Inspirals of rotating black holes and their gravitational waves

Abstract

This thesis investigates spin-induced precession in quasi-circular binary black hole systems at the 2PN and 3.5PN post-Newtonian orders. We conduct sim- ulations of equal-mass binaries with both aligned and misaligned spin configu- rations, and unequal-mass binaries with misaligned spins exclusively. At 2PN order, we employ a Hamiltonian formalism to analyze the conservative dynamics, verifying conservation laws and showing that while the total spin magnitude pro- vides a useful global characterization, the system's behavior depends strongly on the relative orientations of the individual spins and orbital angular momentum. At 3.5PN order, we use equations of motion incorporating radiation reaction effects to simulate the inspiral phase, implementing a Kerr-ISCO-based merger detection criterion and examining waveform asymmetries. Our results reveal distinct spin-orbit precession and nutation patterns, particularly enhanced by mass asymmetry. This work contributes to improved gravitational waveform modeling relevant for detection and parameter estimation in current and future gravitational wave observations. 1

Tato pra ́ce se zaby ́va ́ precesı ́ zpu ̊sobenou spiny v kvazikruhovy ́ch syste ́mech dvojic c ̌erny ́ch de ̌r, a to na u ́rovni 2PN a 3.5PN postnewtonovske ́ aproximace. Prova ́dı ́me simulace dvojhve ̌zd se stejnou hmotnostı ́ se spiny orientovany ́mi jak souhlasne ̌, tak nesouhlasne ̌, a rovne ̌z ̌ simulace dvojhve ̌zd s ru ̊znou hmot- nostı ́, pr ̌ic ̌emz ̌ v te ̌chto pr ̌ı ́padech zkouma ́me vy ́hradne ̌ konfigurace s nesouh- lasne ̌ orientovany ́mi spiny. Na 2PN u ́rovni pouz ̌ı ́va ́me Hamiltonovsky ́ formalis- mus pro analy ́zu konzervativnı ́ dynamiky, ove ̌r ̌ujeme za ́kony zachova ́nı ́ a ukazu- jeme, z ̌e zatı ́mco celkova ́ velikost spinu poskytuje uz ̌itec ̌nou globa ́lnı ́ charakter- istiku, chova ́nı ́ syste ́mu silne ̌ za ́visı ́ na relativnı ́ orientaci jednotlivy ́ch spinu ̊ a orbita ́lnı ́ho momentu hybnosti. Na 3.5PN u ́rovni implementujeme algoritmus pro detekci slouc ̌enı ́c ̌erny ́ch de ̌r na za ́klade ̌ Kerrova ISCO polome ̌ru a zkouma ́me pru ̊be ̌h spira ́lova ́nı ́ a projevy asymetriı ́ v gravitac ̌ne ̌vlnove ́m signa ́lu. Vy 'sledky ukazujı ́ vy ́raznou precesi a nutaci, zejme ́na pr ̌i hmotnostnı ́ nerovnova ́ze. Tato pra ́ce pr ̌ispı ́va ́ ke zleps ̌enı ́ modelova ́nı ́ gravitac ̌ne ̌vlnovy ́ch tvaru ̊, jez ̌ je za 'sadnı ́ pro interpretaci souc ̌asny ́ch i budoucı ́ch...