Schwarzschild-de Sitter时空中有质量标量场渐近衰减的两种机制
Two Regimes of Asymptotic Fall-off of a Massive Scalar Field in the Schwarzschild-de Sitter Spacetime
AI总结：
该研究揭示Schwarzschild-de Sitter时空中有质量标量场的渐近衰减由de Sitter分支拟正则模主导，依μM大小分为纯指数衰减和振荡指数衰减两种机制，并推广至带电及高维黑洞情形。
AI中文摘要：
众所周知，Schwarzschild-de Sitter时空中无质量标量场在渐近晚期$t \rightarrow \infty$的衰减行为遵循指数规律。相比之下，渐近平直Schwarzschild背景中的有质量标量场呈现出被幂律包络的振荡（正弦）拖尾衰减。我们证明，Schwarzschild-de Sitter时空中有质量标量场的渐近衰减是指数型的。具体而言，当$μM \gg 1$时（其中$μ$和$M$分别代表场的质量和黑洞质量），指数衰减同时伴随振荡。反之，在小$μM$的机制下，衰减是纯指数型的，没有振荡。这种衰减机制的差异凸显了一个事实：对于渐近de Sitter时空，是一类特定的拟正则模分支而非“拖尾”主导了渐近晚期的衰减。Schwarzschild-de Sitter时空存在两类拟正则模分支：经非零$Λ$项修正的渐近平直黑洞模式，以及经黑洞存在修正的真空de Sitter时空模式。我们表明，后一类分支是导致渐近衰减的原因。当$μM$较小时，纯de Sitter时空的模式是纯虚数（非振荡）的，而在中等和大$μM$情况下，它们同时具有实部和虚部，这就产生了两种渐近衰减的图景。此外，我们还证明，带电黑洞和高维黑洞的渐近衰减也呈指数型。
英文摘要：
The decay behavior of a massless scalar field in the Schwarzschild-de Sitter spacetime is well-known to follow an exponential law at asymptotically late times $t \rightarrow \infty$. In contrast, a massive scalar field in the asymptotically flat Schwarzschild background exhibits a decay with oscillatory (sinusoidal) tails enveloped by a power law. We demonstrate that the asymptotic decay of a massive scalar field in the Schwarzschild-de Sitter spacetime is exponential. Specifically, if $μM \gg 1$, where $μ$ and $M$ represent the mass of the field and the black hole, respectively, the exponential decay is also oscillatory. Conversely, in the regime of small $μM$, the decay is purely exponential without oscillations. This distinction in decay regimes underscores the fact that, for asymptotically de Sitter spacetimes, a particular branch of quasinormal modes, instead of a "tail", governs the decay at asymptotically late times. There are two branches of quasinormal modes for the Schwarzschild-de Sitter spacetime: the modes of an asymptotically flat black hole corrected by a non-zero $Λ$-term, and the modes of an empty de Sitter spacetime corrected by the presence of a black hole. We show that the latter branch is responsible for the asymptotic decay. When $μM$ is small, the modes of pure de Sitter spacetime are purely imaginary (non-oscillatory), while at intermediate and large $μM$ they have both real and imaginary parts, what produces the two pictures of the asymptotic decay. In addition, we show that the asymptotic decay of charged and higher dimensional black hole is also exponential.
