Download General Relativity & Black Holes

General Relativity &
Black Holes
Jenn Felder and Nikki Linn
Physics 220
4 Forces in Nature
1.
2.
3.
4.
Weak Force (radioactivity)
Strong Force (nuclei)
Electromagnetic Force
Gravity
Gravity plays the
dominant role in
the universe
• Long-range
• Always Attractive (predictable)
Problem
• Newton’s law of universal
gravitation (F=GmM/r^2) has
discrepancies on a
cosmological scale.
Solution
• Einstein’s General Theory of
Relativity
Recall the Special
Theory of Relativity
• Inertial reference frames
(constant velocity)
• Laws of physics are same in all
inertial reference frames
• Speed of light is constant
Principle of Equivalence
• No difference between
acceleration and gravity
• Spaceship example
• Gravitational mass= inertial
mass
• Gravitational mass: F=GmM/r^2
• Inertial mass: F=ma
• No experiment can determine a
difference
Light Bending
• Spaceship example
• Stopped or v<<c
• Constant v (v~c)
• Accelerating
• Light is affected by gravity
• 3 stars example
• 1919 eclipse
Curved Space
• Light does not always move in
a straight line
• A straight line is not always
the shortest distance between
two points
How to Determine if a
Surface is Curved
1. Triangles
2. Circles
•
•
Positive curve: C>2r
Negative curve: C<2r
Is Our Universe Curved?
• Gauss’ Mountains
• We don’t know
• If positive curvature=
finite (spherical)
• If negative or no curvature=
open (infinite)
Space-time Curvature
• Space-time is curved near
massive bodies (trampoline)
• Extreme curvature of spacetime= black hole
Black Holes:
Theoretically
• Theoretically, how do black
holes occur?
• Why do they appear black?
• Schwarzchild Radius, R=2GM/c2
Black Holes:
Experimentally
• It is possible that
many galaxies,
including our own,
have Black Holes
at the center.
• How is this
inferred?
• What do scientists
examine?
http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html
Pictures of Galaxies in
Which It Seems Black
Holes Exist
Since this galaxy is rotating, we can
measure its speed and radii, and thus
measure the object in the center .
The object at its center is about the same
size as our solar system but weighs
1,200,000,000 times as much as our sun.
We can determine the speed of
rotation of this disk and its size and
thus weigh the size of the invisible
object at the center.
Although the object is no bigger than
our solar system it weighs three
billion times as much as the sun.
Animation of What It Would
Look Like To Approach a
Black Hole
•
•
•
As the observer moves toward the black hole, the original star images
appear pushed away from the black hole This is because the starlight
that originally reached you is now strongly attracted toward the black
hole and hence deflected away from you. Only starlight passing further
from the black hole might now be attracted toward the black hole so
that it is deflected to your eye.
As the computer generated animation continues, the observer stops
just 42 kilometers from the black hole.
http://antwrp.gsfc.nasa.gov/htmltest/gifcity/rsgrow.html
Sources
1.
2.
3.
4.
5.
6.
Giancoli, Douglas C. Physics: Principles with
Applications. Prentice Hall: Upper Saddle River, 1998
http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html
http://www.economist.com/science/displayStory.cfm?st
ory_id=2593048
Nemiroff, Robert. Black Holes and Neutron Stars. 1995. 2
May 2004. http://antwrp.gsfc.nasa.gov/htmltest/rjn_bht.html
“Observational Evidence for Black Holes.” Cambridge
Relativity Public Home Page. 1996 University of Cambridge. 2
May 2004.
http://www.damtp.cam.ac.uk/user/gr/public/bh_obsv.html
“Black Holes.” Imagine the Universe. 2004 NASA. 2 May
2004.
http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_hol
es.html
Acknowledgements
• Thanks Charles!