Pre-Phase A Report - Lisa - Nasa

1.1 Theory of gravitational radiation 9
of this, no real particle experiences only the local part of the external gravitational
field. When a neutron star falls in the gravitational field of some other body (another
neutron star or a massive black hole), its own gravitational field is accelerated
with it, and far from the system this time-dependent field assumes the form of a
gravitational wave. The loss of energy and momentum to gravitational radiation
is accompanied by a gravitational radiation reaction force that changes the motion
of the star. These reaction effects have been observed in the Hulse-Taylor binary
pulsar [6], and they will be observable in the radiation from merging black holes
and from neutron stars falling into massive black holes. They will allow LISA to
perform more stringent quantitative tests of general relativity than are possible with
the Hulse-Taylor pulsar. The reaction effects are relatively larger for more massive
“particles”, so the real trajectory of a star will depend on its mass, despite the
equivalence principle. The equivalence principle only holds strictly in the limit of a
particle of small mass.
This “failure” of the equivalence principle does not, of course, affect the selfconsistency
of general relativity. The field equations of general relativity are partial
differential equations, and they incorporate the equivalence principle as applied to
matter in infinitesimally small volumes of space and lengths of time. Since the mass
in such regions is infinitesimally small, the equivalence principle does hold for the
differential equations. Only when the effects of gravity are added up over the whole
mass of a macroscopic body does the motion begin to deviate from that predicted
by the equivalence principle.
• Special relativity. The second foundation stone of general relativity is special
relativity. Indeed, this is what led to the downfall of Newtonian gravity: as an instantaneous
theory, Newtonian gravity was recognized as obsolete as soon as special
relativity was accepted. Many of general relativity’s most distinctive predictions
originate in its conformance to special relativity.
General relativity incorporates special relativity through the equivalence principle:
local freely falling observers see special relativity physics. That means, in particular,
that nothing moves faster than light, that light moves at the same speed c with
respect to all local inertial observers at the same event, and that phenomena like
time dilation and the equivalence of mass and energy are part of general relativity.
Black holes in general relativity are regions in which gravity is so strong that the
escape speed is larger than c : this is the Michell-Laplace definition as well. But
because nothing moves faster than c, all matter is trapped inside the black hole,
something that Michell and Laplace would not have expected. Moreover, because
light can’t stand still, light trying to escape from a black hole does not move outwards
and then turn around and fall back in, as would an ordinary particle; it never makes
any outward progress at all. Instead, it falls inwards towards a complicated, poorlyunderstood,
possibly singular, possibly quantum-dominated region in the center of
the hole.
The source of the Newtonian gravitational field is the mass density. Because of
E = mc2 , we would naturally expect that all energy densities would create gravity
in a relativistic theory. They do, but there is more. Different freely falling observers
Corrected version 2.08 3-3-1999 9:33