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General Relativity
Chapter 8
Introduction
GR is Einstein’s theory of gravitation that
builds on the geometric concept of space
time introduced in SR.
Is there a more fundamental explanation of
gravity than Newton’s law?
GR makes specific predictions of deviations
from Newtonian gravity.
Curved spacetime
Gravitational fields alter the rules of
geometry in spacetime producing “curved”
space
For example the geometry of a simple
triangle on the surface of sphere is different
than on a flat plane (Euclidean)
On small regions of a sphere, the geometry is
close to Euclidean
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How does gravity curve spacetime?
•With no gravity, a ball thrown upward continues upward
and the worldline is a straight line.
•With gravity, the ball’s worldline is curved.
•It follows this path because the spacetime surface on
which it must stay is curved.
•To fully represent the trajectory, need all 4 spacetime
dimensions curving into a 5th dimension(!)
•Hard to visualize, but still possible to measure
t
t
x
x
No gravity
gravity
Principle of Equivalence
A uniform gravitational field in some
direction is indistinguishable from a uniform
acceleration in the opposite direction
Keep in mind that an accelerating frame
introduces pseudoforces in the direction
opposite to the true acceleration of the
frame (e.g. inside a car when brakes are
applied)
Elevator experiment
•First, elevator is supported and not
moving, but gravity is present.
Equate
forces on the person to ma
(=0 since a=0)
•F
s
 mg = 0
so
F
s
= mg
•F
s
gives the weight of the person.
•Second, no gravity, but an upward
acceleration a.
The only force on the
person is F
s
and so
•F
s
= ma
or
F
s
= mg if “a” value is the
same as “g”
•Person in elevator cannot tell the
difference between gravitational field and
accelerating frame
•Third, there is gravity and the elevator is
also in freefall
•Fs  mg = mg
or
Fs = 0
•“Weightless”
Let upward
forces be
positive,
thus gravity
is g
See also http://www.pbs.org/wgbh/nova/einstein/relativity/
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Einstein was bothered by what he saw as a dichotomy in the
concept of "mass." On one hand, by Newton's second law
(
F=ma
), "mass" is treated as a measure of an object’s
resistance to changes in movement. This is called
inertial mass
.
On the other hand, by Newton's Law of Universal Gravitation,
an object's mass measures its response to gravitational
attraction. This is called
gravitational mass
. As we will see,
Einstein resolved this dichotomy by putting gravity and
acceleration on an equal footing.
The principle of equivalence is really
a statement that
inertial and
gravitational masses are the same
for any object.
This also explains why all objects have the same
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This note was uploaded on 02/13/2012 for the course AST 3019 taught by Professor Sarajedini during the Spring '08 term at University of Florida.
 Spring '08
 Sarajedini
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