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

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Discussion Overview

The discussion centers around the concept of linearized general relativity (GR) and its relationship to Riemannian geometry. Participants explore the nature of linearized GR, its mathematical formulation, and its implications in the context of both general relativity and potential alternative models of spacetime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants describe linearized gravity as using perturbations of flat spacetime to approximate the metric, specifically represented as g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu }.
  • One participant notes that linearized GR is commonly mentioned in GR literature, suggesting its foundational role in understanding the theory.
  • Another participant shares their experience with Ohanian and Ruffini's book, describing it as a gentle introduction but not recommending it for advanced study.
  • A question is raised about the possibility of applying perturbations of Newtonian spacetime to approximate both the Minkowski metric in special relativity (SR) and the Lorentzian metric in GR.
  • One participant speculates on the idea that if the universe's spacetime were fundamentally Newtonian, it could be influenced by a Higgs-like field that produces the effects observed in SR and GR.

Areas of Agreement / Disagreement

Participants express varying opinions on the utility and depth of Ohanian's book, with some viewing it as suitable for beginners while others suggest it lacks depth for advanced learners. The discussion includes speculative ideas about the nature of spacetime, indicating that multiple competing views remain without consensus.

Contextual Notes

Some assumptions about the nature of spacetime and the applicability of perturbation methods remain unresolved, as do the implications of the proposed Higgs-like field concept.

waterfall
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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?
 

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