PES 106        Spring 2003 Previous Lecture General Astronomy II Next Lecture

Lecture Notes:

Lives of Stars: Black Holes

text: Chapter 14 Section 3

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Black Holes:

remnant of very high mass star after collapse

• size:
  • infinitely small - collapse to a point !
• mass
  • 3 - 20 x Mass of Sun
  • rest of mass was lost in earlier stages of life
• density
  • infinitely high
• temperature
  • ????
• luminosity
  • zero - light can not escape
• magnetic field
  • ????

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General Relativity

We are used to thinking

• of straight lines
• of flat spaces
• of space and time as separate

Shortest distance between two points is a straight line?

Not if you are on the surface of a globe: great circle routes are curved

Two parallel lines never meet ?

Imagine two people at the equator. They each walk straight North (parallel to one another). They meet at the North pole.

Treat time as a Fourth Dimension

• up-down
• left-right
• front-back
• future-past

Assume the speed of light is the maximum speed that anything can accelerate up to.

Geometry of Space-Time

space-time is not "flat" - it is warped by mass

objects follow a "straight" line in warped space (like Great Circle route)

light also follows a straight line in warped space => light is bent by massive objects

this is different from Newtonian physics since light has no mass

Two models (General Relativity and Classical Physics) give different predictions

Studies during a solar eclipse confirmed that light is bent passing the sun

Time is also distorted - clocks run slower near a massive object

From Newton's law of gravity, can calculate the speed needed for object to escape from a planet or star's gravity

Escape velocity depends on

• mass of the star
  • more mass => need higher speed to escape
• size of the star
  • smaller radius => need higher speed to escape

If mass is high enough and radius is small enough, escape velocity can equal speed of light

=> even light can not escape

for a typical black hole's mass, this happens at a radius of about 10 - 100 kilometers

called the "Schwarzchild radius" or the "Event horizon"

light can not escape from inside this distance

=> we can not see inside and do not know what is happening

Black Hole properties

can not tell what black hole is made of

can measure

• mass (from gravitational interactions with other objects)
• charge
• angular momentum

Observing black holes

no light to observe from inside the Schwarzchild radius

• black holes in binary star systems
  • accretion disk
    • charged particles move very quickly producing x-rays
  • orbit of companion star
    • hard to tell a big neutron star from a small black hole
  • gravity waves
    • carry away energy and cause stars to get closer together
• Hawking radiation - continuous spectrum
  • black holes are not totally "black"
  • very small amount of radiation
  • Wien's Law gives temperature near absolute zero
  • causes evaporation of black holes

Living near a black hole !

What if you are orbiting a star as it becomes a black hole?

NOT sucked in

mass is same - no change in gravity at your orbit

What if you are on the surface of the star as it becomes a black hole?

• star is contracting
• surface gets closer to center
• surface gravity gets stronger
• eventually difference in gravity between head and feet would stretch you out

  

What if you are in a space ship flying near a black hole?

pull of gravity might deftect you as you pass by

could be a problem if you go straight into one !!

Here is more description of black holes: http://www.pbs.org/wnet/hawking/strange/html/blackh.html

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