Pre-Phase A Report - Lisa - Nasa

8 Chapter 1 Scientific Objectives
1.1 Theory of gravitational radiation
1.1.1 General relativity
There are a number of good textbooks that introduce general relativity and gravitational
waves, with their astrophysical implications [1, 2, 3, 4]. We present here a very brief
introduction to the most important ideas, with a minimum of mathematical detail. A
discussion in the same spirit that deals with other experimental aspects of general relativity
is in Reference [5].
Foundations of general relativity. General relativity rests on two foundation stones:
the equivalence principle and special relativity. By considering each in turn, we can learn
a great deal about what to expect from general relativity and gravitational radiation.
• Equivalence principle. This originates in Galileo’s observation that all bodies fall
in a gravitational field with the same acceleration, regardless of their mass. From
the modern point of view, that means that if an experimenter were to fall with
the acceleration of gravity (becoming a freely falling local inertial observer), then
every local experiment on free bodies would give the same results as if gravity were
completely absent: with the common acceleration removed, particles would move at
constant speed and conserve energy and momentum.
The equivalence principle is embodied in Newtonian gravity, and its importance has
been understood for centuries. By assuming that it applied to light — that light
behaved just like any particle — eighteenth century physicists predicted black holes
(Michell and Laplace) and the gravitational deflection of light (Cavendish and von
Söldner), using only Newton’s theory of gravity.
The equivalence principle leads naturally to the point of view that gravity is geometry.
If all bodies follow the same trajectory, just depending on their initial velocity
and position but not on their internal composition, then it is natural to associate
the trajectory with the spacetime itself rather than with any force that depends
on properties of the particle. General relativity is formulated mathematically as a
geometrical theory, but our approach to it here will be framed in the more accessible
language of forces.
The equivalence principle can only hold locally, that is in a small region of space and
for a short time. The inhomogeneity of the Earth’s gravitational field introduces
differential accelerations that must eventually produce measurable effects in any
freely-falling experiment. These are called tidal effects, because tides on the Earth
are caused by the inhomogeneity of the Moon’s field. So tidal forces are the part
of the gravitational field that cannot be removed by going to a freely falling frame.
General relativity describes how tidal fields are generated by sources. Gravitational
waves are time-dependent tidal forces, and gravitational wave detectors must sense
the small tidal effects.
Ironically, the equivalence principle never holds exactly in real situations in general
relativity, because real particles (e.g. neutron stars) carry their gravitational fields
along with them, and these fields always extend far from the particle. Because
3-3-1999 9:33 Corrected version 2.08