classical gravity, including cosmology, black hole physics, and

gravitational wave physics. The work will be done utilizing a variety of

analytical, approximate, and computational methods. They will continue

investigation of black hole interactions and the gravitational radiation

produced in these interactions. These interactions will be modeled using

existing computer codes, and these codes will also be extended to describe

the formation of black holes in cosmological settings.

These black hole investigations are important cosmologically because
it

seems from astronomical observations that most or all galaxies contain
a

black hole within them. Further, cosmological evidence shows that many
or

most galaxies have undergone merger, suggesting that their black holes
may

have merged. There are planned experiments to detect gravitational

radiation from spaceborne detectors, which would be sensitive to such

mergers. The same computational description will also apply to stellar-mass

black hole systems, which may be the strongest signals first detected
in

the (ground based) LIGO detector, which is currently under construction.

Accurate prediction of expected gravitational waves allows a more precise

search and, therefore, greater sensitivity in the observation of such

signals. Further, the understanding of these signals will have a direct

connection to understanding the phenomena that caused them and will
shed

new light on the behavior of strong field gravity.

What do the Figures (links below) show?

They show preliminary computer simulations of the grazing collision
of

a pair of spinning black holes. These collisions are 3-dimensional

situations and what we show are snapshots of the gravitational field

(Gxx) and a measure of error (Normalized Hamiltonian constraint) as

measured in one plane which initially contains the holes. The
spin of

each of the holes is half of its maximum possible value (pointing out

of the plane shown in the figures), and the black holes are initially

moving toward one another at half the speed of light.

Black holes are defined by their horizons, boundaries between what can

be seen (outside the hole), and what can not (inside). Inside
the

black hole are typically strong singularities. Computation

of singularities is difficult; and because they are inside the

horizons, it is unnecessary. Hence, we excise the interior, and

computer nothing there. These are the flat, roughly circular,
areas

in the figures. Initially we have two holes, moving together
(two

flat excised regions). After a time of about 4 (in units based
on

how long it would take light to go half the radius of one hole) the

black holes have merged -- we find a single bigger horizon

(technically, the apparent horizon). At a time of 5M, we switch to
excising the

interior of this larger hole.

The Gxx plots show a plot of one of the components of the

gravitational field. The values of the field outside the excised

region describe the distortions that lead to gravitation radiation,

and the strength of that radiation. (We have not yet computed
the

actual radiation.)

Care in simulations requires that we carefully check errors. The

page showing the Hamiltonian constraint provides this. The important

points are that there is some error (every computational simulation

must approximate aspects of the system) but it is manageable, and is

not large near the excision regions. And, we have carried

out tests to verify that the errors get controllably smaller as we

take more refined computational simulations.

At the outer boundaries or the computational domain, the errors do

become large. These are not essential problems, but interfere
with

understanding the evolution of the radiation. We are addressing
the

boundary problem and improvements are expected soon.

for t<5 W = 0.0

for t>5.3125 W = 1.0

otherwise W = 1 - 3((t-5.3125)/(5-5.3125))**2 + 2((t-5.3125)/(5.-5.3125))**3