This paper describes the early success in evolving binary black hole spacetimes using a numerical code based on generalized harmonic coordinates. The code is capable of simulating binary systems for extended periods, allowing the extraction of information about the orbit, merger, and gravitational waves emitted during the event. An example simulation of a binary composed of two equal mass, non-spinning black holes is presented, showing the evolution through a single plunge-orbit, merger, and ringdown. The resulting black hole is estimated to be a Kerr black hole with an angular momentum parameter \( a \approx 0.70 \). While the lack of resolution prevents an accurate estimate of the energy emitted, a rough calculation suggests that about 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.
The paper outlines the numerical method used, including the discretization of the field equations, the use of harmonic coordinates, adaptive mesh refinement, dynamical excision, and constraint damping. The results from the simulation of a scalar field constructed binary system are discussed, showing the evolution of the black hole mass and angular momentum over time. The gravitational waves emitted during the merger are estimated using the Newman-Penrose scalar \( \Psi_4 \), and the total energy radiated is calculated. The paper concludes with future directions, including improving simulation accuracy, exploring a broader range of initial conditions, and extracting more geometric information from the simulations.This paper describes the early success in evolving binary black hole spacetimes using a numerical code based on generalized harmonic coordinates. The code is capable of simulating binary systems for extended periods, allowing the extraction of information about the orbit, merger, and gravitational waves emitted during the event. An example simulation of a binary composed of two equal mass, non-spinning black holes is presented, showing the evolution through a single plunge-orbit, merger, and ringdown. The resulting black hole is estimated to be a Kerr black hole with an angular momentum parameter \( a \approx 0.70 \). While the lack of resolution prevents an accurate estimate of the energy emitted, a rough calculation suggests that about 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.
The paper outlines the numerical method used, including the discretization of the field equations, the use of harmonic coordinates, adaptive mesh refinement, dynamical excision, and constraint damping. The results from the simulation of a scalar field constructed binary system are discussed, showing the evolution of the black hole mass and angular momentum over time. The gravitational waves emitted during the merger are estimated using the Newman-Penrose scalar \( \Psi_4 \), and the total energy radiated is calculated. The paper concludes with future directions, including improving simulation accuracy, exploring a broader range of initial conditions, and extracting more geometric information from the simulations.