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Special relativity is generalised to accommodate noninertial reference frames.
This is done via the principle of relativity, illustrated in figure
15 and stated below.
It is not possible to distinguish (in a closed system) between the
effects produced by a gravitational field and those produced by an acceleration
of the closed system
Figure 15:
Graphic depiction of the principle of equivalence.

This principle allows one to replace the effects of gravity by equivalent effects
based on the geometry of spacetime. Once gravity is ``abolished'' in this way,
and there is no ``force of gravity'' then all (gravitating) objects will have motions
described by Newton's First Law. That is, those in motion will continue in a straight line
at constant velocity. However, ``straight line'' now means only locally straight (locally
parallel to a coordinate axis in space). However, the geometry of space is now ``warped''
(no longer Euclidean) in such a way that the objects actual trajectory is ``similar'' to that
calculated in the classical way. Einstein wrote down a Field Equation which allowed
the warping of the geometry of spacetime to be calculated given a certain mass distribution.
The trajectory of the moon around the earth is locally straight in a spacetime region
warped by the presence of the earth's mass. Such ``straight lines'' are called geodesics,
defined as the shortest distance between two points in a curved space. This is illustrated
in figure 16.
Figure 16:
In General Relativity, the warping of the geometry of spacetime
due to mass distributions accounts for the effects of ``gravitational attraction''.

This is not simply an alternative but equivalent way of looking at gravity. It would not be such
a disturbing idea if that were so ! It is easy to see that dramatic new ``gravitational''
effects may be predicted.
 Because mass distributions warp spacetime, a photon, which also has to travel along
a geodesic (locally straight line in the warped space), will also be affected
by the mass distribution. Thus General Relativity predicts that photons are
subject to gravitational attraction ! Note that the classical theory

(60) 
did not predict this for the photon ().
 Very dense matter can warp space so much that nothing, no particles (not even light) can
ever escape, once they pass closer than a certain distance,
known as the event horizon. Such objects are known as black holes. The density of nuclear
matter, when aggregated in amounts equivalent to a large star, is sufficient to
realise a black hole.
General Relativity is now widely accepted, following three major experimental verifications :
 The perihelion precession of mercury is beyond that expected by classical theories,
but exactly that predicated by General Relativity.
 The gravitational redshift of light
(ie loss of energy (
) by light as it escapes
a gravitating body), as predicted by General Relativity has
been quantitatively verified.
 The bending of light in a gravitational field has been verified spectacularly
during a lunar eclipse of the sun, and more recently by gravitational lensing.
Black holes have not yet been definitely verified, although there are many strong
candidates in the cosmos, and further compelling theoretical evidences.
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Up: Relativistic Mechanics [8 lectures]
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Simon Connell
20060221