# Program

## Day 1 (school), Monday, July 1st

Chair: Vitor Cardoso

08:00-09:00 Registration and coffee

09:00-09:10 **Welcome** from organization committee

09:10-10:10 Geraldine Servant: GWs from the primordial universe: scalar field cosmology, axions & DM10:10-10:30 Coffee break

10:30-11:30 Katy Clough: Studying fundamental fields with numerical relativity

**11:30-12:30 Sam Dolan: Superradiance, BHs and instabilities_Lec1**

12:30 -14:00 Lunch

Chair: Yifan Chen

14:00-15:00 Geraldine Servant: **GWs from the primordial universe: scalar field cosmology, axions & DM**15:00-16:00 Sam Dolan: Superradiance, BHs and instabilities_Lec2

**16:00-16:30 Coffee break**

16:30-17:30 Katy Clough:

**Studying fundamental fields with numerical relativity**

17:30-18:00 Discussion with all speakers

## Day 2 (school), Tuesday, July 2nd

Chair: Valentin Boyanov

09:00-10:00 Eugen Radu: BH uniqueness and dirty BHs10:00-10:30 Coffee break

10:30-11:30 Maria Alessandra Papa: GWs from monochromatic sources: data analysis_Lec1

**11:30-12:30 Francisco Duque:**

**EMRIs or evolution of binaries in fundamental fields**lecture note_EMRIEMRI_BosonCloud

12:30 -14:00 Lunch

Chair: Chen Yuan

14:00-15:00 Francisco Duque: **EMRIs or evolution of binaries in fundamental fields**15:00-16:00 Maria Alessandra Papa: GWs from monochromatic sources: data analysis_Lec2

**16:00-16:30 Coffee break**

16:30-17:30 Eugen Radu:

**BH uniqueness and dirty BHs**

17:30-18:00 Discussion with all speakers

## Day 3 (workshop), Wednesday, July 3rd

Chair: Enrico Cannizzaro

08:00-08:45 Registration and coffee

08:45-09:00 **Welcome** from organization committee

09:00-09:30 William East: Uncovering the signatures of BH superradiance09:30-10:00 Hidetoshi Omiya: Impact of self-interaction on the axion cloud in the relativistic regime

**10:00-10:30 Coffee break**

10:30-11:00 Jamie McDonald: Superradiance in stars

11:00-11:30 Diego Blas: Bridging the muHz gap in the GWs spectrum

11:30-12:00 Discussion

12:00 -14:00 Lunch

Chair: Xiao Xue

14:00-14:30 Ornella Piccinni: GWs and Ultralight Bosons: observations from Spinning BHs14:30-15:00 Hyungjin Kim: Probing ultralight DM with GW detectors

15:00-15:30 Coffee break

15:30-16:00 Yue Zhao: Probing Axions with EHT Polarimetric Measurements

**16:00-16:30 Lam Hui: Symmetries and nonlinearities in BH perturbation theory**

16:30-17:00 Discussion

17:00-19:30 Reception + Poster session + voting

## Day 4 (workshop), Thursday, July 4th

Chair: Richard Brito

09:00-09:30 Nicolas Sanchis-Gual: Dynamical bosonic stars and GWs09:30-10:00 Joshua Eby: A Solar Halo of Ultralight DM

10:00-10:30 Coffee break

10:30-11:00 Pedro Cunha: Beyond the Kerr paradigm: Hairy BHs and the fate of the Light ring Instability

11:00-11:30 Caio Macedo: Compact binaries in astrophysical environments

**11:30-12:00 Discussion**

12:00-14:00 Lunch

Chair: Yifan Chen

14:00-15:30 Specialized Topic Session

Miniworkshop on Gravitational Molecule

Vitor Cardoso: Black hole chemistry

Diogo Ribeiro: Analogue Binaries & Superradiance

Katy Clough: Scalar field accretion onto binariesJun Zhang: Cloud Mass Transfer and Common Envelope Evolution

Rodrigo Vicente: Gravitational Molecule

Day 5 (workshop), Friday, July 5th

Chair: Thomas Spieksma

09:00-09:30 Arianna Foschi: Constraint the mass of boson clouds at the Galactic Center09:30-10:00 Rodrigo Vicente: Looking for ultralight scalars with LIGO-Virgo-KAGRA binaries

10:00-10:30 Coffee break

10:30-11:00 Andrea Maselli: DM signatures around dirty BH binaries

**11:00-11:30 Dina Traykova: Gravitational drag effects — the numerical way**

11:30- Discussion + Poster winner + Farewell

## Lectures:

- Katy Clough:
**Studying fundamental fields with numerical relativity**

In this hands-on class we will try out the code engrenage which is a python based, spherically symmetric numerical relativity code with a dynamical gauge that is helpful for understanding the principles employed in larger 3+1D codes, but without many of the additional complexities of highly optimised code and without needing a supercomputer. Full background material for the code can be found in the wiki - I will not expect familiarity with this but it will certainly be useful if you take a look in advance.

