1. Agujeros Negros Pablo Cuartas Restrepo Ing. Mecánico UdeA MSc Astronomía UNAL quarktas@gmail.com

2. BLACK HOLES What supports a star against Gravity? Core of a Main Sequence Star  ~ 10 2 g/cm 3 White Dwarf  ~ 10 7 g/cm 3 Neutron Star  ~ 10 14 g/cm 3 Black Hole  > 10 16 g/cm 3 Gas Pressure Resists Gravity Electron Degeneracy Balances Gravity Neutron Degeneracy Gravity wins over all other forces Singularity GRAVITY WINS!! ~

3. There is in space a small black hole through which, say our astronomers, the whole damn thing, the universe, must one day fall. That will be all “Cosmic Comics” – Nemerov 1975

4. Albert Einstein (1879-1955) Special Theory of Relativity (1905) 1.All observers measure the same velocity of light irrespective of their motion. 2.The laws of physics are the same no matter what the speed of the observer. 3.The velocity of light is a constant of nature, and it is the maximum allowed speed in nature.

5. General Theory of Relativity (1916) A Theory of Gravity Gravity is a manifestation of the curvature of space – more correctly the “curvature of space-time” By Black Hole we mean any region where curvature of space-time is great enough to prevent light from escaping. No light out, No information out. Another Universe? Wonderland?

6. GRAVITY  GEOMETRY Gravity is no longer described as a force, but as the curvature of “space-time”. A spacecraft in orbit around the Earth tries to follow a “straight” path – however, space-time is curved and makes things fall toward the Earth! 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 curvature. Empty space  Flat space-time Space with matter  Curved space-time

7. Thought 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? Because the ship is accelerating “upward,” the ball will be left behind. Compare this to a rocket sitting on Earth Everything is the same! You feel your weight (1g). The ball falls, etc.

8. Accelerating Rocket Now imagine the same rocket at rest in the Earth’s gravitational field. The same thing happens. The Principle of Equivalence: Acceleration and Gravity – no difference

9. Escape Velocity What goes up does not come down if v > v esc What goes up does not come down if v > v esc From the Earth, v esc ~ 11 km/sec. From the Earth, v esc ~ 11 km/sec. When v esc > c even light cannot escape. This is a BLACK HOLE. Physics:

10. Light Rays from a Collapsing Star

11. Black Hole size Schwarzschild Radius: EVENT HORIZON SCHWARZSCHILD RADIUS GRAVIATIONAL RADIUS } all same thing Locus of points inside which no information can cross to the outside

12. One Solar Mass Black Hole Schwarzschild Radius R ~ 3 km Photon Sphere R ~ 4.5 km Singularity EVENT HORIZON SCHWARZSCHILD RADIUS GRAVIATIONAL RADIUS } all same thing Light Paths Curved Space!

13. Death of a Massive Star Original Mass > 15 M SUN Core Mass > 2 M SUN Very fast core collapse BLACK HOLE Mass RSRSRSRS  (g/cm 3 ) 3 x 10 8 M SUN 15 M SUN SunEarth 6 AU 45 km 3 km 9 mm 0.2 8 x 10 13 2 x 10 16 2 x 10 27 A large Black Hole doesn’t have to be dense! ~

14. Black Holes Types

15. Candidates for Black Holes Collapsed massive starsCollapsed massive stars Nuclei of Globular ClustersNuclei of Globular Clusters Nuclei of GalaxiesNuclei of Galaxies QuasarsQuasars Astrophysicists 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 Holes Stephen HawkingMini – Black Holes Stephen Hawking During the Big Bang, the density was so high that Earth- size mass Mini-BH could have formed – Each less than a centimeter in size.

16. Black holes have their own distinctive anatomy, consisting of: Singularity Event horizon Accretion disk Gas jets

17. 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

18. 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.

19. 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.

20. 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.

21. 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.

22. Astronomers describe three types of black holes: –Supermassive black holes –Stellar black holes –Miniature black holes Artist’s conception

23. 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.

24. The Hubble Space Telescope has imaged a number of galaxies believed to have black holes at their centers.

25. 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.

26. Masa del SMBH central de algunas galaxias

27. Stellar Motions at the Galactic Center

28. Radio Image of the Galactic Center

29. X-ray Images of the Galactic Center

30. 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.

31. 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.

32. Cygnus X-1 Best evidence for a Stellar Black Hole Spectroscopic Binary Blue Supergiant ~15 M SUN Invisible Companion ~8 M SUN Cygnus X-1 emits X-rays and  -ray bursts, like an X-ray binary neutron star, but the companion is too massive to be a neutron star  BLACK HOLE?

33. 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.

34. 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.

35. 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 spectrum of a black hole.

36. Non-spinning black holeSpinning 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.

37. 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.

38. Causalidad

39. Diagrama de Penrose

40. Conos de luz (Futuro)

42. Agujeros de dos en dos

43. Agujero de gusano

44. Singularidad Anular

45. La Máquina del Tiempo