Maintained by:
Ian Vega (vega at phys.ufl.edu)
Steven Detweiler (det at phys.ufl.edu)

MOTIVATION:

The orbit and inspiral of a compact object into a substantially more massive black hole presents a complication for traditional numerical analysis. A numerical grid must be fine enough to resolve the geometry in the vicinity of the small object, where the metric appears to be that of the compact object with tidal distortions from the large hole. But the grid must be coarse enough to reach the wave zone of the binary, so that the waveforms might be carefully monitored. In addition, the time scale for the effect of radiation reaction is long compared with the orbital period, and the waveform from many orbits will be used in the data analysis. Together, the dramatically different length and time scales present a formidable challenge for the study of an extreme mass ratio inspiral (EMRI).

We have an approach to this numerical problem which removes the difficulty of the two disparate length scales, and reduces the analysis to that for a linear field on a fixed background geometry. The field has a source which has structure only on a length scale comparable to the large black hole. And its evaluation contains all of the information needed for analyzing both the waveform as well as all self-force effects.

Our intention is to provide public domain C++ code which evaluates the "smooth source" for a variety of physically interesting problems. This will allow any numerical relativity group which has the capability of solving a wave equation, with proper boundary conditions, in a fixed background geometry to get up to speed solving self-force problems in relativity.

ANNOUNCEMENTS:

Working code: We have available working C++ code, in the public domain, that calculates the "effective source" for a point scalar-charge orbiting a Schwarzschild black hole.

A related toy problem in Newtonian physics is the representation of the electromagnetic field of a spherical, charged object inside a grounded odd shaped box with the usual boundary conditions on the box. A brief description of a numerical solution to this problem has the same flavor as our approach to self-force problems in extreme-mass-ratio-inspiral.

We also have proof of principle with a detailed technical analysis of the self-force on a scalar charge in a circular orbit about a Schwarzschild black hole. This is published in PRD vol.77, 084008 (2008).

With collaborators Peter Diener and Wolfgang Tichy, we also have a full scale application of the effective source approach to self-force problems. This is published in PRD vol.80, 084021 (2009). We have two different 3+1 codes that evaluate the "regular" field associated with a point charge in a circular orbit about a black hole, calculate the self-force acting back on the charge and provide the waveforms. The analysis compares well with our 1+1 analysis described above and with our earlier frequency domain analyses.

Currently, we are working on second-order self-force analyses, and are using code inside this file

Future projects:
Scalar point charge in a generic orbit of the Schwarzschild geometry.
Point mass in a generic orbit of the Schwarzschild geometry.
Scalar point charge in a generic orbit of the Kerr geometry.
Point mass in a generic orbit of the Schwarzschild geometry.

Acknowledgments:
This effort has been supported in part by the University of Florida College of Arts and Sciences and Physics Department, and also by The National Science Foundation through grants No. 0555484 and No. 0855503 with the University of Florida. Some of the numerical results described here were performed at the University of Florida High- Performance Computing Center (URL: http://hpc.ufl.edu).