Stellar RemnantsStellar Remnants

White Dwarfs, Neutron Stars and White Dwarfs, Neutron Stars and Black HolesBlack Holes

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1.1. When a white dwarf forms, is the former star When a white dwarf forms, is the former star always at the end of its life cycle? What can always at the end of its life cycle? What can happen to it?happen to it?

2.2. Does degeneracy still exist in stellar Does degeneracy still exist in stellar remnants?remnants?

3.3. What is the Chandrasekhar number and what What is the Chandrasekhar number and what does it mean?does it mean?

4.4. What is the exclusion principle?What is the exclusion principle?

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1.1. What is the exclusion principle?What is the exclusion principle?

2.2. How does a low-mass star become a How does a low-mass star become a high-mass stellar remnant?high-mass stellar remnant?

3.3. What is gravitational red-shift?What is gravitational red-shift?

4.4. What happens to a white dwarf as mass What happens to a white dwarf as mass is added to it?is added to it?

5.5. If you pack electrons too closely, they If you pack electrons too closely, they remain in what state?remain in what state?

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1.1. What is a nova and how do they occur?What is a nova and how do they occur?

2.2. What is a Roche Lobe?What is a Roche Lobe?

3.3. What is a LaGrange Point?What is a LaGrange Point?

4.4. What is a mass transfer stream?What is a mass transfer stream?

5.5. What is an accretion disk?What is an accretion disk?

6.6. What is a neutron star?What is a neutron star?

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1.1. What was the mission objective for Apollo 13?What was the mission objective for Apollo 13?

2.2. Where was Apollo supposed to land?Where was Apollo supposed to land?

3.3. Who was the mission commander?Who was the mission commander?

4.4. Who was the mission pilot?Who was the mission pilot?

5.5. What mishap occurred on board that What mishap occurred on board that threatened the mission?threatened the mission?

6.6. What additional problems (2) did the crew What additional problems (2) did the crew encounter?encounter?

7.7. What were the solutions to those problems?What were the solutions to those problems?

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1.1. What is electron degeneracy and which stellar remnant What is electron degeneracy and which stellar remnant is it associated with?is it associated with?

2.2. What is neutron degeneracy and which stellar remnant What is neutron degeneracy and which stellar remnant is it associated with?is it associated with?

3.3. What two forces provide equilibrium to white dwarfs?What two forces provide equilibrium to white dwarfs?

4.4. What two forces provide equilibrium to neutron stars?What two forces provide equilibrium to neutron stars?

5.5. Why can nothing escape from inside the event horizon Why can nothing escape from inside the event horizon of a black hole?of a black hole?

6.6. What happens to white dwarfs that exceed the What happens to white dwarfs that exceed the Chandrasekhar limit?Chandrasekhar limit?

7.7. Contrast Type I supernovae with Type II supernovae.Contrast Type I supernovae with Type II supernovae.

WORDDefinition

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Example/Characteristic Example/Characteristic

Used correctly in a sentence

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Word Wall Elements

Example/Characteristic

Vocabulary for Word Wall ElementsVocabulary for Word Wall Elements

Type I SupernovaType I Supernova

Type II SupernovaType II Supernova

Roche Lobe/LaGrange PointRoche Lobe/LaGrange Point

White Dwarf/NovaWhite Dwarf/Nova

Neutron Star/PulsarNeutron Star/Pulsar

Black Hole/Schwarzschild Radius/Event HorizonBlack Hole/Schwarzschild Radius/Event Horizon

Event Horizon/Escape VelocityEvent Horizon/Escape Velocity

White Dwarfs and LightWhite Dwarfs and LightAs light loses energy its wavelengths As light loses energy its wavelengths begin to increase and they are begin to increase and they are stretched toward the red end of the stretched toward the red end of the spectrum. This phenomenon is spectrum. This phenomenon is called called gravitational redshiftgravitational redshift. The . The amount of shift depends on the amount of shift depends on the star’s mass. star’s mass.

