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BLACK HOLESBLACK HOLESWhat supports a star against Gravity?What supports a star against Gravity?
Core of a Main Sequence StarCore of a Main Sequence Star
~ 10~ 1022 g/cm g/cm33
White DwarfWhite Dwarf
~ 10~ 1077 g/cm g/cm33
Neutron StarNeutron Star
~ 10~ 101414 g/cm g/cm33
Black HoleBlack Hole
> 10> 101616 g/cm g/cm33
Gas Pressure Gas Pressure Resists GravityResists Gravity
Electron Degeneracy Electron Degeneracy Balances GravityBalances Gravity
Neutron Neutron DegeneracyDegeneracy
Gravity wins over all Gravity wins over all other forcesother forces
SingularitySingularity
GRAVITY WINS!!GRAVITY WINS!!~
There is in space a small black holeThere is in space a small black hole
through which, say our astronomers,through which, say our astronomers,
the whole damn thing, the universe,the whole damn thing, the universe,
must one day fall. That will be allmust one day fall. That will be all
““Cosmic Comics” – Nemerov 1975Cosmic Comics” – Nemerov 1975
Albert Einstein (1879-1955)Albert Einstein (1879-1955)Special Theory of Relativity (1905)Special Theory of Relativity (1905)
1.1. All observers measure the All observers measure the same velocity of light same velocity of light irrespective of their irrespective of their motion.motion.
2.2. The laws of physics are The laws of physics are the same no matter what the same no matter what the speed of the observer.the speed of the observer.
3.3. The velocity of light is a The velocity of light is a constant of nature, and it constant of nature, and it is the maximum allowed is the maximum allowed speed in nature.speed in nature.
General Theory of Relativity (1916)General Theory of Relativity (1916)A Theory of GravityA Theory of Gravity
Gravity is a manifestation ofGravity is a manifestation of
the curvature of space – more correctlythe curvature of space – more correctly
the “curvature of space-time”the “curvature of space-time”
By By Black HoleBlack Hole we mean any region we mean any region
where curvature of space-time is great where curvature of space-time is great
enough to prevent light fromenough to prevent light from
escaping.escaping.
No light out, No information out.No light out, No information out.
Another Universe? Wonderland?Another Universe? Wonderland?
GRAVITY GRAVITY GEOMETRY GEOMETRYGravity is no longer described as a force, but as the curvature of Gravity is no longer described as a force, but as the curvature of
“space-time”.“space-time”.
A spacecraft in orbit around the Earth tries to follow a “straight” A spacecraft in orbit around the Earth tries to follow a “straight” path – however, space-time is curved and makes things fall toward the path – however, space-time is curved and makes things fall toward the Earth!Earth!
Space-time is curved and matter is the source of the curvature.Space-time is curved and matter is the source of the curvature.
Matter is also the source of gravitation, so gravity is related to the Matter is also the source of gravitation, so gravity is related to the curvature.curvature.
Empty space Empty space Flat space-timeFlat space-time
Space with matter Space with matter Curved space-timeCurved space-time
Thought ExperimentThought Experiment• You are in a rocket, far out in space.You are in a rocket, far out in space.• The rocket accelerates.The rocket accelerates.• You feel yourself being pulled “down” at 1 g.You feel yourself being pulled “down” at 1 g.• You let go of a ball in your hand, and it “falls” to the floor.You let go of a ball in your hand, and it “falls” to the floor.
Why?Why? Because the ship is Because the ship is acceleratingaccelerating “upward,” the ball “upward,” the ball will be left behind.will be left behind.
Compare this to a Compare this to a rocket sitting rocket sitting on Earthon Earth
Everything is the same!Everything is the same!You feel your weight (1You feel your weight (1gg).).The ball falls, etc.The ball falls, etc.
Accelerating RocketAccelerating Rocket
Now imagine the same rocket at rest in the Earth’s Now imagine the same rocket at rest in the Earth’s gravitational field.gravitational field.
The same thing happensThe same thing happens..
The Principle of Equivalence:The Principle of Equivalence:
Acceleration and Gravity – Acceleration and Gravity – no differenceno difference
Escape VelocityEscape Velocity
What goes up does What goes up does notnot come down if come down if v > vv > vescesc
From the Earth, From the Earth, vvescesc ~ ~ 11 km/sec.11 km/sec.
