Turbulence、重力和多信使天文地震学
Turbulence, Gravity, and Multimessenger Asteroseismology
摘要：
第IA部分：我们提出了相对论标度关系的数值测量$(2+1)$维共形流体湍流，其表现优于其非相对论版本。在过去的研究中，我们发现不可压缩湍流的能谱表现出$k^{-2}$标度，而不是Kolmogorov/Kraichnan期望的$k^{-5/3}$。第IB部分：我们计算的分形维数$D$的湍流反deSitter黑膜重建边界流体数据使用流体重力对偶。我们的值$D=2.584(1)$是一致的上限$D\leq 3$，解决了最近的索赔，$D=3+1/3$。我们描述了如何协变定义的分形维数的地平线的空间部分，我们推测分配一个“自助”的价值，整个地平线。第二部分：我们报告的进展，实现流体代码与后牛顿（PN）重力球对称。PN形式主义通过椭圆方程将流体、其自引力和黑洞耦合起来。这消除了辐射模式，允许更大的时间步长，这有助于研究具有很长时间尺度的系统，例如。潮汐扰动事件第三部分：旋转核心坍缩超新星的星震学是可能的多信使战略。结果表明，在引力波和中微子的发射中，核心的$l=2$，$m=0$，$n\gtrsim 2$，$f\lesssim 280$ Hz模式是负责的。中微子发射的角谐函数与中微子球周围的模式能量一致，其中$r\sim 70$ km。因此，中微子携带的信息模式在外部区域的核心，而引力波探测深内核$r \lesssim 30$公里。
英文摘要：
Part IA: We present numerical measurements of relativistic scaling relations in $(2+1)$-dimensional conformal fluid turbulence, which perform favourably over their non-relativistic versions. As seen with incompressible turbulence in past studies, we find that the energy spectrum exhibits $k^{-2}$ scaling rather than the Kolmogorov/Kraichnan expectation of $k^{-5/3}$. Part IB: We compute the fractal dimension $D$ of a turbulent anti-deSitter black brane reconstructed from boundary fluid data using the fluid-gravity duality. Our value of $D=2.584(1)$ is consistent with the upper bound $D\leq 3$, resolving a recent claim that $D=3+1/3$. We describe how to covariantly define the fractal dimension of spatial sections of the horizon, and we speculate on assigning a `bootstrapped' value to the entire horizon. Part II: We report progress implementing a fluid code with post-Newtonian (PN) gravity in spherical symmetry. The PN formalism couples a fluid, its self-gravity, and a black hole via elliptic equations. This eliminates radiative modes, allowing larger time steps, which is helpful for studying systems with very long time scales, eg. tidal disruption events. Part III: Asteroseismology of rotating core-collapse supernovae is possible with a multimessenger strategy. We show an $l=2$, $m=0$, $n\gtrsim 2$, $f\lesssim 280$ Hz mode of the core is responsible for emission in gravitational waves and neutrinos. The angular harmonics of the neutrino emission is consistent with the mode energy around the neutrinospheres, where $r\sim 70$ km. Thus, neutrinos carry information about the mode in the outer region of the core, whereas gravitational waves probe the deep inner core $r \lesssim 30$ km.
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