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1.1. What is a gravitational red shift?What is a gravitational red shift?

2.2. When a star reaches the end of its When a star reaches the end of its evolutionary cycle, is it necessarily the evolutionary cycle, is it necessarily the end of its life?end of its life?

3.3. Is light a particle or a wave? Why?Is light a particle or a wave? Why?

Stellar RemnantsStellar Remnants

All stars must eventually die. Space All stars must eventually die. Space is littered with their bodies. Because is littered with their bodies. Because they have exhausted their fuel, they they have exhausted their fuel, they no longer shine. The environment in no longer shine. The environment in which they were created made them which they were created made them quite exotic. Stellar forces have quite exotic. Stellar forces have crushed white dwarfs to the point crushed white dwarfs to the point that a piece the size of an ice cube that a piece the size of an ice cube would weigh around 16 tons.would weigh around 16 tons.

Stellar RemnantsStellar RemnantsNeutron stars have been crushed to Neutron stars have been crushed to the point that their electrons and the point that their electrons and protons have been merged. In the protons have been merged. In the most massive stars, the stars have most massive stars, the stars have collapsed so completely that their collapsed so completely that their immense gravity warps space to the immense gravity warps space to the extent that no light escapes from extent that no light escapes from them.them.

Dead Doesn’t Mean Dead Doesn’t Mean InconspicuousInconspicuous

While these remnants are dead as While these remnants are dead as far as stellar evolution is concerned, far as stellar evolution is concerned, many still effect those things around many still effect those things around them. Some steal matter from there them. Some steal matter from there companions until they explode while companions until they explode while some collapse even more until they some collapse even more until they reach an explosive end.reach an explosive end.

White DwarfsWhite Dwarfs

White dwarfs, the White dwarfs, the remnants of small remnants of small mass stars, have a mass stars, have a diameter about the diameter about the size of the Earth. size of the Earth. While they do not While they do not shine, they do shine, they do radiate heat. The radiate heat. The average surface average surface temperature of a temperature of a white dwarf is white dwarf is about 10,000 K. about 10,000 K.

White DwarfsWhite DwarfsThe composition of the star is mainly The composition of the star is mainly carbon and oxygen with a thin carbon and oxygen with a thin surface layer of hydrogen and surface layer of hydrogen and helium. There is far too little gas to helium. There is far too little gas to ever combust, however. White ever combust, however. White dwarfs simply continue to cool and dwarfs simply continue to cool and reach a core temperature of around reach a core temperature of around 20,000 K. 20,000 K.

White DwarfsWhite DwarfsIt would take longer than the It would take longer than the Universe has existed for one to cool Universe has existed for one to cool to the extent it would no longer be to the extent it would no longer be detected. These remnants are called detected. These remnants are called black dwarfsblack dwarfs..

The Structure of a White The Structure of a White DwarfDwarf

There density and lack of fuel make There density and lack of fuel make white dwarfs different from ordinary white dwarfs different from ordinary stars, although they are at hydrostatic stars, although they are at hydrostatic equilibrium. External pressure is equilibrium. External pressure is supplied by an interaction between its supplied by an interaction between its electrons that limit how many can electrons that limit how many can occupy a given volume. This gives the occupy a given volume. This gives the remnant a peculiar property, added remnant a peculiar property, added mass will make the white dwarf shrink.mass will make the white dwarf shrink.

The Structure of a White The Structure of a White DwarfDwarf

Even more crucial, the mass of the Even more crucial, the mass of the remnant must be below critical level or remnant must be below critical level or they will collapse more. Also, because they will collapse more. Also, because they are so dense ( 1 ton/cmthey are so dense ( 1 ton/cm33) the star’s ) the star’s atoms are packed very tightly, this atoms are packed very tightly, this compresses the orbits of the electrons compresses the orbits of the electrons circling their nuclei. The electrons are circling their nuclei. The electrons are packed so tightly that many of them packed so tightly that many of them cannot relax from an excited state into a cannot relax from an excited state into a ground state.ground state.

