ASTR3000: Relativistic
Astrophysics and Cosmology
Part 1: Special Relativity (Ramesh Bhat)
(5 Lectures)
Part 2: General Relativity (Roberto Soria)
(7 Lectures)
Outline
•  Lecture 1: Context, background. Departures from Newtonian
mechanics and perplexities in the propagation of light;
•  Lecture 2: Lorentz-Einstein transformations, length contraction
and time dilation;
•  Lecture 3: Radiation from moving bodies: Doppler factor,
transformation of specific intensity. Relativistic jets in Active
Galactic Nuclei.
•  Lecture 4: More on the Doppler factor. Dynamics and collisions/
scattering of photons and particles.
Outline
• 
First, some comments on the context
for this course - why are theories of
special and general relativity
important in the study of astrophysics
and cosmology;
• 
Second, will lay the basis for special
relativity - Departures from
Newtonian dynamics and
Perplexities in the propagation of
light ;
• 
First 4+1 lectures will revolve around
special relativity (Ramesh Bhat);
• 
Remaining (7) lectures will revolve
around general relativity (Roberto
Soria);
General comments
•  Special relativity is important when the
speed of objects, relative to some observer,
becomes significant compared to the
speed of light (which has a constant speed
for all observers – central postulate of SR):
–  Emission from accelerated electrons;
–  Frequency of emission from distant galaxies;
Relative Right Ascension (arcsec)
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Pulsars;
Massive black holes;
Gravitational lenses;
The Universe (weak fields)!
•  First 4 lectures draw from the listed
textbook, Special Relativity by A.P.
French (on reserve in library)
-5
•  General relativity important when matter/
energy is in presence of strong
gravitational fields (massive objects):
Relative Declination (arcsec)
5
0
10
15
10
5
0
-5
-10
-15
Context (1): Radio galaxies
Active galactic nuclei (AGN) consist
of a supermassive black hole and
accretion disk that accelerates
material (electrons or positrons) into
a relativistic jet.
Because of the high speed of the jet
and geometry, the jet can appear
superluminal - a special relativistic
effect.
Relative Right Ascension (arcsec)
-5
Relative Declination (arcsec)
5
0
10
15
10
5
0
-5
-10
-15
Context (2) - pulsars
Pulsars are small (~10 km diameter)
and massive (~1.4 solar masses)
objects, therefore have a very strong
gravitational field.
How much stronger than at the
surface of the Earth (9.8 m/s2)?
When in orbit around a companion,
pulses from the pulsar are delayed
because of bending of the light by the
gravitational field of the companion
(Shapiro delay).
A general relativistic effect.
More special relativity in astrophysics…..
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Nuclear burning in stars (E=mc2);
Modified brightness (Doppler beaming);
…
…
Precursor knowledge for Radiation Process (4th year);
Departures from Newtonian dynamics
Principle of relativity: the laws of
physics appear the same in many
different frames of reference
Special relativity: Principle of
relativity applies not just to a limited
range of phenomena. In particular,
motion of order the speed of light is
not to be placed in a separate
category
A single proposition: In every
observation of the passage of light
from one point to another through
empty space, the time taken is simply
the relative separation of the points
divided by a universal constant c.
Motion of the observer relative to the
light source does not affect this
result.
y
y
v
x, x
Galileo/Newton - Galilean transformation
Fail when v/c > 0.05
In Newtonian mechanics, when a
constant force is applied to an object,
it gets faster, without limit.
The fundamental concept of
Newtonian mechanics is
encapsulated in the equation:
F=ma
Transfer more energy to the mass,
speed increases as square root of
the energy.
Without limit.
Fails when speed of mass approaches
speed of light, c.
Show movie (Bertozzi’s expt).
Derive the speed of a mass in
Newtonian mechanics.
SPEED OF LIGHT SEEMS TO HAVE
A SPECIAL STATUS IN PHYSICS.
Light (radiation) - Photons are
special:
Photons have the properties
of matter, like momentum.
In vacuum
photons
Non-Newtonian behaviour.
Go and find the speed of light (c), as
measured for:
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X-rays;
Visible light;
Infrared;
Radio waves.
Compare the values of c.
Nichols & Hull (1901)
Illustrate energy - momentum
relationship for photons
Experimental evidence for
a Newtonian-like interpretation
of momentum for photons
L
Matter and energy: A gedanken
(thought) experiment
t=0
E=cp
m
Einstein s box
Derive relationship between
energy and matter.
Δx
proton – proton chain reaction (this
version dominant in solar mass stars).
Determine the energy released in
this reaction.
Motion under a constant force.
t=Δt=L/c
Where are we?
We have derived (via a series of assertions for which there is experimental evidence and
results of thought experiments) some of the key results of special relativity.
–  Mass and energy are equivalent and this is postulated as a universal law.
–  The speed of light is a limiting speed in physics. Matter cannot go faster.
–  Moving matter has more mass than matter at rest (concept of rest mass).
–  Physics departs from the Newtonian interpretation when speeds approach c
- physics requires major revision.
The speed of light and the properties of light are central to the development
of special relativity.
We explore some of the problems in the understanding of radiation that
emerged in the late 19th century, that led to the development of special
relativity.
Perplexities in the propagation of light
Light and its properties (e.g. speed) are
significant in physics, as seen from previous
slides - impacts the dynamics of matter
(surprising!!).
Light has a speed, relative to what, in what
frame of reference?
Stellar aberration
Stationary telescope
Light: Stream of particles
Light: A wave - triumph of 19th century
physics (explanations for diffraction,
polarisation, interference etc).
Ether: proposed as the medium through
which light propagates - defines a
fundamental frame of reference.
α
β
Moving telescope - due to motion
of Earth in its orbit around the Sun.
Late 19th century, question was: what are
the properties of the ether? Is it detectable?
This is an easily observed effect. The
conclusion is that the Earth moves through
the ether, without disturbing it.
Famous experiment in search for the ether:
Michelson-Morley experiment.
Motion of Earth
through ether
Monochromatic
light source
Assuming Galilean addition of velocities, a
path difference between the two arms of
the interferometer is established, due to
the motion of the Earth through the ether.
l1
l2≠l1
If the interferometer is rotated by 90
degrees, a different path difference is
established and the fringes will shift.
No shift in fringes at all.
Conclusion: Earth must be stationary
relative to the ether. Direct conflict with
observations of stellar aberration.
Wave theory of light in major
conflict: major revison required.
Einstein provides the answer:
1)  The ether does not exist (light waves
propagate without a medium);
2)  Light has the same speed in all inertial
frames of reference. Galilean
transformations are thrown away.
3)  Special relativity proceeds from point 2.