By Dr. Harold Williams of Montgomery College Planetarium

1. Black Bubbles (Holes), Gravity to the Max: or how c, G, and M make a bubble in the fabric of time-space (reality)! Or How to Fall Into a Black Hole By Dr. Harold Williams of Montgomery College Planetarium http://montgomerycollege.edu/Departments/planet/ Given in the planetarium Saturday 16 November 2013

2. Black Hole in front of the Milky Way, out galaxy with 10 Solar Masses and viewed from 600km away

4. 0 Black Holes have a minimum mass Stars when they die either become white dwarfs (Chandrasekhar limit: 1.4 Msun), neutron stars where there is a mass limit, too, or Black Holes Neutron stars can not exist with masses > 3 Msun We know of no mechanism to halt the eventual collapse of a compact stellar object with > 3 Msun. It will collapse into a surface – an Event Horizon: But only at the end of time relative to an outside observer. => A black hole!

5. Escape Velocity Equation • Newtonian gravity • Ves=√(2GM/R) • Ves, escape velocity in m/s • G, Newtonian universal gravitational constant, 6.67259x10-11m3/(kg s2) • M, mass of object in kg • R, radius of object in m

6. Black Holes • John Michell, 1783: would most massive things be dark? • Modern view based on general relativity • Event horizon: surface of no return • Near BH, strong distortions of spacetime

7. 0 The Schwarzschild Radius => There is a limiting radius where the escape velocity reaches the speed of light, c: 2GM Vesc = c ____ Rs = c2 G = gravitational constant M = mass; c=speed of light in a vacuum Rs is called the Schwarzschild radius.

8. Postulates of General Relativity • All laws of nature must have the same form for observers in any frame of reference, whether accelerated or not. • In the vicinity of any given point, a gravitational field is equivalent to an accelerated frame of reference without a gravitational field • This is the principle of equivalence

9. Mass – Inertial vs. Gravitational • Mass has a gravitational attraction for other masses, mg ‘ • Mass has an inertial property that resists acceleration, mi . Fi = mi a • The value of G was chosen to make the values of mg and mi equal

10. Einstein’s Reasoning Concerning Mass • That mg and mi were directly proportional was evidence for a basic connection between them. • No mechanical experiment could distinguish between the two. • He extended the idea to no experiment of any type could distinguish the two masses.

11. Implications of General Relativity • Gravitational mass and inertial mass are not just proportional, but completely equivalent. • A clock in the presence of gravity runs more slowly than one where gravity is negligible. • The frequencies of radiation emitted by atoms in a strong gravitational field are shifted to lower frequencies • This has been detected in the spectral lines emitted by atoms in massive stars.

12. More Implications of General Relativity • A gravitational field may be “transformed away” at any point if we choose an appropriate accelerated frame of reference – a freely falling frame. • Einstein specified a certain quantity, the curvature of spacetime, that describes the gravitational effect at every point.

13. Curvature of Spacetime • There is no such thing as a gravitational force • According to Einstein • Instead, the presence of a mass causes a curvature of spacetime in the vicinity of the mass. • This curvature dictates the path that all freely moving objects must follow

14. General Relativity Summary • Mass one tells spacetime how to curve; curved spacetime tells mass two how to move • John Wheeler’s summary, 1979 • The equation of general relativity is roughly a proportion: Average curvature of spacetime a energy density • The actual equation can be solved for the metric which can be used to measure lengths and compute trajectories

15. General Relativity • Extension of special relativity to non uniform acceleration magnitudes. • Free-fall is the “natural” state of motion. • Time + space (timespace) is warped by gravity.

16. 0 Schwarzschild Radius and Event Horizon No object can travel faster than the speed of light => nothing (not even light) can escape from inside the Schwarzschild radius We have no way of finding out what’s happening inside the Schwarzschild radius.

17. 0

18. 0 “Black Holes Have No Hair” Matter forming a black hole is losing almost all of its properties. black holes are completely determined by 3 quantities: mass angular momentum (electric charge) The electric charge is most likely near zero

19. 0 The Gravitational Field of a Black Hole Gravitational Potential Distance from central mass The gravitational potential (and gravitational attraction) at the Schwarzschild radius of a black hole becomes infinite.

