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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
GravitationalRedshift
ObservationalEvidence forBlack Holes
Black Holes and Theory of Relativity
Einsteins Elevator
11/18/2008
My Office Hours:Tuesday 3:30 - 4:30 PM206 Keen Building
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
GravitationalRedshift
ObservationalEvidence forBlack Holes
Outline
1 Black Holes
2 Einsteins Theories of Relativity
Special Relativity
General Relativity
3 Space Travel Near Black Holes
Gravitational Redshift
4 Observational Evidence for Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
GravitationalRedshift
ObservationalEvidence forBlack Holes
Outline
1 Black Holes
2 Einsteins Theories of Relativity
Special Relativity
General Relativity
3 Space Travel Near Black Holes
Gravitational Redshift
4 Observational Evidence for Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
GravitationalRedshift
ObservationalEvidence forBlack Holes
Black Holes
The mass of a neutron star cannot exceed about threesolar masses. If a core remnant is more massive thanthat, nothing will stop its collapse, and it will becomesmaller and smaller and denser and denser.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
GravitationalRedshift
ObservationalEvidence forBlack Holes
Black Holes
The mass of a neutron star cannot exceed about threesolar masses. If a core remnant is more massive thanthat, nothing will stop its collapse, and it will becomesmaller and smaller and denser and denser.
Eventually the gravitational force is so intense thateven light cannot escape. The remnant has become ablack hole.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Black Holes
The radius at which the escape speed from theblack hole equals the speed of light is called theSchwarzschild radius.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Black Holes
The radius at which the escape speed from theblack hole equals the speed of light is called theSchwarzschild radius.
Remember escape speed:
v (in km/s) = 11.2
mass of body (in Earth masses)
radius of body (in Earth radii)
Earths Schwarzschild radius is about a centimeter;the Suns is about 3 km.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Black Holes
The radius at which the escape speed from theblack hole equals the speed of light is called theSchwarzschild radius:
Schwarzschild radius = 3 km
M
Once the black holehas collapsed, the Schwarzschild
radius takes on another meaning it is now the eventhorizon. Nothing within the event horizon can escapethe black hole.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Outline
1 Black Holes
2 Einsteins Theories of Relativity
Special Relativity
General Relativity
3 Space Travel Near Black Holes
Gravitational Redshift
4 Observational Evidence for Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Special Relativity
1 The speed of light is the maximum possiblespeed, and it is always measured to have thesame value by all observers.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Speed of Light
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Michelson-Morley Experiment
1887: Michelson and Morley attempted to determine
Earths motion relative to the absolute space throughwhich light supposedly moved by measuring the speed of
light at different times of the day and on different days of
the year.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Michelson-Morley Experiment
1887: Michelson and Morley attempted to determine
Earths motion relative to the absolute space throughwhich light supposedly moved by measuring the speed of
light at different times of the day and on different days of
the year.
Far from measuring the
properties of absolute
space, the experiment
demolished the entire
concept.
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Special Relativity
1 The speed of light is the maximum possiblespeed, and it is always measured to have thesame value by all observers.
2 There is no absoluteframe of reference, and no
absolutestate of rest.
Bl k H l
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Lorentz Contraction
=1
1 v2/c2
Bl k H l
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Lorentz Contraction
When measuring the length of the moving meterstick,you do so by noting the positions of the two ends atthe same time, according to your clock.
However, those two events the two measurementsyou make do notoccur at the same time as seen bythe moving observer. In relativity, time is relative, andsimultaneity (the idea that two events happen at the
same time) is no longer a well-defined concept.
Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Time Dilation
Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Special Relativity
1 The speed of light is the maximum possiblespeed, and it is always measured to have thesame value by all observers.
2 There is no absoluteframe of reference, and no
absolutestate of rest.3 Spaceand timeare not independent, but are
unifiedas spacetime.
Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
General Relativity
Special relativityis equivalent to Newtonian mechanicsin describing objects that move much more slowly thanthe speed of light, but it differs greatly in its predictionsat relativistic velocities.
Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
General Relativity
Special relativityis equivalent to Newtonian mechanicsin describing objects that move much more slowly thanthe speed of light, but it differs greatly in its predictionsat relativistic velocities.
What about Newtons law of gravity? Much more complex mathematical problem in the
framework of relativity!
Black Holes
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Black Holesand Theory of
Relativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
General Relativity
Special relativityis equivalent to Newtonian mechanicsin describing objects that move much more slowly thanthe speed of light, but it differs greatly in its predictionsat relativistic velocities.
What about Newtons law of gravity? Much more complex mathematical problem in the
framework of relativity!
In 1915 Einstein said:
It is impossible to tell, from within a closed system,whether one is in a gravitational field, or accelerating.
Black Holes
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
General Relativity
Equivalence Principle
It impossible to tell, fromwithin a closed system, ifone is in a gravitationalfield, or accelerating.
Black Holes
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
General Relativity
Equivalence Principle
It impossible to tell, fromwithin a closed system, ifone is in a gravitationalfield, or accelerating.
