Black Holes&

Relativity

Einstein and Relativity• 1905 – Theory of Special Relativity

– Time dilation and length contraction

– Space and time are intertwined

– Matter and energy are equivalent

1916 – Theory of General Relativity Describes the effects of gravity on spacetime

•What is “relative” in relativity?

Relativity only needs to be dealt with at speeds approaching the speed of light.

–Since we do not experience extreme speeds & gravity, we have no common sense about relativity

–motion…all motion is relative

same for everyone

•The laws of nature are the same for everyone

–the speed of light (in a vacuum), c, is the

Objects moving relative to each other are in different reference frames, like the plane and ground below

•A ball moves forward in a plane moving at 900 km/hr

Thought Experiments

You could also observe that you are moving away.

I

I

Thought Experiments

I

I

I’

Thought Experiments

Very High Speed

I

I

•I

me

me

my point of view

(a) An observer moving with the space ship observes a light flash moving vertically

between the mirrors . (b) A stationary observer observes the flash

moving along a diagonal path.

The longer distance taken by the light flash in following the diagonal path must be divided by a correspondingly longer time interval to yield an unvarying value for the speed of light.

•Time dilation formula:

As you go faster and faster time slows down.

2)/(1' cvtt rest

moving

The effects on time can be ignored for small velocities, but increase asymptotically as velocity approaches the speed of light.

As speed increases, length in the direction of motion decreases. Lengths in the

perpendicular direction do not change.

2)/(1' cvLL Length contraction

Now, if a pair of scissors lies directly across your field of view, it will appear at its maximum length. Rotating it makes it appear shorter. This is depicted in the following figure.

The degree of foreshortening would depend on the angle that the pair of scissors is rotated.

Rotation here is 48 degrees, so that its length appears to be two thirds what it was.

That's almost what happens with space and time when things move. The object is "rotated" out of one of the space dimensions and into the time dimension. If you were in space and a rocket ship moved by you extremely rapidly (close to the speed of light), it would appear shorter. That's because the front of the ship has been "rotated" into the future, and the rear of the ship has been "rotated" into the past. At any instant , you see the projection of the rocket into the three dimensions of space .

MASS increase

2)/(1 cvMoving mass rest mass

•The faster an object moves, the more massive it becomes.

Toward a New Common Sense Suppose I move by you at close to the speed of

light…you will see my time run slower, m length contract, and my mass increase

But what do I see?… I am stationary; I see you moving by at high speed in the opposite direction.

Inside my vehicle, I am not aware of any slow down, every thing seem normal.

Since the laws of nature are the same for everyone, I see your time run slower, your length contract, and your mass increase

How can we test Relativity ? In 1887, the Michelson-Morley experiment

used an interferometer to show that the speed of light is not affected by the Earth’s motion around the Sun.•subatomic particles have been accelerated to speeds of 0.9999 c and no matter how much energy we put in, they never reach c, but their masses increase.

•A + meson particle decays in 18 nsec when at rest, but at high velocities, it lives longer,proving time dilation

Consequences of General Relativity

More Consequences of General Relativity

Ticket to the Stars• Although we can not travel faster than the speed of light…• special relativity will make the journey seem shorter if we

can travel close to the speed of light

• Time moves more slowly for the space traveler.

• Space travelers can reach distant stars in their lifetimes, but their friends and family will not be there to greet them when they return home to Earth.

•The End, relatively speaking

Black Holes

The End-States for Low and High Mass Stars

Initial Stellar Mass Final Core Mass Final State

1 - 8 0.5 - 1.4 White dwarf

8 - 30 1.4 - 3.0 Neutron Star

> 30 > 3.0 Black hole

Gravity as curved space

First, about Black Holes :

not have enough mass.

If the sun could become a black hole, it would not change the orbit’s or the planets

Treat it like a snake, don’t get near it and it won’t bother you.

Lastly, I am not the writer of the message, I am only the carrier of the message. I’ll tell you what I know. Astronomers do not agree on everything about B.H.

