Gravitational Waves from Simulated Mergers of 2 and 3 Black Holes

In this project, we simulate the collision of two and three black holes using NRPy+ (`Python-based code generation for numerical relativity and beyond’) module and BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation, and extract the resulting gravitational waveforms. Using Brill-Lindquist initial data and sixth-order finite differences, we evolve the system using the BSSN formulation and compute the gravitational-wave signal via the Weyl scalar ${\psi }_4$. To assess numerical error, we plot the Hamiltonian constraint and observe that constraint violations are significantly higher in the three-black-hole collision. Unexpected gravitational recoil is also detected, which may influence waveform extraction and that is left for further investigation. Despite the limitations in computational resources imposed by the Google Colab, we successfully model the merger of a binary black hole system, and we were able to extract the corresponding gravitational waves.