**Please do make sure you have an installation of python3** (I recommend Anaconda for new python users) **and download and run the black hole example following the instructions in the wiki before the lecture**. This process should take around half an hour if all goes smoothly, and the example should run in a minute or so. If you have any problems you can email me at k.clough@qmul.ac.uk to ask for advice.

In the class the goal will be to add a real scalar field to the black hole example, and see how it dynamically forms a distinctive profile (given analytically by the Heun functions) around the BH. If we have sufficient time, we can also try to add self interactions in the field and view their effects.

- Sam Dolan:
**Superradiance, BHs and instabilities**

In these two talks I will explore the related topics of superradiance, Penrose processes, the laws of black hole mechanics, superradiant instabilities and the “black hole bomb” proposal. In particular, I aim to cover:

Lecture 1: Superradiance.

- A toy model for superradiance: the Klein paradox;

- Superradiance in a flowing fluid;

- Superradiance for a charged black hole;

- Superradiance as a consequence of laws of black hole mechanics;

- The Penrose process for rotating black holes;

- Exercise: Separation of variables for the Klein-Gordon equation on Kerr spacetime.

Lecture 2: Superradiant instabilities.

- A key paper: “Floating Orbits, Superradiant Scattering and the Black-hole Bomb”;

- An ultralight scalar field on Kerr spacetime: the radial equation;

- The spectrum of quasi-bound states of the Kerr black hole;

- Approximations for the instability growth rate;

- Massive photons and massive gravitons;

- Black holes as particle detectors: proposals.

References:

Press and Teukolsky, Nature 238, 211 (1972).

Brito, Cardoso and Pani, Lect.Notes Phys. 971 (2020) [arXiv:1501.06570].

Dolan, Physics 10, 83 (2017). [link].

Arvanitaki et al. Phys.Rev.D 81, 123530 (2010). [arXiv:0905.4720].

- Eugen Radu:
**BH uniqueness and dirty BHs**

We start by reviewing a number of uniqueness results in Einstein-Maxwell theory, for a four-dimensional asymptotically flat spacetime. We next discuss a number of physically interesting dirty/hairy black hole (BH) solutions, considering both classical results and recent developments. These were first the Einstein-Yang-Mills BHs together with their generalizations with Higgs field, and also the solutions with Skyrme hair. More recent examples are the BHs with a scalar field violating the energy conditions or non-minimally coupled to gravity (including scalarized solutions), and also the spinning synchronized BHs with a massive, complex scalar or vector field.

- Francisco Duque:
**EMRIs or evolution of binaries in fundamental fields**

In these lectures we are going to use standard techniques from Black-Hole Perturbation Theory to understand what is the effect that the presence of a superradiant (scalar) cloud around a supermassive black hole has on the trajectory of a stellar-mass compact body around it. We will then use our results to assess if future GW observations can help probing ultralight fields using the inspiral stage of binary coalescences.

Workshop talks:

- William East:
**Uncovering the signatures of BH superradiance**

Black hole superradiance can be a powerful tool to look for new ultralight bosonic fields that may be weakly coupled to ordinary matter. In this talk, I will discuss the gravitational wave and--in some cases--electromagnetic signals that may arise when oscillating ultralight boson clouds develop through superradiance. I'll highlight some recent work to more accurately model the gravitational waveform from such sources, and to design new search methods targeting the black holes that form as remnants of compact object mergers.

- Hidetoshi Omiya:
**Impact of self-interaction on the axion cloud in the relativistic regime**

The superradiant instability provides a promising avenue for detecting ultra-light axions through the formation of axion clouds around black holes. To effectively observe these axions, it is crucial to have a precise understanding of the cloud's evolution and its observable signatures. In this talk, I will discuss the impact of axion self-interaction on both the evolution of the cloud and its observable phenomena, focusing on the relativistic regime where the Compton wavelength of the axion and the size of the black hole are comparable. In particular, I will demonstrate that self-interaction can produce gravitational wave signals in the low-frequency regime.

