论文标题
孟沃斯基后的第一种动荡重力方法
First Post-Minkowskian approach to turbulent gravity
论文作者
论文摘要
我们计算在米诺科斯基近似后一阶内由湍流能量张量引起的度量波动。发现湍流能量级联原则上可以干扰黑洞形成的过程，从而导致这两种高度非线性现象之间的潜在强烈耦合。进一步发现，幂律湍流能量$ e（k）\ sim k^{ - n} $生成度量波动比例缩放，例如$ x^{n-2} $，其中$ x $是距离Spacetime中任意来源的四维距离。 This highlights the onset of metric singularities whenever $n <2$, meaning that $2d$ fluid turbulence ($n=3$) yields smooth %(differentiable) metric fluctuations, scaling like $x$, while $3d$ turbulence ($n=5/3$) yields a weakly singular metric $x^{-1/3}$and purely random fluctuations, $n=1$, generate a $ 1/x $奇异性。最后，也讨论了度量波动对测试颗粒测量运动的影响，作为一种潜在技术，以提取有关波动时空的光谱特征的信息。
We compute the metric fluctuations induced by a turbulent energy-matter tensor within the first order Post-Minkowskian approximation. It is found that the turbulent energy cascade can in principle interfere with the process of black hole formation, leading to a potentially strong coupling between these two highly nonlinear phenomena. It is further found that a power-law turbulent energy spectrum $E(k) \sim k^{-n}$ generates metric fluctuations scaling like $x^{n-2}$, where $x$ is a four-dimensional distance from an arbitrary origin in spacetime. This highlights the onset of metric singularities whenever $n <2$, meaning that $2d$ fluid turbulence ($n=3$) yields smooth %(differentiable) metric fluctuations, scaling like $x$, while $3d$ turbulence ($n=5/3$) yields a weakly singular metric $x^{-1/3}$and purely random fluctuations, $n=1$, generate a stronger $1/x$ singularity. Finally, the effect of metric fluctuations on the geodesic motion of test particles is also discussed as a potential technique to extract information on the spectral characteristics of fluctuating spacetime.
