math></EquationSource> </InlineEquation>. We further construct several featured quantities to illustrate it, and formalize the anomaly-induced gravitational wave strain deformation.</p>

Superradiant growth anomaly magnification in evolution of vector bosonic condensates bounded by a Kerr black hole with near-horizon reflection

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发表日期：

2025年2月21日

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Nayun Jia,
Yin-Da Guo,
Gui-Rong Liang,
Zhan-Feng Mai,
Xin Zhang

摘要

Ultralight vector particles can form evolving condensates around a Kerr black hole (BH) due to superradiant instability. We study the effect of near-horizon reflection on the evolution of this system: by matching three pieces of asymptotic expansions of the Proca equation in Kerr metric and considering the leading order in the electric mode, we present explicit analytical expressions for the corrected spectrum and the superradiant instability rates. Particularly, in high-spin BH cases, we identify an anomalous situation where the superradiance rate is temporarily increased by the reflection parameter ℛ, which also occurs in the scalar scenario, but is largely magnified in vector condensates due to a faster growth rate in dominant mode. We point out that the condition for the growth anomaly in the adiabatic case is that information carried per particle exceeds a certain value $\delta I/\delta N >2\pi k_{\mathrm{B}}\sqrt{(1+\mathcal{R})/(1-\mathcal{R})}$ $δ I / δ N > 2 π k_{B} \sqrt{(1 + R) / (1 - R)}$ . We further construct several featured quantities to illustrate it, and formalize the anomaly-induced gravitational wave strain deformation.