论文标题
标量速度不稳定性在重力背景下：存在和生长速率
Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate
论文作者
论文摘要
众所周知，Klein Gordon（kg）方程$ \ boxφ+ m^2φ= 0 $在$ MINKOWSKI SPACETICE $ MIXIVE MINKOWSKI SPACETIME $ MINGET MINKOWOWSKI SPACETIME $ MINGE MINGETEM = 0 $的大尺度上的速度不稳定模式（$ k^2 <\ vert m \ vert^2 $）。 \ vert $在$ k = 0 $时实现。我们在Reissner-Nordström-Desitter（RN-DS）背景时空中调查了这些不稳定性，带有质量$ M $，充电$ Q $，宇宙常数$λ> 0 $和多个范围。通过使用乌龟坐标$ r _*$求解事件和宇宙学视野之间的kg方程，我们确定了与不稳定性相对应的新兴Schrodinger型Regge-Wheeler方程的界限。我们发现，临界值$ m_ {cr} $，因此，尽管$ m^2 <m_ {cr}^2 $绑定状态和不稳定性出现，但仍等于平坦的空间值$ m_ {cr} = 0 $对于$ m = 0 $ = 0 $的REGGE-WHEELER潜在的本地负面性质，尽管本地的背景度量参数的所有值。但是，与平面案例相比，$ m^2 <0 $的速度不稳定性的增长率$ω$显着降低，而背景度量的所有参数值（$ω（q/m，m，m^2λ，mm）<\ vert m \ vert m \ vert $）。在接近极端的Schwarzschild-desitter（SDS）黑洞的情况下，速度不稳定性的寿命增加至关重要，其中$ q = 0 $，宇宙学的地平线几乎等于事件范围（$ξ\ equiv 9m^2λ\ simeq 1 $）。这种延迟不稳定性生长的物理原因似乎是宇宙学的存在，该地平线往往会缩小乌龟坐标中regge-wheeler潜力的负范围。
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.