When When vvescesc > > cc
even light cannot escape.even light cannot escape.
This is a This is a BLACK HOLE.BLACK HOLE.
R
GMvesc
2
Physics:Physics:
Light Rays from a Collapsing StarLight Rays from a Collapsing Star
Black Hole sizeBlack Hole sizeSchwarzschild Radius:Schwarzschild Radius:
R
GMc
cv
M
Mc
GMR
esc
S
2
When
km 3
2
SUN
2
EVENT HORIZONEVENT HORIZON
SCHWARZSCHILD RADIUSSCHWARZSCHILD RADIUS
GRAVIATIONAL RADIUSGRAVIATIONAL RADIUS} all same thing
Locus of points inside which no information can cross to the outsideLocus of points inside which no information can cross to the outside
One Solar Mass Black HoleOne Solar Mass Black HoleSchwarzschild Schwarzschild RadiusRadius
R ~ 3 kmR ~ 3 km
Photon SpherePhoton Sphere
R ~ 4.5 kmR ~ 4.5 km
SingularitySingularity
EVENT HORIZONEVENT HORIZON
SCHWARZSCHILD RADIUSSCHWARZSCHILD RADIUS
GRAVIATIONAL RADIUSGRAVIATIONAL RADIUS} all same thing
Light PathsLight Paths
Curved Space!Curved Space!
Death of a Massive StarDeath of a Massive Star
Original Mass > 15 MOriginal Mass > 15 MSUNSUN
Core Mass > 2 MCore Mass > 2 MSUNSUN
Very fast core collapseVery fast core collapse
BLACK HOLEBLACK HOLE
MassMass RRSS (g/cm(g/cm33))
3 x 103 x 1088 M MSUNSUN
15 M15 MSUNSUN
SunSun
EarthEarth
6 AU6 AU
45 km45 km
3 km3 km
9 mm9 mm
0.20.2
8 x 108 x 101313
2 x 102 x 101616
2 x 102 x 102727
A large Black Hole doesn’t have to be dense!A large Black Hole doesn’t have to be dense!
~
Type of Black Hole Mass Angular Momentum ChargeSchwarzschild black hole M>0 J=0 Q=0Kerr black hole M>0 J>0 Q=0Kerr-Newman black hole M>0 J>0 Q≠0Reissner-Nordström black hole M>0 J=0 Q≠0
Black Holes Types
Candidates for Black HolesCandidates for Black Holes• Collapsed massive starsCollapsed massive stars
• Nuclei of Globular ClustersNuclei of Globular Clusters
• Nuclei of GalaxiesNuclei of Galaxies
• QuasarsQuasarsAstrophysicists theorize that miniature black
holes might have formed at the moment
the universe was created, but we have no proof
of their existence. Miniature black holes would
have event horizons as small as the width of an
atomic particle and contain as much matter
as Mt. Everest. Quantum theory suggests
that these black holes—if they exist—may
evaporate over time.
• Mini – Black HolesMini – Black Holes Stephen Hawking Stephen Hawking
During the During the Big BangBig Bang, the density was so high that Earth-, the density was so high that Earth-size mass Mini-BH could have formed – Each less than a size mass Mini-BH could have formed – Each less than a centimeter in size.centimeter in size.
Black holes have their own distinctive anatomy, consisting of:
• Singularity
• Event horizon
• Accretion disk
• Gas jets
The center of a black hole is a point of zero size called the singularity. At the singularity, space-time has infinite curvature and matter is crushed to infinite density. Space and time, as we know them, cease to exist.
singularity
The event horizon is the rim or boundary of a black hole where escape velocity equals the speed of light. Once inside the event horizon, neither particles nor light can escape.
The “dark” center in the x-ray illustration on the left shows the event horizon of the black hole. Compare to the neutron star on the right.
At the event horizon, dimensions as we know them become distorted. To an outside observer, light and time would seem to stand still. An object falling into a black hole would appear to slow and stop at the event horizon.
An accretion disk is a flat sheet of gas and dust surrounding a black hole. Material spirals inward as it loses energy due to friction from huge gravitational tides.
Black holes may have gas jets caused by the interaction of gas particles with strong, rotating magnetic fields.
Artist’s conception of a black hole with gas jets and an accretion disk.
