let's build an extreme-mass ratio inspiral waveform generator!

last updated: 12.10 AM, Oct 10, 2024

what | Gravitational waves are the emergent medium to probe our understanding of gravity, with increasing relevance in the age of gravitational wave astronomy. Current experiments (LIGO/Virgo/Kagra) are sensitive to gravitational waves stemming from the collision of stellar-mass black holes of roughly comparable masses. While an excellent probe for gravity in the strong-field regime, analytical treatments are extremely difficult to perform and in practice one resorts to numerical relativity. However, future experiments, like the Laser Interferometer Space Antenna (LISA), will be sensitive to the gravitational waves stemming from the collision of small, stellar mass black holes with giant, supermassive black holes. In such “extreme-mass ratio inspirals” (for short: EMRIs) it is possible to perform perturbative computations, since the large mass ratio allows one to approximate the small orbiting black hole as a point particle. The goal of this course is to understand how a fundamental model of gravity (say, general relativity) can be used to estimate the shape of the gravitational waves stemming from such an EMRI, using perturbative and largely analytical techniques. To that end, we will develop a simple Mathematica sheet that will generate such a gravitational wave pattern (to zeroth order, with necessary simplifications in resolution and accuracy). In a second step, we will consider a modified version of gravity, and explore how this qualitatively changes the gravitational wave pattern. |

when | Oct 7, 8, 10, 2024; 09.00–10.30 & 10.45–12.15 |

where | room 6/1, location: physics high rise |

contact | Jens Boos (jens.boos@kit.edu) |

URL | http://www.spintwo.net/Courses/EMRI-101/ |

- 2024-10-07 (lecture #1): key aspects of differential geometry (Lie derivative, geodesics, conserved quantities)
- 2024-10-07 (lecture #2): geodesics of the Schwarzschild black hole, bound orbits
- 2024-10-08 (lecture #1): linearized gravity
- 2024-10-08 (lecture #2): the quadrupole formula and inspiralling orbits in the Schwarzschild spacetime
- 2024-10-10 (lecture #1): waveform estimation for Schwarzschild inspirals
- 2024-10-10 (lecture #2): waveforms for other geometries & comparison to Schwarzschild

- emri-101-lecture-notes-v3.pdf Lecture notes

- emri-101-code-c1-killing-vectors-v1.nb Mathematica file checking the Killing vectors for a static and spherically symmetric metric
- emri-101-c2-schwarzschild-derivation-v1.nb Mathematica file to derive the Schwarzschild metric
- emri-101-c3-schwarzschild-geodesics-v1.nb Mathematica file to analyze Schwarzschild geodesics
- emri-101-c4-schwarzschild-inspirals-v1.nb Mathematica file to analyze Schwarzschild inspirals
- emri-101-c5-schwarzschild-waveforms-v1.nb Mathematica file to analyze Schwarzschild waveforms
- emri-101-c6-reissner-norstroem-waveforms-v1.nb Mathematica file to analyze Reissner–Nordström waveforms
- emri-101-c7-comparison-v1.nb Mathematica file to compare the Schwarzschild and Reissner–Nordström waveforms

- emri-101-d1-schw-plus-tau-10-1000.dat waveform data file (Schwarzschild, plus polarization; t=10..1000)
- emri-101-d2-schw-cross-tau-10-1000.dat waveform data file (Schwarzschild, cross polarization; t=10..1000)
- emri-101-d1-schw-plus-tau-0-50.dat waveform data file (Schwarzschild, plus polarization; t=0..50)
- emri-101-d2-schw-cross-tau-0-50.dat waveform data file (Schwarzschild, cross polarization; t=0..50)
- emri-101-d3-reiss-plus-tau-0-50.dat waveform data file (Reissner–Nordström, plus polarization; t=0..50)
- emri-101-d4-reiss-cross-tau-0-50.dat waveform data file (Reissner–Nordström, cross polarization; t=0..50)