General Relativity & Black Holes Jenn Felder and Nikki Linn Physics 220

4 Forces in Nature 1.Weak Force (radioactivity) 2.Strong Force (nuclei) 3.Electromagnetic Force 4.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 space- time= black hole

Black Holes: Theoretically Theoretically, how do black holes occur? Why do they appear black? Schwarzchild Radius, R=2GM/c 2

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?

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.

Sources 1.Giancoli, Douglas C. Physics: Principles with Applications. Prentice Hall: Upper Saddle River, ory_id= http:// ory_id= Nemiroff, Robert. Black Holes and Neutron Stars May “Observational Evidence for Black Holes.” Cambridge Relativity Public Home Page University of Cambridge. 2 May “Black Holes.” Imagine the Universe NASA. 2 May es.html es.html

Acknowledgements Thanks Charles!