论文标题
改进的衰减估计值和$ c^2 $ - 杂质的稳定性在球形对称性的爱因斯坦 - 刻录场系统中
Improved decay estimates and $C^2$-asymptotic stability of solutions to the Einstein-scalar field system in spherical symmetry
论文作者
论文摘要
我们研究了溶液对爱因斯坦（无质量）标量场系统的特征初始价值问题的渐近稳定性，具有正宇宙常数。我们在未来的零锥上开出了球形对称的初始数据，其腐烂轮廓范围比以前考虑的更大。然后得出新的估计值，以证明，对于小数据，该系统具有独特的全局经典解决方案。我们还表明，该解决方案在（Bondi）时间呈指数衰减，并且径向衰减本质上是多项式，尽管在某些特殊情况下包含对数因素。这种改进的渐近分析使我们能够证明，在初始数据的适当和自然的衰减条件下，未来的渐近解决方案是可区分的，直至和包括空间无效，并在无限属性附近接近Sitter解决方案。此外，我们分析了溶液的衍生物的衰减，直至二阶，显示了在这种情况下De Sitter吸引子的（均匀）$ C^2 $ - 杂质的稳定性。这对应于宇宙无头发猜想的令人惊讶的强烈认识。
We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a future null cone with a wider range of decaying profiles than previously considered. New estimates are then derived in order to prove that, for small data, the system has a unique global classical solution. We also show that the solution decays exponentially in (Bondi) time and that the radial decay is essentially polynomial, although containing logarithmic factors in some special cases. This improved asymptotic analysis allows us to show that, under appropriate and natural decaying conditions on the initial data, the future asymptotic solution is differentiable, up to and including spatial null-infinity, and approaches the de Sitter solution, uniformly, in a neighborhood of infinity. Moreover, we analyze the decay of derivatives of the solution up to second order showing the (uniform) $C^2$-asymptotic stability of the de Sitter attractor in this setting. This corresponds to a surprisingly strong realization of the cosmic no-hair conjecture.