Astronomers describe three types of black holes:
– Supermassive black holes
– Stellar black holes– Miniature black
holes
Artist’s conception
Supermassive black holes can have masses equivalent to billions of suns. They are believed to exist in the centers of most galaxies. Orbiting stars may be captured and their mass added to the black hole.
The Hubble Space Telescope has imaged a number of galaxies believed to have black holes at their centers.
Strong X-ray emissions and high central stellar speeds in M104, the Sombrero Galaxy, lead astronomers to speculate that a supermassive black hole, perhaps a billion times the mass of our Sun, lies at its core.
Masa del SMBH central de algunas galaxias
Galaxy SMBH Mass Log SMGH Mass Velocity dispersionunits: 10^6 solar masses units: km/sec
M31 450 8.7 160M32 2.6 6.4 75
NGC 821 37 7.6 209NGC 1023 44 7.6 205NGC 1068 17 7.2 151NGC 2787 41 7.6 140NGC 3377 110 8.0 145NGC 3031 68 7.8 170NGC 3245 210 8.3 205NGC 3379 100 8.0 206NGC 3384 16 7.2 143NGC 3998 560 8.7 297NGC 3608 190 8.3 182NGC 4253 42 7.6 130NGC 4261 520 8.7 315NGC 4291 310 8.5 242NGC 4342 300 8.5 225NGC 4459 70 7.8 167NGC 4473 140 8.1 190NGC 4486 300 8.5 375NGC 4564 56 7.7 162NGC 4596 78 7.9 136NGC 4549 200 8.3 385NGC 4697 17 7.2 177NGC 4742 14 7.1 90NGC 5128 240 8.4 150NGC 5845 370 8.6 234NGC 6251 600 8.8 290NGC 7052 330 8.5 266NGC 1459 2600 9.4 350
Stellar Motions at the Galactic CenterStellar Motions at the Galactic Center
Radio Image of the Galactic CenterRadio Image of the Galactic Center
X-ray Images of the Galactic CenterX-ray Images of the Galactic Center
Stellar black holes are produced by the collapse of dying stars, and have masses 3 to greater than 10 times that of our Sun. Over a dozen have been detected by their effects on a binary companion star.
Artist’s conception of a stellar mass black hole drawing in matter from its binary companion.
Gas drawn from the companion star heats up and emits X-rays, providing our best evidence for the existence of black holes within our own galaxy.
Cygnus X-1Cygnus X-1Best evidence for a Stellar Black HoleBest evidence for a Stellar Black Hole
Spectroscopic BinarySpectroscopic Binary
Blue Supergiant Blue Supergiant ~15 M ~15 MSUNSUN
Invisible CompanionInvisible Companion ~8 M ~8 MSUNSUN
Cygnus X-1 emits X-rays and Cygnus X-1 emits X-rays and -ray bursts, like an X-ray binary neutron -ray bursts, like an X-ray binary neutron star, but the companion is too massive to be a neutron star star, but the companion is too massive to be a neutron star BLACK BLACK
HOLE?HOLE?
The image on the right is the signature of a supermassive black hole in Galaxy M84, as seen by Hubble’s Space Telescope Imaging Spectrograph (STIS). The photo on the left shows the slice of space that STIS was analyzing.
Using X-rays, scientists can measure the heat and speed of orbiting material, and from this can detect the presence of a black hole. The mass of the black hole can be determined by the speed of the gas.
Chandra X-ray image of galaxy cluster A2104.
Scientists used the Chandra X-ray Observatory to study XTE J1118+480, a black hole binary system. This "X-ray nova," so-called because it undergoes occasional eruptions followed by long periods of dormancy, contains a Sun-like star orbiting a black hole.
Chandra image of the spectrumof a black hole.
Non-spinning black hole Spinning black hole
Astronomers used Chandra and XMM-Newton observations to investigate the spin of three stellar black holes. A spinning black hole drags space around with it and allows atoms to orbit nearer to the black hole than is possible for a non-spinning black hole.
Black holes capture more than light and matter: they capture our imaginations. The bizarre notion of an infinitely small point of infinite density punching a hole in the fabric of space-time, challenges our very concept of the universe perhaps more than any other astronomical phenomenon.
Causalidad
Diagrama de Penrose
Conos de luz (Futuro)
Agujeros de dos en dos
Agujero de gusano
Singularidad Anular
La Máquina del Tiempo
