In Gμν=(8πG/c⁴)Tμν, what do the indexed tensors describe?

• Curvature and stress-energy
• Coordinate names and a choice of coordinate origin
• Two independent lists of coordinate labels

Which tensor records local curvature measured through infinitesimal parallel-transport loops?

• The list of coordinate labels alone
• The vector's coordinate components alone
• The Riemann tensor

If one vector returns unchanged around one small loop, every local curvature component must be zero.

Circle one:   True   False

For a nearly static weak field and slow matter, which equation does the Einstein field equation recover?

• An equation making all gravitational potentials zero
• An equation removing all dependence on mass density
• Newton's equation ∇²Φ=4πGρ

A vector returns rotated after parallel transport around a small contractible loop in a smooth region. What does this establish?

• The entire region must have zero curvature
• Curvature affects transport around that loop
• Changing the vector by hand measures the same thing

In the displayed convention Gμν=κTμν, what coupling κ is fixed by matching Newtonian gravity?

• 8πG/c⁴
• 8πG/c²
• 8πc⁴/G

With zero cosmological constant, a vacuum region has Rμν=0. Must its full Riemann tensor also vanish?

• Yes; every contraction determines every component
• Yes; vacuum removes all possible tidal effects
• No; tidal curvature can remain

A student gives Tμν everywhere and claims this alone selects one spacetime metric. What information can still be needed?

• Only a different name for each coordinate
• Initial or boundary data
• Only a different symbol for Newton's constant