# Help with PPN formalism parameters (gamma/beta) - is Hartle correct?

1. Sep 4, 2014

### ssj2poliwhirl

I am confused by the classical parameters used in the Parametrized Post-Newtonian formalism, and how they are derived - Hartle Chapter 10 goes over it, but it contradicts what I have read from other sources/papers.

Every source I have seen agrees that GR predicts/is defined by γ = 1, β = 1, but there are differences in how the metric tensor gμν is written for the squared term in g00;

Hartle writes it as;
g00 = -[1 - 2M/r + 2(β-γ)(M/r)^2]
[this is not the exact statement written in Hartle, but it is the equivalent expansion based on his 'derivation']

while other papers I have seen write it as;
g00 = -[1 - 2M/r + 2(β)(M/r)^2]

ie: the factor of the squared term is (β - γ) in Hartle, and just β in other sources.

Can anyone confirm which is correct, and why? Based on the purpose of the PPN formalism, it doesn't make sense why two parameters would be used for the same component.
By Hartle's definition, the squared term will go to 0 for GR, TBH I don't even really get where that equation came from... the explanation doesn't make too much sense to me unfortunately.

I asked my lecturer briefly and he agreed with the Hartle version, I don't quite remember his reasoning but I just wanted to confirm.

Examples of papers that use only the β factors:
http://www.aanda.org/articles/aa/pdf/2003/07/aa3222.pdf
http://www.einsteins-theory-of-relativity-4engineers.com/support-files/PPN-formalism.pdf

Additionally, Wikipedia and Clifford Will's paper use the full 10 parameter expansion (I am not sure how this is derived), which *seems* to agree with using a factor of β, not (β - γ).
The Confrontation between General Relativity and Experiment;