Chapter 22 Neutron Stars and Black Holes
22.1 Neutron Stars
After a Type 1 supernova, little or nothing remains of the original star
After a Type 2 supernova, part of the core may survive. It is very dense—as dense as an atomic nucleus—and is called a neutron star
22.5 Black Holes
High-mass stars → Type 2 Supernova (core collapse supernova) → neutron stars → (if mass > 3 solar mass) Black Hole
Properties can be measured from outside:
mass
charge
angular momentum
The radius at which the escape speed from the black hole equals the speed of light is called the Schwarzschild radius
Critical radius is proportional to mass
The Earth’s Schwarzschild radius is about a centimeter; the Sun’s is about 3km
Once the black holes has collapsed, the Schwarzschild radius takes on another meaning— it is the event horizon, or the “surface” of a black hole
Nothing within the event horizon can escape the black hole
22.6 Einstein’s Theories of Relativity
Special relativity:
The speed of light is the maximum possible speed, and it is always measured to have the same values by all observers
There is no absolute frame or reference, and no absolute state of rest
Space and Time are not independent but are unified as spacetime. There is no absolute, universal time
Consequence of Special Relativity:
Time dilation
Length contraction
Space Travel
Example: A space traveler was traveling at 99.9% of c to a galaxy 100 light years away. When he is back, according to the Earth’s calendar, 200 years have passed. According to his calendar, only 9.94 years have passed
Time Travel
Cause-and-effect Relation, “Terminator”
“Back to the Future,” time travelers can change history
“Twelve Monkeys”, Time travelers can modify some details of history, but can’t change the fate
“The One”, parallel universe
Time travelers are only observers
General Relativity:
It is impossible to tell from within a closed system whether one is in a gravitational field or accelerating
Matter tends to wrap spacetime, and in doing so redefines straight lines ( the path a light beam would take):
A black hole occurs when the “ indentation” caused by the mass of the hole become infinitely deep
More Precisely 22-1: Special Relativity
Michelson and Morley experiment: in the late 19th century, to measure the variation in the speed of light with respect to the direction of the Earth’s motion around the Sun
They found no variation—light always traveled at the same speed. This later became the foundation of special relativity.
Taking the speed of light to be constant leads to some counterintuitive effects—length contraction, time dilation, the relativity of simultaneity, and the mass equivalent of energy
More Precisely 22-2: Tests of General Relativity
Deflection of starlight by the sun’s gravity was measured during the solar eclipse of 1919; the results agreed with the predictions of general relativity
22.7 Space Travel Near Black Holes
The gravitational effects of a black hole are unnoticeable outside of a few Schwarzschild radii—black holes do not “suck in” material any more than an extended mass would
Matter encountering a black hole will experience enormous tidal forces that will both heat it enough to radiate, and tear it apart
Similarly, a photon escaping from the vicinity of a black hole will use up a lot of energy doing so; it cannot slow down, but its wavelength gets longer and longer
A probe nearing the event horizon of a black hole will be seen by observers as experiencing a dramatic redshift as it gets closer, so that time appears to be going more and more slowly as it approaches the event horizon
This is called a gravitational redshift—it is not due to motion, but to the large gravitational fields present
The probe, however, does not experience any such shifts; time would appear normal to anyone inside
Black holes cannot be observed directly, as their gravitational fields will cause light to bend around them