## 物理学：Peldan black hole with Quintessence

the metric of Peldan black hole with Quintessence is

$ds^2=-N(\rho)^2 dt^2 +\frac{1}{L(\rho)^2}d\rho^2+\rho^2d\phi^2$

where

$L(\rho)^2=N(\rho)^2=\frac{\rho^2}{l^2}-2b^2 \ln \rho -M +Q_s$

where $$Q_s$$ is the Quintessence term, which is

$Q_s=-\frac{c}{\rho^{3\omega_q+1}}$

# 声能

$W=W_{\mathrm {potential} }+W_{\mathrm {kinetic} }=\int _{V}{\frac {p^{2}}{2\rho _{0}c^{2}}}dV+\int _{V}{\frac {\rho _{0}v^{2}}{2}}dV$

• $$V$$ – 流体的体积
• $$p$$ – 声压
• $$v$$ – 流体质点速度
• $$\rho_0$$ – 流体静态密度
• $$c$$ – 声速

## 声能密度

$\epsilon ={\frac {p^{2}}{2\rho _{0}c^{2}}}+{\frac {\rho _{0}v^{2}}{2}}$

## 平均声能量密度

${\bar {\epsilon }}={\frac {p_{e}^{2}}{\rho _{0}c^{2}}}$

## 参考

1.  L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, 1999. Fundamentals of Acoustics, fourth edition (Wiley).第5.8节。
2. ^ 杜功焕、朱哲明、龚秀芳，声学基础，第二版，第4.7节。

## 科普讲座：时间是什么

1.4-时间的本质是什么？（中英字幕）【PBS Space Time】

1.5-物质与时空的真正含义（中英字幕）【PBS Space Time】

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# Why two shadows bend when close together

This is called the Shadow Blister Effect. Essentially it’s a bit of an illusion caused by two penumbras, or fuzzy regions at the edge of an objects shadow. As they overlap, they seem to bridge because the prenumbras start to mix and create a darker shaded area. The eye doesn’t consider the penumbra to be part of the shadow since its brighter than the shadow, but when they merge they are dark enough to be considered by the eye to be part of the shadow.