20. 0 General Relativity Effects Near Black Holes An astronaut descending down towards the event horizon of the black hole will be stretched vertically (tidal effects) and squeezed laterally unless the black hole is very large like thousands of solar masses, so the multi-million solar mass black hole in the center of the galaxy is safe from turning a traveler into spaghetti .

21. 0 General Relativity Effects Near Black Holes Time dilation Clocks starting at 12:00 at each point. After 3 hours (for an observer far away from the black hole): Clocks closer to the black hole run more slowly. Time dilation becomes infinite at the event horizon. Event horizon

22. 0 Observing Black Holes No light can escape a black hole => Black holes can not be observed directly. If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity. Newton’s version of Kepler’s third Law. Mass > 3 Msun => Black hole!

23. Detecting Black Holes • Problem: what goes down doesn’t come back up • Need to detect effect on surrounding stuff Hot gas in accretion disks Orbiting stars Maybe gravitational lensing

24. 0 Compact object with > 3 Msun must be a black hole!

25. Stellar-Mass Black Holes • To be convincing, must show that invisible thing is more massive than NS • First example: Cyg X-1 • How many stellar mass black holes are there? ANSWER

26. Scientist witness apparent black hole birth, Washington Post, Tuesday, November 16, 2010. http://chandra.harvard.edu/photo/2010/sn1979c/

27. SN 1979C

28. Stars at the Galactic Center

29. Gamma Ray Bubble in Milky Way

30. Spectrum

32. Black Holes and their Galaxies

33. Gravitational Waves • Back to rubber sheet • Moving objects produce ripples in spacetime • Close binary BH or NS are examples • Very weak!

34. Gravitational Wave Detectors

35. Numerical Relativity • For colliding BH, equations can’t be solved analytically Coupled, nonlinear, second-order PDE! • Even numerically, extremely challenging Major breakthroughs in last few years • Now many groups have stable, accurate codes • Can compute waveforms and even kicks

36. Colliding BH on a Computer: From NASA/Goddard Group

37. What Lies Ahead • Numerical relativity continues to develop Compare with post-Newtonian analyses • Initial LIGO is complete and taking data • Detections expected with next generation, in less than a decade • In space: LISA, focusing on bigger BH Assembly of structure in early universe?

38. Testing General Relativity • General Relativity predicts that a light ray passing near the Sun should be deflected by the curved spacetime created by the Sun’s mass • The prediction was confirmed by astronomers during a total solar eclipse

39. Other Verifications of General Relativity • Explanation of Mercury’s orbit • Explained the discrepancy between observation and Newton’s theory • Time delay of radar bounced off Venus • Gradual lengthening of the period of binary pulsars (a neutron star) due to emission of gravitational radiation

40. Black Holes • If the concentration of mass becomes great enough, a black hole is believed to be formed • In a black hole, the curvature of space-time is so great that, within a certain distance from its center (whose radius, r, is defined as its circumference, C, divided by 2π, r=C/2π), all light and matter become trapped on the surface until the end of time.

41. Black Holes, cont • The radius is called the Schwarzschildradius • Also called the event horizon • It would be about 3 km for a star the size of our Sun • At the center of the black hole is a singularity • It is a point of infinite density and curvature where space-time comes to an end (not in our universe!)

42. All Real Black Holes will be Rotating, Kerr Solution • Andrew J. S. Hamiton & Jason P. Lisle (2008) “The river model of black holes” Am. J. Phys. 76 519-532, gr-qc/0411060 • Roy P. Kerr (1963) “Gravitational field of a spinning mass as an example of algebraically special metrics” Phys. Rev. Lett. 11 237--238 • Brandon Carter (1968) “Global structure of the Kerr family of gravitational fields” Phys. Rev. 174 1559-1571

43. General Relativity Without Tensor • √A/4π-R if A=4πR2 the surface area of a sphere then √A/4π-R=0 • But if A is the area of a sphere of radius R then √A/4π-R=GM/(3c2), with mass M enclosed in the sphere, but 2GM/c2=Rs • So √A/4π-R=Rs/6 • Rs for the Earth is 8mm which is very small compared to the radius of the Earth, which is 6,378.1km. • Rs for the Sun is 3km which is very small compared to the radius of the Sun, which is 695,500km.