- Jamie McDonald:
**Superradiance in stars**

Superradiance is a generic phenomenon which can occur for any rotating body (which need not be a black hole!). Superradiance necessarily requires some channel for dissipation into the central rotating body. For rapidly rotating neutron stars, this can be provided by a direct coupling between the superradiant field and the particle constituents of the star. I will show how to connect the microphysical scattering rates in the star to an effective damped equation of motion for the field, outlining the power of quantum field theory to allow us to carry out this calculation from first principles. From there, we will see how superradiance emerges naturally when the star is set rotating. Finally, I will conjecture a “no-go” theorem which states that owing to fifth forces and stellar cooling, which limits the size of couplings to very light fields, stars may be typically protected from efficient superradiance.

- Diego Blas:
**Bridging the muHz gap in the GWs spectrum**

I’ll discuss some ideas, and possible follow ups, to detect GWs in the muHz band using the Moon’s orbital motion and the orbits of artificial satellites.

- Ornella Piccinni:
**GWs and Ultralight Bosons: observations from Spinning BHs**

Recent theoretical advancements in the study of ultralight dark matter particles have led to extensive experimental efforts using gravitational wave detectors to search for ultralight bosons. In this talk, I will explore how we can detect these particles through their gravitational interactions, focusing on systems that form clouds around spinning black holes. I will discuss the expected gravitational wave signals produced as these boson clouds dissipate and how Earth-based interferometers like LIGO, Virgo, and KAGRA can detect these signals. Additionally, I will cover the data analysis challenges we face in conducting these searches and the strategies used to overcome them. I will summarize the main findings from our observational efforts so far, which provide insights into the potential existence and properties of ultralight bosons in our universe. These efforts offer exciting possibilities for gaining new understandings of the mysterious dark side of the universe.

- Hyungjin Kim:
**Probing ultralight DM with GW detectors**

In this talk, I will discuss two types of density fluctuations -- coherent and stochastic -- that occur in any ultralight dark matter halo. I will then discuss a few possible ways to detect such ultralight dark matter density fluctuations using gravitational wave detectors, for instance, interferometers, pulsar timing array, and astrometry.

- Yue Zhao:
**Probing Axions with EHT Polarimetric Measurements**

With high spatial resolution, polarimetric imaging of a supermassive black hole, like M87* or Sgr A*, by the Event Horizon Telescope can be used to probe the existence of ultralight bosonic particles, such as axions. Such particles can accumulate around a rotating black hole through the superradiance mechanism, forming an axion cloud. When linearly polarized photons are emitted from an accretion disk near the horizon, their position angles oscillate due to the birefringent effect when traveling through the axion background. Recently, the polarization properties of the radiation near the supermassive black hole M87* are measured in four individual days. This is exactly what is needed to test the existence of a dense axion cloud. We apply the azimuthal distribution of EVPA measured by the EHT and study the axion-photon coupling. The EHT data can rule out a considerable portion of the axion parameter space for the axion mass window from 10^−21 to 10^−20 eV, which was unexplored by previous experiments.

- Lam Hui:
**Symmetries and nonlinearities in BH perturbation theory**

We will discuss two recent developments in black hole perturbation theory:

(1) the exact symmetries governing linear static (tidal) perturbations around black holes, and (2) nonlinear quasinormal modes.

- Nicolas Sanchis-Gual:
**Dynamical bosonic stars and GWs**

Bosonic stars are theoretical exotic compact objects made of ultralight bosonic particles that could account for part of dark matter. In this talk, I will review some recent results on the stability and dynamical formation of these objects. Then I will talk about bosonic star mergers, the emission of gravitational waves, and what we could learn about them from a real gravitational wave event, if these objects exist in the Universe.

- Joshua Eby:
**A Solar Halo of Ultralight DM**

Ultralight dark matter (ULDM) is known to form self-gravitating bound states through relaxation of the field, through gravity or self-interactions. The canonical example is a *boson star*, which is self-gravitating and has been studied for decades. In this talk, I will discuss a related but distinct bound state known as a *gravitational atom*, which is bound by the gravitational potential of some external astrophysical body (e.g. a star). Strikingly, the direct capture of ULDM from the background halo to such bound states, boosted by Bose enhancement and gravitational focusing, can be fast enough to give rise to large DM overdensities on astrophysically-relevant timescales. As a result, for strong-enough self-interactions we predict the rapid formation of a solar halo of ULDM around our own Sun in the range of axion masses 10^{-15} eV < m < 10^{-13} eV, giving rise to modifications of the local density and DM velocity at the position of Earth and near the Sun. I will conclude by briefly discussing extensions of these ideas, including gravitational atoms bound to other objects and some proposals for astrophysical signals from other star systems.

