I am reading the book Gravitational waves vol 1 by Maggiore. On page 190 he writes down an equation for the magnitude of the velocity: $$\frac{d|\vec{u}|}{dt}=-\frac{\dot{a}}{a}|\vec{u}|\tag{$*$}$$ where $|\vec{u}|^2= g_{ij} u^i u^j$. He is using the metric: $$ds^2=-c^2 dt^2+a^2(t)\left[\frac{dr^...

The volume of a sphere in flat space is: $$V = \frac{4}{3}\pi r^3.$$ In curved space, $r$ itself is dependent on position, so, in spherical coordinates, $$r=r(r, \phi, \theta) .$$ Assuming a spherical symmetric spacetime, for example the Schwarzschild metric: $$ds^2=-Bc^2dt^2+Adr^2+r^2d\Omega.$$ ...

I was reading my old physics textbook (from middle school), and it mentioned something about the idea of having non-existing attractive forces between particles like air. "We would live in a very dull world." This made me wonder, what would've happened if there are no bonds between air particles,...

I was just wondering if anyone had computed this. I read that the pressure in the Sun's core is 3.84 trillion psi. Obviously the mass of an Earth-sized object in the core would be millions of times that of Earth. So how much volume would the mass of Earth occupy? Would it be more than a billiard...