1F03_2020C24.pdf - 1 Chapter 24 Black Holes and Curved...

Chapter 24
Black Holes and Curved Spacetime
Astronomy 1F03
1

Introducing General Relativity
2
Stellar remnants:
• White dwarfs
• Neutron stars
• Black holes → need relativity
Credit:

Equivalence Principle
3
Stationary or constant speed
Normal weight
Accelerating down
Lighter than normal
Accelerating up
Heavier than normal
Cable breaks
No apparent weight
Credit: OpenStax figure 24.3
Or stationary in
space far from any
massive objects
Or in space far from
any massive objects
and accelerating up
at 9.81 m/s 2

Gravity or Acceleration?
• Ball and people fall at same
rate
• Ball stays in straight line (unlike
normally)
4
Credit: OpenStax figures 24.4 and 24.5

Paths of Light and Matter
• Does light not obey the equivalence principle?
• Does light not travel in straight lines?
• Einstein said the latter; mass bends spacetime
5
Credit: OpenStax figure 24.6

Spacetime and Gravity
• Shortest paths on Earth follow great circles (e.g., lines of
longitude, equator)
• “Matter tells spacetime how to curve; spacetime tells
matter how to move” John Wheeler
• Rubber sheet analogy for spacetime:
6
Credit: OpenStax figure 24.8

GR Test 1: Advance of Mercury’s Perihelion
7
• Sun distorts spacetime around it
more than Earth because of its
greater mass
• Sun’s effect on Mercury already
measured but not explained
• Each successive perihelion
moves with respect to the last
• Newton: 531”/century
• Einstein and observations:
574”/century
Credit:

GR Test 2: Deflection of Starlight
During total solar eclipse look for stars that you
shouldn’t be able to see (because they’re directly
behind the Sun) but you can see because of the
spacetime bending
8
Credit: OpenStax figure 24.10

Time in General Relativity
9
• Stronger gravity causes time to slow down
• Test 1: 1959 Harvard physics building clock runs slower at bottom than at top
• Test 2: 1976 Viking spacecraft; time delays for radio waves sent near Sun
• Lots of modern applications (see later slides)
Credit: OpenStax figure 24.11

Gravitational Redshift
10
• Time runs slower in higher g
• Frequency (inverse of time) gets
smaller
• Speed of light is constant; wavelength