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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 Planetariumhttp://montgomerycollege.edu/Departments/planet/
Given in the planetarium Saturday 19 November 2011
Black Hole in front of the Milky Way, out galaxy with 10 Solar Masses and viewed from 600km away
Black HolesJust 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!
Escape VelocityVelocity 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
vescIf you could compress
Earth to a smaller radius => higher escape velocity
from the surface.
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
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
The Schwarzschild Radius
=> There is a limiting radius where the escape velocity
reaches the speed of light, c:
Vesc = cRs = 2GM ____ c2
Rs is called the Schwarzschild radius.
G = gravitational constant
M = mass; c=speed of light in a vacuum
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
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
'
2g g
g
m mF G
r
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
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
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
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
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
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
Schwarzschild Radius and Event Horizon
No object can travel faster than the speed of light
Þ We have no way of finding out what’s
happening inside the Schwarzschild radius.
=> nothing (not even light) can escape from inside
the Schwarzschild radius
Þ “What is wrong with this picture.”
“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
The Gravitational Field of a Black Hole
Distance from central mass
Gra
vita
tion
al
Po
ten
tial
The gravitational potential (and gravitational attraction force) at the Schwarzschild
radius of a black hole becomes infinite.
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 .
General Relativity Effects Near Black Holes
Time dilation
Event horizon
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.
Observing Black HolesNo 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!
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
Compact object with > 3 Msun must be a
black hole!
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!
• Scientist witness apparent black hole birth,
Washington Post, Tuesday, November 16, 2010.
http://chandra.harvard.edu/photo/2010/sn1979c/
SN 1979C
Jets of Energy from Compact Objects
Some X-ray binaries show jets perpendicular
to the accretion disk
Black Hole X-Ray Binaries
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
Accretion disks around black holes
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.
Stars at the Galactic Center
Spectrum
Black Holes and their Galaxies
Gravitational Waves
• Back to rubber sheet• Moving objects
produce ripples in spacetime
• Close binary BH or NS are examples
• Very weak!
Gravitational Wave Detectors
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
Colliding BH on a Computer: From NASA/Goddard Group
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?
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
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
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.
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!)
Penrose Diagram of Spherical Black Hole
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
The River Model of Black Holes
• http://jila.colorado.edu/~ajsh/insidebh/waterfall.html
• Andrew J.S. Hamilton
