Gravitational Self-Force and Extreme Mass-Ratio Inspiral
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An eccentric orbit of the Kerr spacetime.
Image credit: Steve
Drasco. |
The motivation for some
of my work comes from the
so-called
"extreme mass-ratio inspiral" (EMRI). When a neutron star or
stellar
black hole is scattered into a close orbit about a supermassive black
hole, the orbit begins to slowly decay due to the emission of
gravitational radiation. These orbits can be quite intricate
(see figure to the right, or view movies
here),
and
the resultant gravitational radiation carries detailed
information
about the system, offering a unique glimpse into the astrophysics of
galactic centers as well as a precision test of strong field general
relativity. However, detecting such a signal in a noisy
interferometer like LISA will require waveform templates that track the
orbit with exquisite precision. Producing such templates will
require going beyond the test-body approximation for the compact object
to include the influence of its own gravitational field on its motion,
i.e., one must include
gravitational
self-force effects. I have worked on
the
foundations
of
this problem, on the
role
of the central body, on
alternative
gauge
(coordinate) choices, and on
including
next-to-leading order effects. This research appeals to me because of the way it combines fundamental and astrophysical questions.
Black Hole Bobbing and Kicks
A diagram illustrating a kinematical effect that
makes spinning bodies bob. |
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Numerical simulations of binary black holes with spin
revealed some
surprising behavior: a
bobbing up and down motion prior to merger, leading to a large kick
velocity that has the appearance of an inertial continuation of the
bobbing motion.
We looked at whether similar effects could be found
in analogous--but simpler--systems. We
found that the bobbing
effect is in fact ubiquitous, occuring whenever two spinning
bodies are held in orbit by any sort of force. For example,
two spinning balls connected by a string will display this
behavior! The kick, however, is more special and can only
occur for systems that possess field momentum which can be
radiated to infinity. After studying an electromagnetic
analog as
well as the gravitational case directly, we concluded that bobbing and
kicks are
basically unrelated phenomena, which can nevertheless appear
correlated for spinning black holes because the spin parameter
happens to control both the bobbing and the kick. We bolstered this conclusion by giving an
electromagnetic example in which large kicks can be obtained with no bobbing at all.
Motion in Modified Gravity
In recent years many modified gravity theories have been
proposed to explain the acceleration of the universe without the need
for dark energy. To be viable, such theories must also pass
solar-system tests, binary pulsar tests, and (eventually) gravitational-wave tests. With the aim of finding
a model-independent method of such tests, I investigated the motion of
bodies in the very general context of an arbitrary theory following
from a covariant lagrangian in four spacetime dimensions and having
second-order field equations. Remarkably, there is a universal
force law for the motion of bodies in such theories,
involving certain
effective charges for a body that entirely encode the predictions of
any specific
theory for the body. These charges may be computed using surface-integral formulae, giving rise to specific predictions.
Cooling a Black Hole with a Moon
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Spacetime diagram for a Kerr black hole with a
corotating moon. |
The physical (Hawking) temperature of a stationary, isolated
black hole is given by its classical surface gravity. For
general, nonstationary or interacting black holes, the surface
gravity is not defined and there is no natural candidate for the
temperature.
We
studied a particular dynamical black hole
spacetime for which the surface gravity can in fact still be defined in
the
usual way: a Kerr black hole that corotates with an orbiting moon.
Here, the system is "stationary in a rotating frame", giving
sufficient symmetry. (The event horizon is a Killing horizon
of
the helical Killing field.) From the basic
elements of the Hawking calculation, it is clear that this surface
gravity must represent the semi-classical temperature of the tidally
perturbed black hole; we thus have a first example of an
interacting black hole whose Hawking temperature is well-defined.
We find a simple expression for the change in surface
gravity/temperature caused by the orbiting particle, which in
particular is negative: the moon has a cooling effect on the black
hole. This work was
featured
in New Scientist.