The Structure of a White The Structure of a White DwarfDwarf

This leads to degeneracy pressure This leads to degeneracy pressure (as you know). The physical law (as you know). The physical law called the called the exclusion principleexclusion principle limits limits the number of electrons that can be the number of electrons that can be squeezed into a volume. When a gas squeezed into a volume. When a gas is squeezed to this extent it heats up is squeezed to this extent it heats up but does not create a corresponding but does not create a corresponding increase in the star’s pressure.increase in the star’s pressure.

Degeneracy Pressure and the Degeneracy Pressure and the Chandrasekhar LimitChandrasekhar Limit

Added mass makes the dwarf shrink Added mass makes the dwarf shrink despite degeneracy. The additional despite degeneracy. The additional gravitational forces created by this gravitational forces created by this additional mass squeezes the star additional mass squeezes the star even more. The remnant creates even more. The remnant creates enough degeneracy pressure to enough degeneracy pressure to overcome these additional forces until overcome these additional forces until its mass reaches the Chadrasakher its mass reaches the Chadrasakher Limit, about 1.4 solar masses.Limit, about 1.4 solar masses.

Degeneracy Pressure and the Degeneracy Pressure and the Chandrasekhar LimitChandrasekhar Limit

Physicists believe Physicists believe that when the that when the Chadrasekher Limit Chadrasekher Limit is reached that the is reached that the white dwarf may white dwarf may attain densities attain densities necessary to necessary to develop high mass develop high mass star formations such star formations such as neutron stars and as neutron stars and black holes. black holes.

White Dwarfs and LightWhite Dwarfs and LightAs light escapes from a body it has As light escapes from a body it has to work against that body’s gravity, to work against that body’s gravity, like a ball rolling up hill. Light, like a ball rolling up hill. Light, however, cannot slow down, but it however, cannot slow down, but it can lose energy. Light’s energy can lose energy. Light’s energy determines its frequency. determines its frequency.

White Dwarfs in Binary White Dwarfs in Binary SystemsSystems

Isolated dwarfs cool off and Isolated dwarfs cool off and eventually disappear, but in a binary eventually disappear, but in a binary systems this is not necessarily true. systems this is not necessarily true. Some dwarfs capture gas from their Some dwarfs capture gas from their neighboring companion. The gas is neighboring companion. The gas is rich in hydrogen. This gas builds rich in hydrogen. This gas builds until it reaches the point of ignition.until it reaches the point of ignition.

White Dwarfs in Binary White Dwarfs in Binary SystemsSystems

But, as we have seen, nuclear burning in a But, as we have seen, nuclear burning in a degenerate gas can get explosive. This degenerate gas can get explosive. This detonating gas is expelled into space detonating gas is expelled into space where it forms an expanding sphere of hot where it forms an expanding sphere of hot gas. When this phenomenon was first gas. When this phenomenon was first witnessed by ancient astronomers it was witnessed by ancient astronomers it was called “nova stella”, for new star. We use called “nova stella”, for new star. We use the shortened form today, the shortened form today, novanova..

Mass Transfer in Binary Mass Transfer in Binary SystemsSystems

Both the dwarf and the companion Both the dwarf and the companion are surrounded by a region in which are surrounded by a region in which all material is gravitationally all material is gravitationally attached to that body. This region is attached to that body. This region is known as a known as a Roche LobeRoche Lobe. It is a . It is a teardrop-shaped boundary, that teardrop-shaped boundary, that should the star expand beyond it, should the star expand beyond it, the material outside it will fall into the material outside it will fall into the other star. the other star.

