Gravitational potentials_澳门葡京手机版app下载

hansw
2024-04-29T14:20:33.138Z
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www.uio.no

I got some questions regarding Phi and Psi and which one is really the gravitational potential? Both of these are informally referred to as “Gravitational Potentials” in the literature and we cosmologist often mix up what we call them.

In most derivations of the Newtonian limit of GR we find that its the g00 component (i.e. “Psi”) that gives us the Newtonian equations (see e.g. this):
x’’=-DPsi
D^2 Psi = 4piG rho
This is why “Psi” is perhaps most often called the Newtonian potential in the literature (see e.g. the discussion in Bertschinger and Ma).

If we look at the perturbations we are implementing in the Newtonian gauge (in the sub-horizon limit k >> Hp where we can ignore small terms like Psi and Phi’ for big terms like k^2 Phi and “delta”’s) then they can be written:...