3. Basics of Spacetime

Question 1

When can galaxies recede faster than the speed of light?

Answer 1

When they are beyond the Hubble distance

- Expansion of the scale factor allows it

Question 2

What is the equivalence principle?

Answer 2

Conditions can be the same in different locations

e.g. acceleration of g standing on earth, or replicated in an accelerating rocket

Question 3

What are the three types of curvature?

Answer 3

Euclidean, spherical, hyperbolic

Question 4

Describe Euclidean curvature

Answer 4

Flat and infinite

a + b + c = pi

Question 5

Describe spherical curvature

Answer 5

Closed and positive curvature

a + b + c = pi + A / R^2

Question 6

Describe hyperbolic curvature

Answer 6

Open, negative curvature
a + b + c = pi - A / R^2
- As R -> infinity, curvature goes flat

Question 7

What do R and A represent in describing spacetime?

Answer 7

A - Area of the triangle on the surface

R - Radius of curvature

Question 8

Give an example of negative curvature when observing a galaxy

Answer 8

Have a big galaxy, and light rays curve downwards from the edges into our eye

• Hyperbolic and negative curvature
• Galaxy appears much smaller

Question 9

What is the equation for Luminosity distance?

Answer 9

d_L = (L / 4 pi f)^1/2

Question 10

What is the equation for proper distance?

Answer 10

d_p(t_e) = c / (1+z) ∫ dt / a(t) [t_emitted, t_0]