Samuel E. Gralla

Gravitational Self-Force and Extreme Mass-Ratio Inspiral

 
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.

Exact Force-Free Magnetospheres

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The undulating current sheet that appears in an exact solution to force-free electrodynamics
 
Many of the most dramatic of observed astrophysical phenomena involve the combination of compact objects, magnetic fields, and relativistic plasma.  Examples include pulsars (rotating, magnetized neutron stars), active galactic nuclei (likely powered by supermassive black holes), and possibly even gamma-ray bursts (if powered by binary neutron stars).  When the magnetic fields are very strong, one may use force-free electrodynamics, a fascinating set of equations that describes the plasma only through its effect on the electromagnetic fields.  Eschewing the traditional 3+1 decomposition and focusing on the (rich and beautiful) spacetime structure of these equations, we have found a large class of exact solutions in black hole spacetimes.  These include non-stationary, non-axisymmetric solutions in Kerr.  The solutions reveal a new type of non-linear force-free wave that propagates through black hole spacetimes without scattering.  Remarkably, the solution class appears sufficiently broad to to describe the far-field magnetosphere of a generic (aligned, inclined, glitching, you-name-it) magnetized neutron star, opening the door to detailed analytical modeling of the outer pulsar magnetosphere.

Cooling a Black Hole with a Moon

 
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 explicitly compute the change in surface gravity/temperature caused by the orbiting particle, finding that it is negative: the moon has a cooling effect on the black hole.  This work was featured in New Scientist.

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, all of which involve motion of bodies.  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.

Black Hole Bobbing and Kicks


A diagram illustrating a kinematical effect that makes spinning bodies bob.
 
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.