chapter 24 black holes “black holes are out of sight!”

Chapter 24Black Holes

“Black Holes are out of sight!”

Black Holes

• Created when core of star is greater than about 5 M

• Called “black” because gravity is so strong that even light can not escape.

• The idea of a black hole is a very strange one.

• To understand them we have to discard some commonsense ideas that we have about space & time.

Newtonian Worldview

According to Newton:

• Space is perfectly uniform and fills the universe like a rigid frame.– Distance between two points is the same no matter

who measures it.

• Time passes at an unchanging rate.– Time elapsed between two events (eg: two lightning

strikes) is the same irrespective of who’s measuring.

Special Theory of Relativity

Einstein’s special theory of relativity is based on two basic principles:

• Your description of physical reality is the same regardless of the constant velocity at which you are moving.– If you are moving in a train at say 100km/h, then the

length of your arm, and the time interval between the ticks of your watch are the same as if your train was moving in any other direction at any other speed (or not moving at all).


• Regardless of your speed or the direction of motion, you always measure the speed of light to be the same. – Suppose you are traveling in a space ship at a speed

of 99% of the speed of light towards a flashlight. You will measure the speed of the photons approaching you to be c, the same as an observer on a stationary space ship would observe it.

– This conflicts with Newtonian view, where the speeds should add up.


• Therefore, speed behaves differently in relativity than we are familiar with.– Since speed involves both space(distance) and

time, they two behave strangely. – According to relativity, space and time seem to be

intertwined, and are not two unrelated entities as described by Newton.

– In relativity we regard the 3 space dimensions and time as a single four dimensional entity called spacetime.

• Einstein made several predictions based on these two principles.

• Length contraction: the length of an object that you measure depends on how the object is moving.– The faster the object moves the shorter its length in

the direction of motion. – Therefore, a railroad car moving past a stationary

observer at the railway station will look shorter to the observer than if it were at rest.


• However, if you were inside the train and measure its length, it will be the same length as measured from the ground when the train is at rest.

• The degree of shortening or length contraction depends on the relative speeds between the observer and the object being measured.

• Although, we cannot see such a shortening in ordinary moving objects (airplanes), it has been observed in fast traveling subatomic particles.


• Time dilation: A clock moving past you runs more slowly than a clock that is at rest.– Suppose you have two identical clocks, one place in

a jet, and the other kept on the ground. When the jet landed the clock on it showed that it has less time elapsed than the one on the ground.

– However, for the passengers on the jet, time flowed at the normal pace, the clock ticked at the regular rate, their hearts beat at the same rate, etc.

– Compared to the people on the ground you have aged less.


• Relativity does not imply that nothing is absolute and every thing is relative – speed of light in a vacuum and the laws of

physics are absolute irrespective of how things are moving.

• These effects are real, and are not illusions. • Einstein’s special theory of relativity also

predicts another relationship E = mc2 .


• According the theory of relativity nothing in this universe can travel faster than the speed of light in a vacuum c = 3.0 108 m/s or 186,000miles/sec


General Theory of Relativity

• Newton’s Theory of gravity was based on the premise that space & time are absolute.

• Not satisfied with this picture, Einstein argued – Gravity causes objects to accelerate (move)– Moving objects affects the length of meter rulers and

the tick of a clock that are moving with the object.Gravity must affect the shape of space & flow of time

• Using a simple thought experiment Einstein showed that gravity must affect the shape of space and the flow of time.


• Einstein showed that there is no way to distinguish between an apple falling to the floor on Earth and the apparent motion of an apple inside an elevator accelerating up in a remote region of the universe(far from the gravitational influences of Earth and other objects)

• 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.

General Theory of Relativity• Einstein built his theory around the observation

that acceleration due to gravity cannot be distinguished from acceleration due to any other force - The equivalence principle.

• The effects of special relativity that apply when objects are accelerated to near the speed of light - space being compressed, clocks slowing down - must also apply to objects moving in intense gravitational fields - near massive objects.

Gravity (massive objects) distorts space and time, causing space to become curved and time to slow down.


