众所周知，Klein Gordon（KG）方程$\Box Φ+ m^2Φ=0$在平坦的Minkowski时空中具有大尺度上的快子不稳定模（$m^2<m_{cr}^2=0$），在$k=0$上获得了最大增长率$Ω_{F}(m)= \vert m \vert$.我们在具有质量$M$、电荷$Q$、宇宙学常数$Λ>0$和多重视界的Reissner-Nordström-deSitter（RN-dS）背景时空中研究了这些不稳定性。通过求解KG方程之间的事件和宇宙学视野的范围内，使用乌龟坐标$r_*$，我们确定了新兴的薛定谔类Regge-Wheeler方程对应的不稳定性的束缚态。我们发现，临界值$m_{cr}$，使$m^2<m_{cr}^2$的束缚态和不稳定性出现，仍然等于平坦的空间值$m_{cr}=0$的背景度量参数的所有值，尽管局部负性质的Regge-Wheeler潜在的$m=0$。然而，对于背景度量（$Ω(Q/M,M^2 Λ, mM)< \vert m \vert$）的所有参数值，与平坦情况相比，$m^2<0$的快子不稳定性的增长率$Ω$显著降低。在$Q=0$和宇宙视界几乎等于事件视界（$ξ\equiv 9M^2 Λ\simeq 1$）的近极端Schwarzschild-deSitter（SdS）黑洞的情况下，快子不稳定性的寿命增加是最大的。不稳定性增长延迟的物理原因似乎是宇宙学视界的存在，它倾向于缩小龟坐标中Regge-Wheeler势的负范围。
英文摘要：
It is well known that the Klein Gordon (KG) equation $\Box Φ+ m^2Φ=0$ has tachyonic unstable modes on large scales ($k^2<\vert m \vert^2$) for $m^2<m_{cr}^2=0$ in a flat Minkowski spacetime with maximum growth rate $Ω_{F}(m)= \vert m \vert$ achieved at $k=0$. We investigate these instabilities in a Reissner-Nordström-deSitter (RN-dS) background spacetime with mass $M$, charge $Q$, cosmological constant $Λ>0$ and multiple horizons. By solving the KG equation in the range between the event and cosmological horizons, using tortoise coordinates $r_*$, we identify the bound states of the emerging Schrodinger-like Regge-Wheeler equation corresponding to instabilities. We find that the critical value $m_{cr}$ such that for $m^2<m_{cr}^2$ bound states and instabilities appear, remains equal to the flat space value $m_{cr}=0$ for all values of background metric parameters despite the locally negative nature of the Regge-Wheeler potential for $m=0$. However, the growth rate $Ω$ of tachyonic instabilities for $m^2<0$ gets significantly reduced compared to the flat case for all parameter values of the background metric ($Ω(Q/M,M^2 Λ, mM)< \vert m \vert$). This increased lifetime of tachyonic instabilities is maximal in the case of a near extreme Schwarzschild-deSitter (SdS) black hole where $Q=0$ and the cosmological horizon is nearly equal to the event horizon ($ξ\equiv 9M^2 Λ\simeq 1$). The physical reason for this delay of instability growth appears to be the existence of a cosmological horizon that tends to narrow the negative range of the Regge-Wheeler potential in tortoise coordinates.
Spontaneous Scalarization of Brane Black Holes: Quantum-Enhanced Tachyonic Instabilities
Institute of Quantum Physics, School of Physics, Central South University（中南大学物理学院量子物理研究所）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；School of Physics, University of Chinese Academy of Sciences（中国科学院大学物理学院）；School of Physics, Xi’an Jiaotong University（西安交通大学物理学院）
Universal Non-Gaussian Signatures from Transient Instabilities
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论科学中心）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Institut d’Astrophysique de Paris, Sorbonne Université, CNRS（巴黎天体物理学研究所，索邦大学，法国国家科学研究中心）；Max Planck Institute for Physics, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所，维尔纳·海森堡研究所）；Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry（马克斯·普朗克-国际先进研究-南洋理工大学粒子物理、宇宙学与几何中心）
