Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters

Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework  Parametrizing the PN metric  Conservation laws  Equations of motion - photons  Equations of motion - massive bodies  Equations of motion - gyroscopes  Locally measured gravitation constant G  The Strong Equivalence Principle Lecture 4: Tests of the PPN Parameters

The PN metric in GR

Effect of a PN gauge change

Parametrizing the post-Newtonian metric

Effect of a Boost

The parametrized post-Newtonian (PPN) framework

Parameter What it measures, relative to general relativity Value in GR Value in scalar tensor theory Value in semi- conservative theories  How much space curvature produced by unit mass? 1(1+  )/(2+  )   How “nonlinear’’ is gravity? 11 +    Preferred-location effects? 00   Preferred-frame effects? 00   00   000  Is momentum conserved? 000  000  000  000 PPN Parameters and their Significance

PPN n-body equation of motion

Newtonian” part of the n-body acceleration

PPN n-body equation of motion

The problem of motion  Geodesic motion  Droste, De Sitter - n-body equations of motion  Lense & Thirring - motion in field of spinning body  Levi-Civita - center-of-mass acceleration  Eddington & Clark - no acceleration  EIH paper & Robertson application  1960s - Fock & Chandrasekhar - PN approximation  the Nordtvedt effect& the PPN framework  numerical relativity - BH head-on collision  discovery of PSR

The Strong Equivalence Principle (SEP)  All bodies fall with the same acceleration Weak Equivalence Principle (WEP)  In a local freely falling frame, all physics is independent of frame’s velocity Local Lorentz Invariance (LLI)  In a local freely falling frame, all physics is independent of frame’s location Local Position Invariance (LPI)

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