What is linearized GR and how does it relate to Riemannian geometry?

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https://www.amazon.com/dp/0393965015/?tag=pfamazon01-20

How many here own this book by Ohanian & Ruffini "Gravitation and Spacetime"?

A review mentions:

"Ohanian introduces linearized GR (in a completely logical and satisfying manner) before Riemannian geometry"

What's linearized GR?

I already own 10 GR books. What's so unique with Ohanian's that I must get one?
 
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Linearized gravity is just using perturbations of flat spacetime to approximate the metric:

[itex]g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu }[/itex]

I've never seen a GR book that doesn't have some mention of linearized GR.
 
I have a copy of Ohanian and have taught out of it. It's a gentle introduction, Ok as a first book but I wouldn't recommend it beyond that.
 
elfmotat said:
Linearized gravity is just using perturbations of flat spacetime to approximate the metric:

[itex]g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu }[/itex]

I've never seen a GR book that doesn't have some mention of linearized GR.

Is it possible to do perturbations of Newtonian spacetime to approximate both the minkowski metric in SR and lorentzian metric in GR?

What if our universe space time were really Newtonian and Spacetime (tm) is just some kind of Higgs-like field that create all those SR and GR effects. Is this possible?