Mass Transfer in Binary Mass Transfer in Binary SystemsSystems

The actual matter is passed through a The actual matter is passed through a mass mass transfer streamtransfer stream. Where this stream passes . Where this stream passes from the meeting Roche Lobes is called the from the meeting Roche Lobes is called the LaGrange PointLaGrange Point. The LaGrange Point is a . The LaGrange Point is a point of gravitational neutrality where the point of gravitational neutrality where the influence of each star counteracts the influence of each star counteracts the gravitational force of its companion. To gravitational force of its companion. To pass the LaGrange point is to put yourself pass the LaGrange point is to put yourself under the gravitational influence of one under the gravitational influence of one member of the binary pair.member of the binary pair.

Binary Pair DiagramBinary Pair Diagram

The Type I SupernovaThe Type I SupernovaThe nova process can repeat itself over The nova process can repeat itself over and over again given that the dwarf does and over again given that the dwarf does not accumulate too much material. If not accumulate too much material. If enough gas gathers to push the dwarf enough gas gathers to push the dwarf over the Chandrasekhar Limit, the star over the Chandrasekhar Limit, the star will collapse unto a will collapse unto a Type I supernovaType I supernova. This . This rapid collapse will eventually cause the rapid collapse will eventually cause the remnant to reignite and blow itself apart.remnant to reignite and blow itself apart.

The Type I SupernovaThe Type I Supernova

The Type I The Type I supernova leaves supernova leaves behind no behind no remnant, but remnant, but completely completely destroys itself. destroys itself. The iron that is in The iron that is in your blood was your blood was probably made probably made this way.this way.

Neutron StarsNeutron StarsIn the 1930’s, astrophysicists Walter In the 1930’s, astrophysicists Walter Baade (like the thing that washes your Baade (like the thing that washes your butt) and Fritz Zwicky (great American butt) and Fritz Zwicky (great American name) proposed the Type II (or high mass name) proposed the Type II (or high mass stellar collapse) supernova. Almost as an stellar collapse) supernova. Almost as an afterthought, they further proposed that afterthought, they further proposed that the core remnant of such an explosion the core remnant of such an explosion would result in a neutron stars.would result in a neutron stars.

Neutron StarsNeutron StarsWhile the neutron star looked good on While the neutron star looked good on paper, no one actually started looking for paper, no one actually started looking for one for some time because astronomers one for some time because astronomers believed them to be too small to observe. believed them to be too small to observe. Theoretically, neutron stars would be tiny Theoretically, neutron stars would be tiny even compared to the small white dwarf.even compared to the small white dwarf.

Neutron StarsNeutron StarsAccording toAccording to Baade and Zwicky’s Baade and Zwicky’s calculations the neutron stars should calculations the neutron stars should have a radius of about 10 kilometers have a radius of about 10 kilometers and a mass of several times that of and a mass of several times that of the Sun. They also predicted that the Sun. They also predicted that neutron stars have a maximum neutron stars have a maximum possible mass (like the white dwarf possible mass (like the white dwarf does) of 2 to 3 solar masses.does) of 2 to 3 solar masses.

Pulsars and the Discovery of the Pulsars and the Discovery of the Neutron StarNeutron Star

Due to a lack pf observational evidence, Due to a lack pf observational evidence, the scientists’ ideas lay dormant for 3 the scientists’ ideas lay dormant for 3 decades until 1967. In that year British decades until 1967. In that year British scientists observed fluctuating radio scientists observed fluctuating radio signals from strange, distant galaxies. A signals from strange, distant galaxies. A graduate student, Jocelyn Bell, noticed an graduate student, Jocelyn Bell, noticed an odd radio signal with a very precise odd radio signal with a very precise repetitive cycle (1.33 seconds). The repetitive cycle (1.33 seconds). The signal was dubbed “LGM-1” for little signal was dubbed “LGM-1” for little green men 1.green men 1.

