A comparison of gravitational wave computation methods in core collapse supernovae with hadron-quark phase transitions

The occurrence of hadron-quark phase transitions in proto-compact stars during core-collapse supernovae (CCSNe) may produce unique kHz gravitational wave signals that can constrain the properties of quark matter. Robust simulations to date have only modeled this phenomenon using static spacetime geometry or limited implementations of general relativity, so their gravitational waveforms are confined to the standard quadrupole formula approximation. However, it is unclear whether this approximation is valid in such a tightly bound system. In this study, we consider the phase transition in CCSNe using the open-source numerical relativity code SpECTRE, which evolves the system with a dynamical spacetime. With this capability, we investigate the validity of various expressions of the quadrupole approximation compared against the more exact Cauchy characteristic extraction of waveforms.