Analyses On Inspiral And Ringdowr Of Gravitational Wave Signals And The Charge Of Black Holes

The successful detection of GW 150914 announced that mankind has entered a gravitational wave(GW)astronomy age.Generally,in GW data analyses,we do not consider the effects of charge since it is often thought to be negligible for an astrophysical black-hole(BH).However,according to the ’no hair’ theorem in general relativity,a BH is fully characterized by its mass,spin,and charge.Fortunately,the information of these parameters is encoded in the GW signal emitted by the binary black hole(BBH)merger event.Thus,it is important and meaningful to study the effects of BH charge on GW signals.GW signal can be divided into three stages,which are inspiral,merger,and ringdown.Among them,the merger stage can only be accessed with numerical relativity(NR)simulation,while the inspiral and ringdown stages can be described analytically with physical meaning.Usually,we expect to study the effects by adding an extra parameter to the current GW waveform analytically,so we will mainly focus on the inspiral and ringdown stages in this thesis.People often infer the relevant parameters of GW events with the Bayesian inference,which can be performed in both frequency-domain and time-domain.Since the GW signals detected by detectors are all in time-domain,we need Fourier transformations in frequency-domain analyses,on the other hand,we have to calculate the inverse of covariance matrices of noises in time-domain analyses.If the GW signal lasts for a long time,we usually perform analyses in frequency-domain due to complexity of matrix inversion and expensive in time-domain.However,when the GW signal is short and has an abrupt start/end,we should perform analyses in time-domain since the frequency-domain analyses will smooth the abrupt start/end non-physically.If the short GW signal does not have an abrupt start/end,we can perform analysis in both time-domain and frequency-domain,nevertheless,the latter is more accessible.We consider the effects of(scalar)charges in several theories as perturbations on inspiral signals.Then we try to give meaningful constraints on them by performing frequency-domain Bayesian inferences.First and foremost,we consider the charge of Kerr-Newman BH in GR.We investigate the possible origins of these charges and place constraints on them by analyzing GW data of O1 and O2.Before this work,constraints are mostly given by estimation based on the fisher-information matrix method.Our work is the first one using the real GW data to give constraints on BH charge,and these constraints are found to be consistent with the following results based on NR simulations.Additionally,we also consider the scalar charges of BH,which are from the dynamical Chern-Simons(dCS)theory and the Einstein-dilation-Gauss-Bonnet(EdGB)theory.Again,the effects from these two theories are also considered as perturbations on inspiral signals.Then,we analyze two typical GW events with two independent methods.We get better constraints that are improved by a factor of approximate 10 in comparison to that set by similar analyses with the first Gravitational-Wave Transient Catalog events.The ringdown stage is described by the superposition of quasinormal modes(QNMs),in the form of damped sinusoids.The QNMs can be decomposed into spinweighted spheroidal harmonics with angular indices(l,m),each consists of a set of overtones(with indices n).The start times of different modes in the ringdown signal are assumed to be the same in previous studies.However,studies based on NR waveforms found that different(l,m)modes have different peak times,which means that different(l,m)modes in the ringdown signal have different start times if we assume they all start from the peak of strain.Thus,according to the first-principle reasons,we assume that different n modes have different start times,too.By performing time-domain Bayesian inference on GW150914,we find that it is hard to draw any positive conclusion currently.Last but not least,we try to constrain the final charge of GW 150914 by analyzing its ringdown signal with charged QNMs under Kerr-Newman spacetime.An analytic solution on charged QNMs is not accessible yet,so we get an approximate formalization of it and prove its availability.Then we perform time-domain Bayesian analyses on the ringdown signal of GW 150914 and get meaningful constraints on the remnant’s charge.In summary,we study both the frequency-domain and the time-domain Bayesian inferences systematically.Furthermore,we skillfully apply them to constrain the BH charge,to test GR,and to investigate whether different overtone modes have the same start time or not.Works in this thesis promote progress in related fields and further demonstrate the potential of time-domain analyses of LIGO/Virgo data and pave the way for more stringent tests of Einstein’s theory with future GW detections.