PulsarsPulsars

Over the next few weeks, the group Over the next few weeks, the group found several more pulsating radio found several more pulsating radio sources that they began to call sources that they began to call “pulsars”. They knew that the “pulsars”. They knew that the pulsating rates were likely related to pulsating rates were likely related to the densities of the objects, so they the densities of the objects, so they realized that the sources were realized that the sources were extremely dense. Calculated densities extremely dense. Calculated densities made it very unlikely that the sources made it very unlikely that the sources were white dwarfs.were white dwarfs.

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1.1. What is a pulsar?What is a pulsar?

2.2. Why do they rotate so rapidly?Why do they rotate so rapidly?

3.3. What do we actually hear coming from a What do we actually hear coming from a pulsar?pulsar?

PulsarsPulsars

In searching for an explanation, In searching for an explanation, astronomers began to take a new look astronomers began to take a new look at Fritz and Zwicky’s 30 year old ideas at Fritz and Zwicky’s 30 year old ideas about neutron stars. It was Italian about neutron stars. It was Italian astronomer Franco Pacini that linked astronomer Franco Pacini that linked the super dense neutron star idea with the super dense neutron star idea with the rapidly pulsating radio signals by the rapidly pulsating radio signals by proposing that the stars didn’t actually proposing that the stars didn’t actually pulse, but rather rotate rapidly. Some pulse, but rather rotate rapidly. Some rotate as fast as 30 times per second.rotate as fast as 30 times per second.

PulsarsPulsarsSo, how can a stellar core spin so So, how can a stellar core spin so rapidly? The answer is simple. It is rapidly? The answer is simple. It is the conservation of angular the conservation of angular momentum. Like an ice skater momentum. Like an ice skater bringing in her arm to spin more bringing in her arm to spin more rapidly, when a star collapses its rapidly, when a star collapses its radius is slashed. radius is slashed.

Conservation of Angular Conservation of Angular MomentumMomentum

The law of conservation of angular The law of conservation of angular momentum states that:momentum states that:

L = MVRL = MVR where L is angular momentumwhere L is angular momentum

M is mass of the objectM is mass of the object

V is rotational velocity of an V is rotational velocity of an objectobject

AndAnd R is the object’s radius.R is the object’s radius.

Conservation of Angular Conservation of Angular MomentumMomentum

Angular momentum must be Angular momentum must be conserved, therefore accordingconserved, therefore according to to L = MVR, if radius decreases L = MVR, if radius decreases then velocity must increase to then velocity must increase to keep L constant.keep L constant.

Emissions from Neutron Emissions from Neutron StarsStars

Like big motors, by varying their Like big motors, by varying their magnetic fields, neutron stars create magnetic fields, neutron stars create an electric field. This electric field an electric field. This electric field strips charged particles off the strips charged particles off the surface of the remnant and hurls surface of the remnant and hurls them at nearly the speed of light out them at nearly the speed of light out into space.into space.

Emissions from Neutron StarsEmissions from Neutron StarsAs these particles ride the neutron star’s As these particles ride the neutron star’s electric field away from the star they electric field away from the star they produce radiation, much like a radio produce radiation, much like a radio transmitter does. This radiation, called transmitter does. This radiation, called non-thermal radiationnon-thermal radiation is funneled through is funneled through the poles and emitted in the shape of a the poles and emitted in the shape of a tight cone.tight cone.

The PulsarThe Pulsar

As these dense bodies rotate at astounding As these dense bodies rotate at astounding speeds, they radiate outward from their speeds, they radiate outward from their magnetic poles. The magnetic and rotational magnetic poles. The magnetic and rotational poles do not coincide and the radiation beams poles do not coincide and the radiation beams obliquely to the axis of rotation. Like a giant obliquely to the axis of rotation. Like a giant lighthouse, only if the Earth lies in the path of lighthouse, only if the Earth lies in the path of the radiation, is it seen.the radiation, is it seen.

