In this project, we analyse the orbital evolution of Extreme Mass Ratio Inspirals (EMRIs) in stationary and axisymmetric spacetimes, according to Einstein's general theory of relativity. A spacetime with a modified Johannsen metric is chosen to evolve the system. The following tasks are performed in this project:
- Evolve the orbits of the secondary around the primary using the geodesic approximation.
- Test the accuracy of the orbital evolution using a constraint equation.
- Visualise the orbits using 3D Cartesian coordinates.
- Model the associated gravitational waveform using the Einstein-quadrupole approximation.
- Investigate the Liouville integrability of the equations of motion using Poincaré map and Rotation number curve.
The relevant physics and assumptions that went into the calculations are included in theory.pdf.
- Python
Install Python 3.9 or higher. Create a virtual environment in the desired directory via:
python3 -m venv <virtual-environment-name>
Example: To create a virtual environment called orbital-analysis, use
python3 -m venv orbital-analysis
Activate the virtual environment with:
source <path-to-virtual-environment>/bin/activate
The virtual environment can be deactivated with:
deactivate
- Jupyter Notebook
Install Jupyter Notebook. It can be installed using pip through:
pip install notebook
To run the notebook:
jupyter notebook
- Additional Requirements
Install the necessary packages listed in requirements.txt via:
pip install -r requirements.txt