• According to Einstein’s General Theory of Relativity, gravity is caused by the curvature of spacetime

• Far away from Earth (or any other source of gravity) spacetime is flat.

• Near the massive objects (Earth) spacetime is warped - clocks slow down & space gets curved.– Apple falls to the ground because that is the natural

trajectory the apple can follow due to the space being curved near Earth.


Gravitational curvature of spacetime: The massive object resides at the bottom of the gravitational well


• Imagine a stretched bed sheet – If you place a ping pong ball on one side of this flat

bed sheet it will not move in any preferred direction– However, now if you first place a heavy stone at the

center of the bed sheet then place the ping pong ball at a corner it will move towards the ‘gravitational well’ at the center - because the bed sheet now is curved and the ball is simply following its natural trajectory in this curved space.

– This is a useful analogy to help you understand Einstein’s gravity - general theory of relativity!


• This explains why the acceleration due to gravity that an object(apple, cannon ball, etc.) will experience is independent of its mass.– The curvature of space has the same effect on all

objects.

• General theory of relativity has profound consequences for the way we think about the universe and these have been put to a variety of vigorous tests - and the theory has passed with flying colors.


• Gravitational redshift: – In his famous equation E = mc2 Einstein showed that

radiation has an equivalent mass, and therefore light must respond to gravity, just like particles do.

– Photons leaving a massive objects suffer gravitational redshift, caused by the photons loosing energy as they climb out of the gravitational “well”.


• The Gravitational Slowing of time:– According to GTR, near a massive object (Earth)

time is warped. – Clocks nearer to the Earth’s surface ticks more

slowly than clocks at a higher elevations.

The gravitational slowing of time and gravitational redshift


The gravitational bending of light: Light bends near a massive object because space near the object is curved and light follows its natural trajectory


The precession of Mercury’s orbit

GTR predicts Black Holes• Newton’s theories are only valid when you

study objects having low speeds (compared to speed of light) and weak gravity.

• The most bizarre prediction of GTR is that of the final outcome of a dying star with mass greater than about 3M. – Nothing can resist the gravitational collapse of such

a star.– GTR predicts that such a star will collapse to a

point!! - all that mass that once was a star collapse to a point??? -

Black Holes

• We can understand the nature of a black hole in terms of escape velocity.– Escape velocity of Earth, i.e. the speed that a rocket

should gain in order to escape Earth gravity is 11 km/s. Sun: 600 km/s.

– Near a black hole the gravity is so strong that the escape velocity exceeds the speed of light - 300,000 km/s.

– Since nothing can travel faster than light, nothing escapes the gravitational pull of such an object - not even light.

Black Holes

The formation of a black hole

Black Holes• Photons emitted by a normal star is only

slightly affected by the star’s gravity.• However, as a star keeps collapsing and

compressing to enormous densities, the surface gravity of the shrinking sphere increases dramatically - and this increases the curvature of the surrounding region.

• Until, the star collapses beyond a certain size, the space around it curves so much that it closes on itself.

Black Holes

• Photons flying out of such an object becomes so redshifted they loose all the energy and cease to exist.

• An object from which neither matter nor radiation can escape is called a Black Hole.

• Near a black hole the spacetime is highly curved, it is as if a hole has been punctured in spacetime (the fabric of the universe)– In other words the gravitational well is infinitely

deep!

Black Holes• Surrounding a black hole there is an imaginary

sphere, where the escape velocity is just equal to the speed of light. This surface is referred to as the Event Horizon. – Beyond this surface nothing is visible.

• The distance from the center of the black hole to the event horizon is called the Schwarzschild radius (RSch).

• All the mass that once was a star has now been crushed to a single point at the center, known a the singularity.

The structure of a black hole

The spacetime structure of a black hole

Black Holes

• Once an object crosses the event horizon, it is gone for ever.

• Bizarre things happen inside a black hole:– Far from a black hole you have the freedom to move

about in space but have no control over the flow of time.

– Inside a black hole however, gravity distorts space & time. You loose your freedom to move in space but gain the ability to affect the passage of time!

– At the singularity space & time are jumbled up - they do not exist as two separate entities.

