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Black holes are never isolated in realistic astrophysical environments; instead, they are often perturbed by complicated external tidal fields. How does a black hole respond to these tidal perturbations? In this talk, I will discuss both the conservative and dissipative responses of the Kerr black hole to a weak and adiabatic gravitational field. The former describes how the black hole would change its shape due to these tidal interactions, and is quantified by the so-called “Love numbers”. On the other hand, the latter describes how energy and angular momentum are exchanged between the black hole and its tidal environment due to the absorptive nature of the event horizon. In this talk, I will describe how the Love numbers of the Kerr black hole in a static tidal field vanish identically. I will also describe how the Kerr black hole's dissipative response implies that energy and angular momentum can either be lost to or extracted from the black hole, with the latter process commonly known as the black hole superradiance. I will end by discussing how these tidal responses leave distinct imprints on the gravitational waves emitted by binary black holes.

"One of the primary sources for the future space-based gravitational wave detector, the Laser Interferometer Space Antenna, are the inspirals of small compact objects into massive black holes in the centres of galaxies. The gravitational waveforms from such Extreme Mass Ratio Inspiral (EMRI) systems will provide measurements of their parameters with unprecedented precision, but only if the waveforms are accurately modeled. Here we explore the impact of transient orbital resonances which occur when the ratio of radial and polar frequencies is a rational number. We introduce a new Effective Resonance Model, which is an extension of the numerical kludge EMRI waveform approximation to include the effect of resonances, and use it to explore the impact of resonances on EMRI parameter estimation. For one-year inspirals, we find that the few cycle dephasings induced by 3:2 resonances can lead to systematic errors in parameter estimates, that are up to several times the typical measurement precision of the parameters. The bias is greatest for 3:2 resonances that occur closer to the central black hole. By regarding them as unknown model parameters, we further show that observations will be able to constrain the size of the changes in the orbital parameters across the resonance to a relative precision of $10\%$ for a typical one-year EMRI observation with signal-to-noise ratio of 20. Such measurements can be regarded as tests of fundamental physics, by comparing the measured changes to those predicted in general relativity."

In recent work, tidal resonances induced by the tidal field of nearby stars or black holes have been identified as potentially significant in the context of extreme mass-ratio inspirals (EMRIs). These resonances occur when the three orbital frequencies describing the orbit are commensurate. During the resonance, the orbital parameters of the small body experience a ‘jump’ leading to a shift in the phase of the gravitational waveform. We study how common and important such resonances are over the entire orbital parameter space. We find that a large proportion of inspirals encounter a low-order tidal resonance in the observationally important regime.

Everybody talks about EMRIs and IMRIs in connection with LISA and the 2030s. However, inspirals into massive black holes are happening at this very moment. Would we be able to recognize them with our current electromagnetic observations? Even more, are we maybe observing these inspirals at the very moment without realising it? We simulated accretion-disks perturbed by light perturbers and deduced that the orbital periods show in the disk variability. I present a list of candidate sources that, based on their variability periods and period derivatives, may contain ongoing inspirals into massive black holes.

"We consider the motion of nonspinning, compact objects orbiting around a Kerr black hole with tidal couplings. The tide-indcued quadrupole moment modifies both the orbital energy and out-going fluxes, so that over the inspiral timescale there is an accumulative shift in the orbital and gravitational wave phase. Previous studies on compact object tidal effects have been carried out in the Post-Newtonian (PN) and Effetive-One-Body (EOB) formalisms. In this work, within the black hole perturbation framework, we propose to characterize the tidal influence in the expansion of mass ratios, while higher-order PN corrections are naturally included. For the equatorial and circular orbit, we derive the leading order, frequency depedent tidal phase shift which agrees with the Post-Newtonian result at low frequencies but deviates at high frequencies. We also find that such phase shift has weak dependence (≤ 10%) on the spin of the primary black hole. Combining this black hole perturbation waveform with the Post-Newtonian waveform, we propose a frequency-domain, hybrid waveform that shows comparable accuracy as the EOB waveform in characterizing the tidal effects, as calibrated by numerical relativity simulations. Further improvement is expected as the next-leading order in mass ratio and the 2PN tidal corections are included. This hybrid approach is also applicable for generating binary black hole waveforms."

