1. Black Bubbles (Holes), Gravity to the Max: or how c, G, and M make a bubble in the fabric of time-space (reality)!
By Dr. Harold Williams
of Montgomery College Planetarium
Given in the planetarium Saturday 17 November 2012
Title slide

2. Black Hole in front of the Milky Way, out galaxy with 10 Solar Masses and viewed from 600km away
Simulated view of a black hole in front of the Milky Way. The hole has 10 solar masses (radius of 30Km) and is viewed from a distance of 600 km.

4. Neutron stars can not exist with masses > 3 Msun
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars:
Neutron stars can not exist with masses > 3 Msun
We know of no mechanism to halt the collapse of a compact object with > 3 Msun.
It will collapse into a surface – an Events Horizon:
But only at the end of time relative to an outside observer.
=> A black hole!

5. Escape Velocity
Velocity needed to escape Earth’s gravity from the surface: vesc ≈ 11.6 km/s.
vesc
Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity.
vesc
If you could compress Earth to a smaller radius => higher escape velocity from the surface.
vesc

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

7. 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
Clergymen John Michell, polymath. Light does not travel infinitely fast, Romer and moons of Jupiter. Ballistic escape possible from John Michell back whole. Tissue paper dissappear totally. Slowly as I get close and near.
John Michell (1784) “On the Means of Discovering the Distance, Magnitude, Etc., of the Fixed Stars, in Consequence of the Diminution of their Light, in case such a Diminution Should Be Found to Take Place in Any of the Them, and Such Other Data Should be Procured from Observations, as Would Be Futher Necessary for That Purpose” Phil. Trans. Roy. Soc. London 74 35

8. 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.

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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

16. General Relativity
Rolled tennis ball on flat floor. Through ball in a parabola arc in gravity. Jump and then throw, now a straight line. Natural motion Newton versus Einstein.
Extension of special relativity to non uniform acceleration magnitudes.
Free-fall is the “natural” state of motion
Time + space (timespace) is warped by gravity

17. 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.
These statements are correct, but the picture is most likely nonsense, R_s=C/2Pi where C is the circumference of the events horizon. What is wrong with this picture!
“What is wrong with this picture.”

19. “Black Holes Have No Hair”
“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

20. The Gravitational Field of a Black Hole
Gravitational Potential
Distance from central mass
Events Horizon is the surface of infinite red shift, and infinite time dilation.
The gravitational potential (and gravitational attraction force) at the Schwarzschild radius of a black hole becomes infinite.

21. 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 .

22. 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.
In a finite amount of time for an in falling clock to the events horizon and infinite amount of time will pass for an outside the event horizon observer.
Time dilation becomes infinite at the event horizon.
Event horizon

23. Observing Black Holes Mass > 3 Msun => Black hole!
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!

24. 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
How do you find one.

25. Compact object with > 3 Msun must be a black hole!
Masses are determined by Newton’s version of Kepler’s third law.
Compact object with > 3 Msun must be a black hole!

26. Stellar-Mass Black Holes
To be convincing, must show that invisible thing is more massive than NS
First example: Cyg X-1
Now more than 17 clear cases, around 2009.
Still a small number!
If you demonstrate that the dark star is more than 3 Solar masses.

27. Scientist witness apparent black hole birth,
Washington Post, Tuesday, November 16, 2010.

28. M100 in Coma Bereniees in Virgo supercluster only 51Milliion LY away on April 15, 1979 with an 8 inch telescope by Gus Johnson in Swanton, Garrett County, MD a middle school teacher showing his pastor M100 when he discovered the SN. Type 2 SN steady x—rays Chandra, Swift, XXM-Newton, and the German ROSAT,
SN 1979C

29. Jets of Energy from Compact Objects
Some X-ray binaries show jets perpendicular to the accretion disk

30. Black Hole X-Ray Binaries
Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on time scales of less than a second)
Sometimes: Quasi-periodic oscillations (QPOs)
Sometimes: Radio-emitting jets

31. Artist drawing!

32. Black-Hole vs. Neutron-Star Binaries
Black Holes: Accreted matter disappears beyond the event horizon without a trace.
Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.

33. Stars at the Galactic Center
Works on the Mac. 3.5x10^6 SOLAR MASSES. Jougling 3 or more chaos.

34. Gamma Ray Bubble in Milky Way
Thanks Lucy Vitaliti of MC, the world is so vast I need all of the help I can get from all of my colleagues! and

35. Spectrum
Inverse Compton scattering, charged particles traveling near the speed of light colliding with low energy photons becoming high energy gamma rays.

36. Hubble Space Telescope image of a 5000 light-year (1
Hubble Space Telescope image of a 5000 light-year (1.5 kiloparsec) long jet being ejected from the active nucleus of the active galaxy M87, a radio galaxy. The blue synchrotron radiation of the jet contrasts with the yellow starlight from the host galaxy.

37. Black Holes and their Galaxies
Supermassive Black Holes
M-sigma Relation
The M-sigma (or MBH-σ) relation is an empirical correlation between the stellar velocity dispersion σ of a galaxy bulge and the mass M of the supermassive black hole at the galaxy's center.
The relation can be expressed mathematically as
A recent study, based on a complete sample of published black hole masses in nearby galaxies, [1] gives
Faber–Jackson relation is an early empirical power-law relation between the luminosity L and the central stellar velocity dispersion σ of elliptical galaxies, first noted by the astronomers Sandra M. Faber and Robert Earl Jackson in The original relation can be expressed mathematically as:
where the index γ is observed to be approximately equal to

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

39. Gravitational Wave Detectors
From Joan Centella.

40. 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
10 of them.

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

42. 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?

43. 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

44. 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

45. 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.

46. Black Holes, cont The radius is called the Schwarzschild radius
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!)

47. Penrose Diagram of Spherical Black Hole
Picture from

48. 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 , gr-qc/
Roy P. Kerr (1963) “Gravitational field of a spinning mass as an example of algebraically special metrics” Phys. Rev. Lett
Brandon Carter (1968) “Global structure of the Kerr family of gravitational fields” Phys. Rev

49. 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.