The sun will not become a black hole, it does

This photo of a Black Hole was taken by

Master H at Oxford College of Emory University.

or does it?

If the core of a star collapses with more than 3 solar masses, no known force can stop the collapse, not electron, or neutron degeneracy.

The star collapses to

The Singularity has infinite density and gravity.

a radius of zero, a point called the Singularity.

The Schwarzschild Black HoleSimplest black holes, static (non-rotating) mass.

•At the center the is the singularity

The Schwarzschild radius defines the Event Horizon, the boundary at which the escape velocity is the speed of light

photon sphere : 1.5 times bigger than

the Schwarzschild radius is where light orbits the BH

What we “see” as the black hole, is the What we “see” as the black hole, is the distance from the singularity where the distance from the singularity where the escape speed is faster than c, the speed escape speed is faster than c, the speed of light. This distance is the of light. This distance is the Schwarzschild radius, or event horizon.Schwarzschild radius, or event horizon.

The core of the star The core of the star is compressed into is compressed into a single point – the a single point – the singularity, with singularity, with zero size and infinite zero size and infinite densitydensity..

We have no way of finding out what’s happening inside the “Event horizon”

Schwarzschild Radius (kilometers) ~ 3 x mass of star (solar masses)The singularity is a region of space-time in which gravitational forces are so strong that the Laws of Physics , break down there.

 

Tidal forces destroy anything falling inward

The tidal forces

of the BH would

begin to stretch anything

falling in.

What if you got inside the Event Horizon ?

A person watching you getting closer and closer to event horizon sees you move more and more slowly because the light from you takes longer and longer to reach the observer.

The light is stretched out and as you cross the horizon your image will hover at the horizon and never reach the observer.

You will actually become invisible way before that because the longer wavelength will change to infrared and to radio etc.

•The probe falling into the black hole experiences huge gravitational tides which stretch vertically and compress horizontally. The probe would be pulled apart disintegrate as it falls inward.

What the observer inside a probe falling into a mass black hole see?

Someone on the probe observes something different. They see the probe cross the event horizon an continue falling toward the black hole’s singularity.

What happens at the singularity?What happens at the singularity?   When our volunteer finally reaches the When our volunteer finally reaches the

singularity, what what happen singularity, what what happen

  

Other theorists suggest that instead, our Other theorists suggest that instead, our volunteer might pass into another universe, volunteer might pass into another universe, that a black hole is just one end of a that a black hole is just one end of a connector tube called a connector tube called a wormholewormhole..

Stephen Hawking believes that his body Stephen Hawking believes that his body would be infinitely crushed and become part would be infinitely crushed and become part of the black hole, turned into energy.of the black hole, turned into energy.

Time slows down as you get closer to a BH. So if you got close to, but outside the Event Horizon, and then escape suing your powerful retro rockets, you will have aged much less than a person waiting for you in a spacecraft far from the BH. General relativity demands that singularities arise under two circumstances

First, a singularity must form during the creation of a black hole.

Second, an expanding universe like ours must have begun as a singularity.

General Relativity predicts Wormholes for Kerr Black Holes, but Astrophysicists are skeptical.

•Could a black hole somehow be connected to another part of spacetime, or some other universe?

Kerr Rotating Black Hole

Surrounding the Event Horizon is a sphere of space time called the Ergosphere, where nothing can remain at rest.

The singularity is smeared out to form a ring around the center of the hole.

If an object is moving fast enough, it can enter the Ergosphere and fly out again. If the object stops it must fall into the Black Hole.

Relativity forbids material objects from traveling faster than light, but allows regions of space-time to move faster than light.

Here space-time is being pulled around the rotating black hole and this is called inertial frame dragging.

“BLACK HOLES HAVE NO HAIR”,•No-hair theorem: All traces of the matter that formed a BH disappear except for:

MASS

ANGULAR MOMENTUM

CHARGECharge is probably neutral

or this is all we can know about a BH.

–Jacob Bekenstein (a Princeton graduate student in 1972, stated that if a black hole has entropy it also must have a temperature.

