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Exploring Black Holes: Gravitational Time Dilation and Cosmic Mysteries in Astronomy 201

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Join us for Lecture 23 of Astronomy 201: Cosmology, where we delve into the enigmatic nature of black holes. Learn about escape velocities from celestial bodies, the concept of the Schwarzschild radius, and how gravitational time dilation affects our perception of time near these cosmic phenomena. We will explore the life cycle of an astronaut falling into a black hole, and the paradox of singularities in the fabric of spacetime. Expand your understanding of the universe's ultimate lock boxes and the challenges of measuring time and distance in curved spacetime.

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Exploring Black Holes: Gravitational Time Dilation and Cosmic Mysteries in Astronomy 201

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  1. Announcements • Thursday, March 8: no office hours • pick up homework # 8 (due March 23) Astronomy 201 Cosmology - Lecture 23

  2. Lecture 23Black holes I: the Universe's ultimate lock box! Astronomy 201 Cosmology - Lecture 23

  3. Gravitational time dilation and redshift • Can be measured by experiments on Earth (challenging, but feasible) • Better: White Dwarfs(very compact objects; mass comparable to that of the Sun, radius comparable to that of the Earth), because they have a stronger gravitational field • Even better: Neutron Stars and Pulsars(very compact objects; mass comparable to that of the Sun, radius only 10-100 km), because they have a very strong gravitational field Astronomy 201 Cosmology - Lecture 23

  4. Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? • Example: Earth • Radius: R = 6470 km = 6.47106 m • Mass: M = 5.97 1024 kg • escape velocity: vesc = 11.1 km/s Astronomy 201 Cosmology - Lecture 23

  5. Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? • Example: Sun • Radius: R = 700 000 km = 7108 m • Mass: M = 21030 kg • escape velocity: vesc = 617 km/s Astronomy 201 Cosmology - Lecture 23

  6. Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? • Example: a solar mass White Dwarf • Radius: R = 5000 km = 5106 m • Mass: M = 21030 kg • escape velocity: vesc = 7300 km/s Astronomy 201 Cosmology - Lecture 23

  7. Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? • Example: a solar mass neutron star • Radius: R = 10 km = 104 m • Mass: M = 21030 kg • escape velocity: vesc = 163 000 km/s  ½ c Astronomy 201 Cosmology - Lecture 23

  8. Flash-back: Newtonian gravity • Can an object be so small that even light cannot escape ?  Black Hole • RS:“Schwarzschild Radius” • Example: for a solar mass • Mass: M = 21030 kg • Schwarzschild Radius: RS = 3 km Astronomy 201 Cosmology - Lecture 23

  9. Some definitions ... • The Schwarzschild radiusRSof an object of mass M is the radius, at which the escape speed is equal to the speed of light. • The event horizon is a sphere of radius RS. Nothing within the event horizon, not even light, can escape to the world outside the event horizon. • A Black Hole is an object whose radius is smaller than its event horizon. Astronomy 201 Cosmology - Lecture 23

  10. Sizes of objects Astronomy 201 Cosmology - Lecture 23

  11. space time Let’s do it within the context of general relativity — spacetime • spacetime distance (flat space): • Fourth coordinate: ct • time coordinate has different sign than spatial coordinates Astronomy 201 Cosmology - Lecture 23

  12. space time Let’s do it within the context of general relativity — spacetime • spacetime distance (curved space of a point mass): Astronomy 201 Cosmology - Lecture 23

  13. space time What happens if R RS • R> RS: everything o.k.: time: +, space:  but gravitational time dilation and length contraction • R RS:time  0 space   • R< RS: signs change!! time: , space: + “space passes”, everything falls to the center infinite density at the center, singularity Astronomy 201 Cosmology - Lecture 23

  14. Structure of a Black Hole Astronomy 201 Cosmology - Lecture 23

  15. What happens to an astronaut who falls into a black hole? • Far outside: nothing special • Falling in: long before the astronaut reaches the event horizon, he/she is torn apart by tidal forces • For an outside observer: • astronaut becomes more and more redshifted • The astronaut’s clock goes slower and slower • An outside observer never sees the astronaut crossing the event horizon. Astronomy 201 Cosmology - Lecture 23

  16. What happens, if an astronaut falls into a black hole? • For the astronaut: • He/she reaches and crosses the event horizon in a finite time. • Nothing special happens while crossing the event horizon (except some highly distorted pictures of the local environment) • After crossing the event horizon, the astronaut has 10 microseconds to enjoy the view before he/she reaches the singularity at the center. Astronomy 201 Cosmology - Lecture 23

  17. Cosmic censorship • Singularity: a point at which spacetime diverges • infinite forces are acting • laws of physics break down • quantum gravity may help ? • no problem as long as a singularity is shielded from the outside world by an event horizon • Hypothesis: Every singularity is surrounded by an event horizon. • There are no naked singularities Astronomy 201 Cosmology - Lecture 23

  18. Near a black hole: bending of light Astronomy 201 Cosmology - Lecture 23

  19. The Photon sphere • The photon sphere is a sphere of radius 1.5 RS. On the photon sphere, light orbits a black hole on a circular orbit. Astronomy 201 Cosmology - Lecture 23

  20. Structure of a rotating black hole • Within the ergosphere (or static sphere) nothing can remain at rest. Spacetime is dragged around the hole Astronomy 201 Cosmology - Lecture 23

  21. No-Hair theorem • Properties of a black hole: • it has a mass • it has an electric charge • it has a spin (angular momentum) • that’s it. Like an elementary particle, but much more massive • Black holes have no hair Astronomy 201 Cosmology - Lecture 23

  22. Questions: • Do they really exist ? • How do we observe something that does not emit light? Astronomy 201 Cosmology - Lecture 23

  23. Announcements • Thursday, March 8: no office hours • pick up homework # 8 (due March 23) Astronomy 201 Cosmology - Lecture 23

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