LISALISA - iucaa

1.1 Theory of gravitational radiation
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, poorly-understood, possibly singular, possibly quantumdominated
region in the center of the hole.
The source of the Newtonian gravitational field is the mass density. Because of E = mc 2 ,
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 measure different
energies and different densities (volume is Lorentz-contracted), so the actual source has to
include not only energy but also momentum, and not only densities but also fluxes. Since
pressure is a momentum flux (it transfers momentum across surfaces), relativistic gravity
can be created by mass, momentum, pressure, and other stresses.
Among the consequences of this that are observable by LISA are gravitational
effects due to spin.
These include the Lense-Thirring effect, which is the gravitational analogue of spin-orbit
coupling, and gravitational spin-spin coupling. The first effect causes the orbital plane
of a neutron star around a spinning black hole to rotate in the direction of the spin; the
second causes the orbit of a spinning neutron star to differ from the orbit of a simple
test particle. (This is another example of the failure of the equivalence principle for a
macroscopic “particle”.) Both of these orbital effects create distinctive features in the
waveform of the gravitational waves from the system.
Gravitational waves themselves are, of course, a consequence of special relativity applied
to gravity. Any change to a source of gravity (e.g. the position of a star) must change the
gravitational field, and this change cannot move outwards faster than light. Far enough
from the source, this change is just a ripple in the gravitational field. In general relativity,
this ripple moves at the speed of light. In principle, all relativistic gravitation theories must
include gravitational waves, although they could propagate slower than light. Theories will
differ in their polarization properties, described for general relativity below.
Special relativity and the equivalence principle place a strong constraint on the source of
gravitational waves. At least for sources that are not highly relativistic, one can decompose
the source into multipoles, in close analogy to the standard way of treating electromagnetic
radiation. The electromagnetic analogy lets us anticipate an important result. The
monopole moment of the mass distribution is just the total mass. By the equivalence
principle, this is conserved, apart from the energy radiated in gravitational waves (the
Corrected version 1.04 9 13-9-2000 11:47