Black Holes

• Therefore, the singularities at the center of a black hole do not obey laws of physics.

• However, the random unpredictable thing that happen inside a black hole is shielded from the rest of the universe by the event horizon, since no information can pass beyond this surface.

• In the words of the british mathematician Roger Penrose: “Nature abhors naked singularities”– In other words, every singularity must be completely

surrounded by an event horizon.

Black Holes• If you were unfortunate enough to fall into a

black hole, you will be stretched like a spaghetti due to the immense tidal forces.

• However, suppose you were able to send a space probe into a black hole and it survives the descent, then from the safety of an orbiting space ship, you will observe that the clock on the probe will slow down and eventually stop upon reaching the event horizon. – In other words, you will observe the space probe

to slow down and it will take an infinite time to reach the event horizon.

Falling into a black hole

As the probe reaches the event horizon, it is distorted in to a long, thin shape, and a distant observer sees the color of the probe change as the light from the probe is redshifted.

The probe will appear to take an infinite amount of time to fall in.

Wormholes and Time Machines

• Einstein discovered that GTR predicts the possibility that black holes could connect our universe to another “parallel” universe via an Einstein-Rosen bridge.

• Such a bridge is called a worm hole.• A worm hole also could be connected to another

part of our own universe. • However, theories suggest that these wormholes

collapse as soon as they are formed.


• Also, since traversing a wormhole means that you are emerging at a different spacetime domain than the one you started with, you could start at present time and emerge at a time in the past (or the future) - time travel!

Evaporation of Black Holes

• Quantum mechanics predict the concept of virtual pairs of particles. – at every point in space pairs of particles and anti-

particles are constantly being created and destroyed.– Usually, this takes place during an extremely brief

moment, that it does not affect the universe and cannot be detected and don't break laws of physics

• However, just outside the event horizon, if such a pair appears, one of them can be pulled into the black hole before they annihilate. The other member can escape to space.

Evaporation of Black Holes

The net result is that some energy is taken from the black hole. This decreases the mass of the black hole according to E = mc2. This was predicted by Stephen Hawking and could provide a way of detecting a black hole - Hawking Radiation

Black Holes in Binary systems

•Black holes do not emit light, and therefore cannot be observed directly.

•However, their gravity is strong and would affect the orbits of close by objects

•Therefore, close binary systems provide us with the best way of detecting a Black Hole.

• Black Hole candidate: Cygnus X-1 X-ray Source


• Cygnus X-1 is a peculiar X- ray source with highly irregular X-ray pulses.

• The companion star of Cygnus X-1 is a 30M B0 supergiant, and from its orbit astronomers can estimate the unseen member is at least a 7M object - a black hole?

• The material from the supergiant gradually spirals in towards the black hole, as it does friction heats up the gas. Very near the event horizon the temperatures reach extremely high levels and the hot gas emit X-rays.


• The argument that Cygnus X-1 is a black hole is not airtight. Some critics have other possible explanations.

• Astronomers have found many other black hole candidates in binary systems

Supermassive Black Holes in Galactic centers

• During the formation of galaxies, the gas at the galactic centers could compress due to its own gravity. – If these regions get sufficiently dense, a black hole

can form.– Since, the amount of gas at the galactic centers are

enormous compared to even the most massive stars, these black holes are referred to as Supermassive blackholes.

• A good example of such a black hole was photographed by the Hubble at the center of the M87 galaxy.

Black Holes in Binary

systems

• By measuring the speed of the material orbiting this tiny bright source of light at the center of M87, astronomers have calculated the mass of it to be three billion solar masses! Others like M87 have been found.

Primordial Black Holes

• In 1970s Stephan Hawking proposed the possibility that during the extremely hot and dense epoch of the universe just after the Bing Bang , local regions could have become dense enough to form black holes that have very small masses - Primordial Black holes – These can have masses as large as Earth’s mass or

smaller than a rain drop. – However, to date we have not seen any evidence of

these exotic objects.

chapter 24 black holes “black holes are out of sight!”

Documents

space time

time elapsed

time interval

speed of light

length contraction

space dimensions

stationary space ship

stationary observer