Speaker
Dr.
Jonathan Thornburg
(Indiana University, Astronomy Dept)
Description
We present a computation of the self-force for a scalar-field particle
on a bound eccentric orbit (which need not be a geodesic) in Kerr spacetime.
Our main interest is in the case of highly eccentric orbits;
here we present results for eccentricities as high as $0.98$.
We use a Lorenz-gauge Barack-Golbourn-Vega-Detweiler effective-source
regularization followed by an $e^{im\phi}$ ("m-mode") Fourier decomposition
and a separate time-domain numerical evolution in $2{+}1$ dimensions for
each $m$. We introduce a finite worldtube which surrounds the particle
worldline and define our evolution equations in a piecewise manner so that
the effective source is only used within the worldtube. Viewed as a spatial
region the worldtube moves to follow the particle's orbital motion.
Our numerical evolution uses Berger-Oliger mesh refinement with
4th~order finite differencing in space and time.
We use slices of constant Boyer-Lindquist time near the black hole,
deformed (following Zenginoglu) so as to be asymptotically hyperboloidal
and compactified near the horizon and near $\mathcal{J}^+$.
Our present implementation is restricted to equatorial geodesic orbits,
but this restriction is not fundamental.
For those configurations where the central black hole is highly spinning,
the particle's periastron passage is near to or within the light ring,
and the orbital eccentricity is $\ge 0.4$, we find that the particle's
periastron passage excites quasinormal modes of the background (Kerr)
spacetime, causing large oscillations (``wiggles'') in the self-force
on the outgoing leg of the orbit, and smaller but still detectable
oscillations in the radiated field at $\mathcal{J}^+$.
Primary author
Dr.
Jonathan Thornburg
(Indiana University, Astronomy Dept)