An theory of gravity keeps its field equations built from the metric alone but drops…
PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Schwarzschild spacetime and the tests of general relativity · Schwarzschild spacetime and the tests of general relativity
The Geometry of Gravity, Ch Solar-system tests, the PPN framework and alternative theories
Problem
An f(R) theory of gravity keeps its field equations built from the metric alone but drops the requirement that they be second order. A screening mechanism is invoked so that the theory mimics general relativity (γPPN≈1) in the high density near the Sun, but is stated to leave γPPN=0.995 unscreened in the much lower density of the outer solar system, near Saturn's orbit (r=1.43×1012m).
((a)) Name the assumption of the Einstein field equations, distinct from the metric-alone assumption, that this class of f(R) theory drops.
((b)) Find the compactness parameter GM⊙/rc2 at Saturn's orbital distance, using GM⊙/c2=1.48km, and confirm the PPN expansion still applies there.
((c)) A spacecraft near Saturn could measure the deflection of quasar light passing the solar limb (b=R⊙=6.96×108m) and determine γPPN to a precision δγPPN=1×10−3. Find the fraction of the total deflection that such a ray acquires on the source side at distances from the Sun beyond Saturn's orbit, and state, with a reason, whether this proposed experiment would discriminate the unscreened f(R) prediction from general relativity.