Extreme Mass Ratio Inspirals (EMRIs) can be classified as dry EMRIs and wet EMRIs based on their formation mechanisms. Dry (or the" loss-cone") EMRIs, previsouly considered as the main EMRI sources for the Laser Interferometer Space Antenna, are primarily produced by multi-body scattering in the nuclear star cluster and gravitational capture. In this Letter, we highlight an alternative EMRI formation channel:(wet) EMRI formation assisted by the accretion flow around accreting galactic-center massive black holes (MBHs). In this channel, the accretion disk captures stellar-mass black holes that are intially moving on inclined orbits, and subsequently drives them to migrate towards the MBH-this process boosts the formation rate of EMRIs in such galaxies by orders of magnitude. Taking into account the fraction of active galactic nuclei where the MBHs are expected to be rapidly accreting, we forecast that wet EMRIs will contribute an important fraction of all EMRIs observed by spaceborne gravitational wave detectors and likely dominate for MBH hosts heavier than a few $10^5 M_\odot$.

"Extreme mass-ratio inspirals (EMRIs) detectable by the Laser Inteferometric Space Antenna (LISA) are unique probes of astrophysics and fundamental physics. Parameter estimation for these sources is challenging, especially because the waveforms are long, complicated, known only numerically, and slow to compute in the most relevant regime, where the dynamics is relativistic. We perform a time-consuming Fisher-matrix error analysis of the EMRI parameters using fully-relativistic numerical waveforms to leading order in an adiabatic expansion on a Kerr background, taking into account the motion of the LISA constellation, higher harmonics, and also including the leading correction from the spin of the secondary in the post-adiabatic approximation. We pay particular attention to the convergence of the numerical derivatives in the Fisher matrix and to the numerical stability of the covariance matrix, which for some systems requires computing the numerical waveforms with approximately 90-digit precision. Our analysis confirms previous results (obtained with approximated but much more computationally efficient waveforms) for the measurement errors on the binary's parameters. We also show that the inclusion of higher harmonics improves the errors on the luminosity distance and on the orbital angular momentum angles by one order and two orders of magnitude, respectively, which might be useful to identify the environments where EMRIs live. We particularly focus on the measurability of the spin of the secondary, confirming that it cannot be measured with sufficient accuracy. However, due to correlations, its inclusion in the waveform model can deteriorate the accuracy on the measurements of other parameters by orders of magnitude, unless a physically-motivated prior on the secondary spin is imposed. This work is based on the pre-print arXiv:2105.07083 ."

Gravitational-wave observations of binary black holes allow new tests of general relativity to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal, otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with general relativity. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more stringent tests of gravity by analyzing large numbers of events together. However, there is a danger that waveform errors can accumulate among events: even if the waveform model is accurate enough for each individual event, it can still yield erroneous evidence for new physics when applied to a large catalog. We presents a simple linearised analysis, in the style of a Fisher matrix calculation, that reveals the conditions under which the apparent evidence for new physics due to waveform errors grows as the catalog size increases. We estimate that, in the worst-case scenario, evidence for a deviation from general relativity might appear in some tests using a catalog containing as few as 10-30 events above a signal-to-noise ratio of 20. This is close to the size of current catalogs and highlights the need for caution when performing these sorts of experiments.

We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for a≳0.9999) with extraordinary precision, ∼ 3-4 orders of magnitude better than for moderate spins, a∼0.9. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analysis, but are verified using both frequentest and Bayesian techniques. We present analytical arguments that explain these high spin precision measurements. The high precision arises from the spin dependence of the radial inspiral evolution, which is dominated by geodesic properties of the secondary orbit, rather than radiation reaction. High precision measurements are only possible if we observe the exponential damping of the signal that is characteristic of the near-horizon regime of near-extremal inspirals. Our results demonstrate that, if such black holes exist, LISA would be able to successfully identify rapidly rotating black holes up to a=1−1e−9 , far past the Thorne limit of a=0.998.

The observation of gravitational waves from 50 pairs of merging black hole and neutron star binaries by the LIGO-Virgo Collaboration offers the first glimpse of the potential to use these populations as tools to study the formation and evolution of compact objects and their stellar progenitors. However, even with dozens of mergers, the dominant formation pathways for merging compact-object binaries remains unconfirmed. Furthermore, even with third generation ground-based detectors, which could potentially discover merging binary black holes across all redshifts out to the epoch of reionization, such mergers only account for a tiny fraction of all black holes formed in the Universe. In this talk I will discuss opportunities to probe the formation environments and scenarios of compact objects using observations from ground- and space-based GW detectors with a particular focus on the complementary source information each detector provides. I will also discuss how GW populations play a role in the larger landscape of observations of compact objects in stellar binaries.