Collisions of Spinning Black Holes

This work investigates a range of problems in
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.

Initial Data

hole 1: (5M, 1M, 0M)

hole2: (-5M, -1M, 0M)

r1=r2 = 2M

v = (0.55,0.06,0)

a = (0,0,0.5)

Single Hole Mask

Weighted Function:

  ! Weight function for multiple hole transition
   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

lapse: alpha = (1-W)alpha_d + (W)alpha_s

shift: shift(x) = (1-W)shift(x)_d + (W)shift(x)_s

Color Map for Snapshots

Gxx:  Red    = 0

        Violet = 3

        Green ~ 1

Nham: Red = -0.4

          Violet = 0.4

          Yellow-green-lightblue  < 30%

Snapshots of Gxx

Snapshots of Normalized Hamiltonian

site courtesy of Luis Lehner and Deirdre Shoemaker