The PulsarThe PulsarEmitting this tremendous radiation Emitting this tremendous radiation field does have its drawbacks, field does have its drawbacks, however. Like dragging an anchor, however. Like dragging an anchor, the field slowly decreases the the field slowly decreases the rotational rate on the pulsar. rotational rate on the pulsar. Eventually, the neutron star/pulsar Eventually, the neutron star/pulsar will cease to rotate and it will then will cease to rotate and it will then become “invisible” to us.become “invisible” to us.

1.1. What did Fritz and Zwicky propose?What did Fritz and Zwicky propose?2.2. What is the estimated mass of a neutron star?What is the estimated mass of a neutron star?3.3. What was the name of the first pulsar, What was the name of the first pulsar,

discovered by Jocelyn Bell?discovered by Jocelyn Bell?4.4. Why do pulsars spin so quickly?Why do pulsars spin so quickly?5.5. What does the law of conservation of angular What does the law of conservation of angular

momentum state?momentum state?6.6. If a star collapses and its radius is reduced, If a star collapses and its radius is reduced,

what happens to its rotational velocity?what happens to its rotational velocity?7.7. The energy released from a neutron star is in The energy released from a neutron star is in

the form of what?the form of what?8.8. What happens to pulsars over time? Why?What happens to pulsars over time? Why?9.9. Are pulsars frequently detected in binary pairs?Are pulsars frequently detected in binary pairs?

Neutron Stars in Binary Neutron Stars in Binary SystemsSystems

Because neutron stars come from Because neutron stars come from supernovae, they rarely exist in supernovae, they rarely exist in binary pairs. The explosive forces binary pairs. The explosive forces that create neutron stars often that create neutron stars often destroy or dislodge their companion.destroy or dislodge their companion.

Black HolesBlack HolesWhen stars that are more massive When stars that are more massive than 10 solar masses reach the end than 10 solar masses reach the end of their lives, they can compress of their lives, they can compress their cores with so much pressure their cores with so much pressure that they rift the fabric of space-that they rift the fabric of space-time. To understand black holes you time. To understand black holes you have to understand have to understand escape velocityescape velocity!!

Escape VelocityEscape Velocity

Escape velocity is Escape velocity is the speed an object the speed an object must attain to must attain to prevent being prevent being drawn back into drawn back into another body’s another body’s gravity. The gravity. The shuttle has to go shuttle has to go about 7 miles per about 7 miles per second to escape second to escape Earth’s gravity.Earth’s gravity.

Escape VelocityEscape Velocity

Mathematically, escape velocity is defined Mathematically, escape velocity is defined as :as :

V = (2GM/R)V = (2GM/R)1/21/2 where: where:V = Escape velocityV = Escape velocityG = Gravitational constant (6.8 10-11 m/s)G = Gravitational constant (6.8 10-11 m/s)M= Mass (kg)M= Mass (kg)R = Radius of object (m)R = Radius of object (m)

Practical ApplicationPractical Application

For example, which has the higher For example, which has the higher escape velocity, our Sun or a white escape velocity, our Sun or a white dwarf with one solar mass?dwarf with one solar mass?

The white dwarf, because its radius is The white dwarf, because its radius is 100 times less has an escape velocity 100 times less has an escape velocity (100(1001/21/2) or 10 times greater than our ) or 10 times greater than our Sun. That's about 6,000 km/sec. Sun. That's about 6,000 km/sec.

See?See?

Practical ApplicationPractical Application

What about a neutron star whose What about a neutron star whose radius is 10radius is 1055 times smaller than the times smaller than the Sun? Its escape velocity jumps to Sun? Its escape velocity jumps to 180,000 m/s or about half the speed 180,000 m/s or about half the speed of light. Further compact a neutron of light. Further compact a neutron star till its radius is four times star till its radius is four times smaller still and its escape velocity smaller still and its escape velocity exceeds the speed of light and a exceeds the speed of light and a black hole is created. black hole is created.

