General Relativity

Question 1

What is the Equivalence Principle?

Answer 1

The Equivalence Principle states that a uniformly accelerating frame is indistinguishable from a uniform gravitational field.

This is used to keep the scale factor only a function of time ( a(t), not a(x,t) )

Question 2

What is the FLRW metric?

Answer 2

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes the universe’s expansion in terms of the scale factor a(t):

ds^2 = c^2 dt^2 − a^2(t) [ dχ^2 + fK^2​(χ) ( dθ^2 + sin2θ dϕ^2 )]

where fK(χ) accounts for spatial curvature.

Question 3

What is the Friedmann equation?

Answer 3

The Friedmann equation describes how the universe expands:

(a/a˙​)^2=((8πG​ρ)/3)−(Kc2/a2)​

Question 4

What do we use the Einstein Field Equation for?

Answer 4

To work with curved spacetime and matter in the same equations. It helps with understanding General Relativity.

Question 5

What is the Einstein Field Equation?

Answer 5

G_uv = (8 * pi * G)/( c^4 ) * T_uv

G_uv and T_uv are systematic tensors.

Question 6

What is Einstein’s Cosmological Constant?

Answer 6

Δ is the number Einstein incorrectly used to make the universe static. It was removed after the universe was uncovered to be expanding, and then added back when dark energy was observed.

Question 7

What is the Geodisc Equation?

Answer 7

The geodesic equation provides the acceleration of a
test particle as a function of the metric and the velocity and position of the particle. (Eq in notes if you don’t remember, its the sum of several vectors of spacetime)

Question 8

Do you remember the derivation for the spatial part of a
curved spacetime?

Answer 8

No –> Check the Notes, write out the process.

Yes –> You’re lying, refer to No.