Chapter 22: Black Holes

• Einstein’s relativity:– Special

– General

– Relativity and black holes

• Evidence of black holes

• Properties of black holes

• Long-time behavior of black holes

Special relativity

• Newton says space and time are perfectly uniform and unchanging. It is always possible to know exactly how fast you are moving through space and time.

• In 1905 Albert Einstein proposed his special theory of relativity describing how motion affects our measurements of distance and time.– Distances and time intervals measured depend on how

the observer is moving.– Einstein’s theory is based on just two basic principles:

Principle 1

• Your description of physical reality is the same regardless of the constant velocity at which you move.– The direction and actual speed don’t matter.

You only need to have a constant velocity.– Called an inertial reference frame.

Principle 2

Regardless of your speed or direction of motion, you always measure the speed of light to be the same.

Consequences of special relativity

• Speed involves both distance and time. Since speed behaves differently in special relativity it shouldn’t be surprising that space and time behave differently as well.– In relativity space and time are intertwined in four-dimensional beast called spacetime.

– Our perception of both length and time depend strongly on our motion.

Length contraction

€

L = L0 1− vc( )

2

L = length of moving object along

direction of motion

L0 = length of the same object at rest

(proper length)

v = speed of moving object

c = speed of light

Time dilation

€

T =T0

1− vc( )

2

T = time interval measured by observer moving

relative to the phenomenon

T0 = time interval measured by observer not moving

relative to the phenomenon (proper time)

v = speed of moving object

c = speed of light

Moving clocks run slow.

Special relativity

• The astronaut with the flashlight will see the astronaut in the spaceship shortened in the direction of motion with a slowly ticking clock.

• These observations aren’t some sort of illusion. They are actual effects due to Einstein’s special relativity.

• Another important outcome of special relativity is E=mc2.

General relativity

• Special relativity is a comprehensive description of light and, by extension, of electricity and magnetism. Einstein’s next goal was to develop a theory describing gravity.– His general theory of relativity did just this

when published in 1915.

Equivalence principle

In a small volume of space, the downward pull of gravity can be accurately and completely duplicated by an upward acceleration of the observer.

Equivalence principle

• This principle allowed Einstein to focus on motion rather than force.

• Einstein envisioned gravity as being caused by curvature of spacetime.

Testing general relativity

Testing general relativity

Testing general relativity

Relativity and black holes

Curved spacetime near a black hole

Detecting black holes

• X-ray source Cygnus X1 detected near B0 supergiant star.

• X-ray emissions are highly variable and flicker on 0.01 s timescale.– This means X-ray source is at

most 3000 km in diameter.

• Cygnus X1 has estimated mass of 7 M.– Given its diameter it is likely a

black hole.

X-rays from Cygnus X1

Vicinity of a rotating black hole

Supermassive black holes in galactic cores

Structure of a nonrotating black hole

• Event horizon: distance where escape speed just equals the speed of light

• Singularity: “region” where all of star’s mass has been crushed to zero volume (and infinite density)– Strength of gravity and

curvature of spacetime are infinite at the singularity

– Laws of physics don’t apply at the singularity. It’s a weird place.

Schwarzchild radius

€

RSch =2GM

c 2

RSch = Schwarzchild radius of black hole

G = Universal constant of gravitation

M = mass of black hole

c = speed of light

Three properties of a black hole

• Once matter passes through the event horizon all information about it disappears except for three quantities:– Mass– Electric charge– Angular momentum

Structure of a rotating black hole

Evaporation of a black hole

• It is possible to get mass back out of a black hole through pair production.

• This happens faster with low mass black holes.– 1010 kg b.h. would need 15

billion years to evaporate while 5 M b.h. would need 1062 years.