- Pedro Cunha:
**Beyond the Kerr paradigm: Hairy BHs and the fate of the Light ring Instability**

The image of M87* and SgrA* by the Event Horizon Telescope (EHT) has created a valuable opportunity to test the nature of Black Hole (BH) candidates in the cosmos. The Kerr hypothesis, which is motivated by multiple uniqueness theorems, states that astrophysical BHs are well described by the Kerr metric. However, alternative Kerr objects with possible astrophysical relevance can be constructed by circumventing these theorems. This talk will discuss the prospect of testing the Kerr hypothesis using shadow observations of the EHT. We will also discuss some existence results for light rings and possible consequences on the stability of horizonless black hole mimickers.

- Caio Macedo:
**Compact binaries in astrophysical environments**

Compact binaries represent the primary focus of contemporary gravitational wave detectors. However, their evolution can significantly deviate from the conventional vacuum scenario when situated within various environments, such as dark matter or accretion disks. In this presentation, we explore the impacts of binaries immersed in a medium. Specifically, we examine the effects of dynamical friction and accretion on eccentricity and center of mass velocity. Additionally, we delve into potential relativistic consequences arising from binaries interacting with bosonic field environments.

- Arianna Foschi:
**Constraint the mass of boson clouds at the Galactic Center**

The motion of S2, one of the stars closest to the Galactic Center (GC), has been measured accurately and used to study the compact object at the centre of the Milky Way. It is commonly accepted that this object is a supermassive black hole but the nature of its environment is open to discussion. In this talk I’m going to show how the motion of S2 can be used to investigate the possibility that dark matter in the form of an ultralight scalar field "cloud'' clusters around SgrA*. I will present some previous results on mass distribution at the GC, explain the theoretical setup, the tools used to fit the available data and finally the results and the constrains we can get from the Galactic Center on the mass of both scalar and vector clouds.

- Rodrigo Vicente:
**Looking for ultralight scalars with LIGO-Virgo-KAGRA binaries**

New ultralight (pseudo)scalar particles arise generically in extensions to the Standard Model. If their de Broglie wavelength is larger than the radii of compact objects (like black holes and neutron stars) they can form large-density halos around these objects, resembling a gravitational (hydrogen) atom. Building up the "gravitational chemistry": when their de Broglie wavelength is larger than the separation distance of compact binaries, they can form global states resembling a gravitational (ionized dihydrogen) molecule. In this talk, I will show that the current observations from the LIGO-Virgo-KAGRA collaboration can already be used to place stringent constraints on the presence of ultralight bosons around compact binary coalescences.

- Andrea Maselli:
**DM signatures around dirty BH binaries**

Asymmetric binaries provide a unique phenomenology among coalescing binary systems, which makes them golden sources for the future space born interferometer LISA. Assembled by a compact object orbiting around a more massive body, such systems emit gravitational waves in the milli-Hz regime, evolving for tens of thousands of orbits before the plunge. Their slow orbital evolution allows to map the binary spacetime with exquisite precision and to perform precision tests for a plethora of fundamental physics scenarios.

In this talk I will review some of the possibilities offered by extreme mass ratio inspirals, focusing in particular on their ability to provide novel insights on the environment in which binaries evolve. I will discuss how non-vacuum spacetimes affect the propagation and generation of gravitational waves, leaving a detectable imprint on the signals emitted by coalescing systems. I will show how future observations can exploit such footprints to infer the properties of astrophysical environments and to constrain, for example, the density of dark matter halos surrounding supermassive black holes.

- Dina Traykova:
**Gravitational drag effects — the numerical way**

Gravitational drag forces such as dynamical friction, momentum accretion and spin-curvature effects are expected to leave an observable imprint on the gravitational wave signal of binary black hole mergers, particularly in the case of an extreme mass-ratio inspiral, where the secondary black hole is immersed in a dark matter cloud. In this talk I will discuss recent developments in characterising these effects in the context of light scalar dark matter. I will focus, specifically, on the numerical calculation of drag forces acting on a single BH moving in the presence of a scalar could at relativistic velocities.