Early SupportersEarly Supporters

The idea of an object The idea of an object whose escape whose escape velocity exceeded the velocity exceeded the speed of light was speed of light was proposed in 1780’s by proposed in 1780’s by English cleric, John English cleric, John Mitchell. Slightly Mitchell. Slightly more than a decade more than a decade later, French later, French mathematician Pierre mathematician Pierre Simon Laplace Simon Laplace entertained the same entertained the same idea. idea.

Go FigureGo Figure

Following their logic and Following their logic and using an improved using an improved escape velocity, you can escape velocity, you can calculate radii needed to calculate radii needed to become a black hole. become a black hole. The formula:The formula:

R = 2GM/cR = 2GM/c2 2 where:where:

G = Gravitational constant G = Gravitational constant (6.8 x 10(6.8 x 10-11-11 m/s) m/s)

M= Mass (kg)M= Mass (kg)

c = speed of lightc = speed of light

Go FigureGo Figure

How small would you have to shrink How small would you have to shrink our Sun for it to become a black our Sun for it to become a black hole? You would have to shrink it to hole? You would have to shrink it to about 3 kilometers across or 1.9 about 3 kilometers across or 1.9 miles. miles.

Why Space is Like a Water Why Space is Like a Water BedBed

Imagine taking a Imagine taking a baseball and placing baseball and placing it in the middle of it in the middle of water bed. The ball water bed. The ball makes a small makes a small depression in the depression in the mattress. You roll a mattress. You roll a marble past the marble past the depression and the depression and the marble it trapped in marble it trapped in the curvature of the the curvature of the mattress and comes mattress and comes to rest beside the to rest beside the baseball.baseball.

Why Space is Like a Water Why Space is Like a Water BedBed

Now, imagine placing a bowling ball Now, imagine placing a bowling ball in the center of the bed. The in the center of the bed. The depression is ever deeper, the depression is ever deeper, the curvature more exaggerated. The curvature more exaggerated. The marble now rolls in father and hits marble now rolls in father and hits the bottom harder. the bottom harder.

The Formation of Black The Formation of Black HolesHoles

We infer from this analogy that We infer from this analogy that strength of attraction between strength of attraction between bodies depends on the amount the bodies depends on the amount the surface into which it is embedded is surface into which it is embedded is curved. Gravity works like this curved. Gravity works like this according to general relativity. according to general relativity.

The Formation of Black The Formation of Black HolesHoles

Now replace the bowling ball with the a Now replace the bowling ball with the a safe and it will tear through the fabric of safe and it will tear through the fabric of the mattress. So too, a black hole is a tear the mattress. So too, a black hole is a tear in the fabric of space time. in the fabric of space time.

The Formation of Black HolesThe Formation of Black HolesA German astrophysicist Karl A German astrophysicist Karl Schwarzschild pioneered the Schwarzschild pioneered the calculations describing the structure calculations describing the structure of black holes. The distance across of black holes. The distance across a black hole is called the a black hole is called the Schwarzschild radius in his honor.Schwarzschild radius in his honor.

Black HolesBlack Holes

If you look at general relativity to find out If you look at general relativity to find out the size of black holes you get the same the size of black holes you get the same answer we got before: answer we got before: R = 2GM/cR = 2GM/c2 2 . .

The Curvature of SpaceThe Curvature of Space

General relativity (Einstein) General relativity (Einstein) predicted these curves in space and predicted these curves in space and they have been proven to exist they have been proven to exist experimentally. The effect of this experimentally. The effect of this curvature can be measured when curvature can be measured when looking at radio or light waves and it looking at radio or light waves and it exactly coincides with predictions.exactly coincides with predictions.

Black HolesBlack Holes

Where this exaggerated curvature Where this exaggerated curvature prevents even light from escaping is prevents even light from escaping is call the event horizon and it call the event horizon and it coincides with the point where coincides with the point where escape velocity is greater than the escape velocity is greater than the speed of light. This marks the point speed of light. This marks the point where nothing can escape from the where nothing can escape from the black holes gravitational attraction.black holes gravitational attraction.