–Hawking (1972): If the Black Hole is a black body at non-zero temperature, it must obeys the laws of thermodynamics and radiate energy.

If nothing can escape from a black hole ; how can it radiate?

Quantum Mechanics says that virtual particles can appear and disappear in space.

Matter and energy can interchange !

3. If a virtual particle falls into a black hole, it will have to take in energy from the black hole to become a real particle and the black hole will lose energy

Hawking Radiation theory

2E mc

HOW FAST DO BHs EVAPORATE?

• Evaporation time proportional to (mass)3

• For 1 solar mass BH: yr66105.1 Smaller masses, evaporate faster.

•A 3 Msun black hole would require about 1063 years to completely evaporate.

•This is about 1053 times the present age of the Universe.

TYPES of Black Holes

• Primordial – can be any size, including very small – created in the Big Bang

• Stellar mass- black holes – must be at least 3 Mo many examples are known

•Massive black holes – about 106 Mo – such as in the center of the Milky Way – many seen•Supermassive black holes – about 109-10 Mo - located in Active Galactic Nuclei, often accompanied by jets – many seen

New theories

The event horizon surrounds the BH and prevents us from seeing the singularity. Could a BH exist without an event horizon? This would be called a naked singularity. This is a real possibility for some BH.

One group has proposed that if orbiting mass falls into the BH in the direction of its spinning and speeds up the BH, the results is this appears to disrupt the BH enough to strip away the event horizon, exposing the singularity.

Since swirling matter is falling into BH they may have found the mechanism that allows naked singularities to exist.

With out an event horizon, processes in the singularity could impinge on the outside world. This might account for unexplained high-energy phenomena that astronomers have seen.

The Big Bang was a naked singularity, we think.

Astro-physicists are trying to combine Relativity with Quantum Mechanics. Quantum Mechanics forbids a singularity and so the singularity would not be an infinite point but rather a highly dense area and the Laws of Physics would still hold. Instead of BH it might become a “Quantum Star”.

HOW TO DETECT BLACK HOLES

1. Binary system where one star has a core mass > 3 solar masses and emitting high energy X-rays.

X-ray binary (artist’s impression)

We can’t see them directly.

HOW TO DETECT BLACK HOLES

2. Orbital motion of stars or gas clouds (supermassive holes)

M87 disk

HOW TO DETECT BLACK HOLES

3. Random motions of stars in galaxy’s nucleus (supermassive holes)

Gas almost never falls directly into a black holeToo much “swirl” (angular momentum) …Funnels in forming an Accretion diskWe “see” a black hole

by the mass falling into it

Signature of a Black Hole

                              

                            

Candidate For Black Hole

Example: Cygnus X-1

Binary Star w/ two objects:

•M=30 Msun primary

(seen)

•M=7 Msun companion

–Too small, too X-ray bright, and too faint at visible wavelengths to be a 7 M star.–Far too massive to be a white dwarf or neutron star.

Evidence for BH A disk of dust fuelling a massive black hole in the centre of a galaxy.

The speed of the gas indicates that the object at the centre of the disk is 1.2 billion times the mass of our Sun.

800 light years

Matter falling into a

black hole often

forms jets

Gravitational lensing• How can a black hole or a neutron star act like a lens?

• The answer comes from Albert Einstein, who proved in 1919 that light follows in the path of the bent time and space which is warped due to the gravitational force of a massive object.

Gravitational Lenses

• Gravitational Lens are observed quite frequently with the Hubble Telescope.

•In many cases, the amount of matter needed to make the gravitational lens is much more than can be accounted for by the visible matter.

•There must be dark matter there as well.

Gravity WavesAccording to general relativity, in a stellar collapse to a black hole, the star loses its magnetic field. The field’s energy radiates in the form of gravitational waves, which are ripples in the very fabric of space time.These waves are also created when neutron stars collide, or even when they are in close orbits around each other.

Gravitational waves are incredibly tiny, and astronomers around the world have begun building detectors to measure these small changes. Once detected , they will provide a new , and unique way of observing the universe.