Unavoidable conclusion:
Spacetime is curved.
Black Holes
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Curved Space
All matter tends to warpspacetime, and in doingso redefines straight lines(the path a light beamwould take).
A black hole occurs whenthe indentation causedby the mass of the holebecomes infinitelydeep.
Black Holes
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Test of General Relativity
Einstein noted that light from a star should be deflectedby a measurable amount as it passes the Sun (1915).
Black Holesd Th f
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Test of General Relativity
In 1919, observers led by the British astronomer Sir
Arthur Eddington succeeded in measuring the deflectionof starlight during an eclipse.
Black Holesand Theory of
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Test of General Relativity
Black Holesand Theory of
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Outline
1 Black Holes
2 Einsteins Theories of Relativity
Special Relativity
General Relativity
3 Space Travel Near Black Holes
Gravitational Redshift
4 Observational Evidence for Black Holes
Black Holesand Theory of
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Space Travel Near Black Holes
The gravitational effects of a black hole are
unnoticeable outside of a few Schwarzschild
radii black holes do not suck in materialany more than an extended mass would.
Black Holesand Theory of
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Black Hole Heating
Matter encountering a black hole
will experience enormous tidal
forces that will both heat it enough
to radiate, and tear it apart.
Black Holesand Theory of
G i i l R d hif
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and Theory ofRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Gravitational Redshift
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshiftas itgets closer,
Black Holesand Theory of
G it ti l R d hift
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yRelativity
Black Holes
EinsteinsTheories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Gravitational Redshift
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshift asit gets closer, so that time appears to be going more and
more slowly as it approaches the event horizon.
Black Holesand Theory of
G it ti l R d hift
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yRelativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Gravitational Redshift
Effect called gravitational redshift:
Its not due to motion, but to thelarge gravitational fields present.
The probe itself, however, does
not experience any such shifts;
time would appear quite normal to
anyone inside.
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshift asit gets closer, so that time appears to be going more and
more slowly as it approaches the event horizon.
Black Holesand Theory of
G it ti l R d hift
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Gravitational Redshift
Effect called gravitational redshift:
Its not due to motion, but to thelarge gravitational fields present.
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshift asit gets closer, so that time appears to be going more and
more slowly as it approaches the event horizon.
Black Holesand Theory of
Gravitational Redshift
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Gravitational Redshift
Similarly, a photon escaping from
the vicinity of a black hole will
use up a lot of energy doing
so; it cannot slow down, however
its wavelength gets longer andlonger.
A probe nearing the event horizon of a black hole will be
seen by observers as experiencing a dramatic redshift asit gets closer, so that time appears to be going more and
more slowly as it approaches the event horizon.
Black Holesand Theory of
R l ti it Whats inside a black hole?
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
What s inside a black hole?
Black Holesand Theory of
Relativity Whats inside a black hole?
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
What s inside a black hole?
1 A time machine ... honestly, according to theory a black
hole takes you back in time.
2 Some travel device: a black hole is like a wormholeand will allow easy travel for future generations.
3 Nobody knows.
Black Holesand Theory of
Relativity Whats inside a black hole?
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
What s inside a black hole?
No one knows, of course; present theory predicts that themass collapses until its radius is zero and its density isinfinite. This is unlikely to be what actually happens.
Until we learn much more about what happens in suchextreme conditions, interiors of black holes will remain amystery.
Black Holesand Theory of
Relativity Outline
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Outline
1 Black Holes
2 Einsteins Theories of Relativity
Special Relativity
General Relativity
3 Space Travel Near Black Holes
Gravitational Redshift
4 Observational Evidence for Black Holes
Black Holesand Theory of
Relativity Observational Evidence
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Observational Evidence
The existence of black-hole binary partnersfor ordinary
stars can be inferred by the effect the holes have on thestars orbit, or by radiation from infalling matter.
Black Holesand Theory of
Relativity Observational Evidence:
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Relativity
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Observational Evidence:
Cygnus X-1
Strong black-hole candidate:
1 Visible partner about 25 M
2 Systems total mass isabout 35 M X-ray source must be
about 10 M
3 Hot gas appears to beflowing from the visible star
to unseen companion4 Short time-scalevariations
indicate that source mustbe very small
Black Holesand Theory of
Relativity Observational Evidence for
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y
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Observational Evidence for
Black Holes
There are several other black hole candidates as well,with caracteristics similar to Cygnus X-1.
The centers of many galaxies contain supermassiveblack holes about 1 million solar masses.
Black Holesand Theory of
Relativity Observational Evidence for
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y
Black Holes
Einsteins
Theories ofRelativity
Special Relativity
General Relativity
Space TravelNear BlackHoles
Gravitational
Redshift
ObservationalEvidence forBlack Holes
Observational Evidence for
Black Holes
Starburst galaxy M82
Recently, some evidence for
intermediate-mass black holeshas been found; these are about100 to 1000 solar masses. Theirorigin is not well understood.
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