Research & Publications

Abstract: We describe a simple and efficient Python code to perform Bayesian forecasting for gravitational waves (GW) produced by Extreme-Mass-Ratio-Inspiral systems (EMRIs). The code runs on GPUs for an efficient parallelised computation of thousands of waveforms and sampling of the posterior through a Markov-Chain-Monte-Carlo (MCMC) algorithm. EMRI_MC generates EMRI waveforms based on the so--called kludge scheme, and propagates it to the observer accounting for cosmological effects in the observed waveform due to modified gravity/dark energy. Extending the code to more accurate schemes for the generation of the waveform is straightforward. Despite the known limitations of the kludge formalism, we believe that the code can provide a helpful resource for the community working on forecasts for interferometry missions in the milli-Hz scale, predominantly, the satellite-mission LISA.

Abstract: We study the accretion of a Schwarzschild black hole due to spherically symmetric perturbations sourced by a minimally-coupled massless scalar field. The back-reaction of the black hole to low-frequency ingoing scalar waves is computed analytically as a second-order perturbative effect, using matched asymptotic expansions to relate the behaviour of the scalar field in the vicinity of the horizon and at null infinity. As an application of our results, we compute the mass increase due to (i) ingoing wave packets with an arbitrary profile and (ii) incoherent radiation. Our results could serve as a model for the back-reaction of environmental scalar fields on black holes.

Abstract: In our previous work, we proposed an algorithm to transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation in harmonic (de Donder) gauge to the Newman-Unti gauge. We then applied this algorithm at linear order and for specific quadratic interactions known as quadratic tail terms. In the present work, we extend this analysis to quadratic interactions associated with the coupling of two mass quadrupole moments, including both instantaneous and hereditary terms. Our main result is the derivation of the metric in Newman-Unti and Bondi gauges with complete quadrupole-quadrupole interactions. We rederive the displacement memory effect and provide expressions for all Bondi aspects and dressed Bondi aspects relevant to the study of leading and subleading memory effects. Then we obtain the Newman-Penrose charges, the BMS charges as well as the second and third order celestial charges defined from the known second order and novel third order dressed Bondi aspects for mass monopole-quadrupole and quadrupole-quadrupole interactions.

Abstract: The dynamics of a binary system moving in the background of a black hole is affected by tidal forces. In this work, for the Kerr black hole, we derive the electric and magnetic tidal moments at quadrupole order, where the latter are computed for the first time in full generality. We make use of these moments in the scenario of a hierarchical triple system made of a Kerr black hole and an extreme-mass ratio binary system consisting of a Schwarzschild black hole and a test particle. We study how the secular dynamics of the test particle in the binary system is distorted by the presence of tidal forces from a much larger Kerr black hole. Our treatment includes strong gravitational effects beyond the post-Newtonian approximation both for the binary system and for the tidal forces since the binary system is allowed to be close to the event horizon of the Kerr black hole. We compute the shifts in the physical quantities for the secular dynamics of the test particle and show that they are gauge-invariant. In particular, we apply our formalism to the innermost stable circular orbit for the test particle and to the case of the photon sphere. Our results are relevant for the astrophysical situation in which the binary system is in the vicinity of a supermassive black hole. 

Abstract: The most general vacuum solution to Einstein’s field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be mapped into each other under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely characterized by a set of conserved celestial charges that consist of the Geroch-Hansen multipole moments, the generalized BMS charges and additional celestial multipoles accounting for subleading memory effects. Transitions among non-radiative regions, induced by radiative processes, are therefore labelled by celestial charges, which are identified in terms of canonical multipole moments of the linearized gravitational field. The dictionary between celestial charges and canonical multipole moments allows to holographically reconstruct the metric in de Donder, Newman-Unti or Bondi gauge outside of sources.

Abstract: We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible by a new parametrization of the metric, in which the displacement from the horizon as well as its expansion rate feature explicitly. Our results are valid in a neighbourhood of the horizon and hold for any scalar field potential and spacetime asymptotics. An exact equation for the accretion rate is also obtained, which generalizes the standard Bondi formula. We also develop a dynamical system approach to study near-equilibrium black holes; using this formalism, we focus on a simple model to show that the near-equilibrium dynamics is characterised by scaling relations among dynamical variables. Moreover, we show that solutions with purely ingoing energy-momentum flux never reach equilibrium. .  

Abstract: The Blandford and Znajek (BZ) split-monopole serves as an important theoretical example of the mechanism that can drive the electromagnetic extraction of energy from Kerr black holes. It is constructed as a perturbative low spin solution of Force Free Electrodynamics (FFE). Recently, Armas et al. put this construction on a firmer footing by clearing up issues with apparent divergent asymptotics. This was accomplished by resolving the behavior around the outer light surface, a critical surface of the FFE equations. Building on this, we revisit the BZ perturbative expansion, and extend the perturbative approach to higher orders in the spin parameter of the Kerr black hole. We employ matched-asymptotic-expansions and semi-analytic techniques to extend the split-monopole solution to the sixth-order in perturbation theory. The expansion necessarily includes novel logarithmic contributions in the spin parameter. We show that these higher order terms result in non-analytic contributions to the power and angular momentum output. In particular, we compute for the first time the perturbative contributions to the energy extraction at seventh- and eighth-order in the spin parameter. The resulting formula for the energy extraction improves the agreement with numerical simulations at finite spin. Moreover, we present a novel numerical procedure for resolving the FFE equations across the outer light surface, resulting in significantly faster convergence and greater accuracy, and extend this to higher orders as well. Finally, we include a general discussion of light surfaces as critical surfaces of the FFE equations.  

Abstract: We investigate the asymptotia of decelerating and spatially flat FLRW spacetimes at future null infinity. We find that the asymptotic algebra of diffeomorphisms can be enlarged to the recently discovered Weyl-BMS algebra for asymptotically flat spacetimes by relaxing the boundary conditions. This algebra remains undeformed in the cosmological setting contrary to previous extensions of the BMS algebra. We then study the equations of motion for asymptotically FLRW spacetimes with finite fluxes and show that the dynamics is fully constrained by the energy-momentum tensor of the source. Finally, we propose an expression for the charges which are associated with the cosmological supertranslations and whose evolution equation features a novel contribution arising from the Hubble–Lemaitre flow.

Abstract: We provide a prescription to compute the gravitational multipole moments of compact objects for asymptotically de Sitter spacetimes. Our prescription builds upon a recent definition of the gravitational multipole moments in terms of Noether charges associated to specific vector fields, within the residual harmonic gauge, dubbed multipole symmetries. We first derive the multipole symmetries for spacetimes which are asymptotically de Sitter; we also show that these symmetry vector fields eliminate the non-propagating degrees of freedom from the linearized gravitational wave equation. We then apply our prescription to the Kerr-de Sitter black hole and compute its multipole structure. Our result recovers the Geroch-Hansen moments of the Kerr black hole in the limit of vanishing cosmological constant.

Abstract: We develop the covariant phase space formalism allowing for non-vanishing flux, anomalies, and field dependence in the vector field generators. We construct a charge bracket that generalizes the one introduced by Barnich and Troessaert and includes contributions from the Lagrangian and its anomaly. This bracket is uniquely determined by the choice of Lagrangian representative of the theory. We then extend the notion of corner symmetry algebra to include the surface translation symmetries and prove that the charge bracket provides a canonical representation of the extended corner symmetry algebra. This representation property is shown to be equivalent to the projection of the gravitational equations of motion on the corner, providing us with an encoding of the bulk dynamics in a locally holographic manner.

Abstract: We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein’s equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.

Abstract: We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.

Abstract: Dual gravitational charges have been recently computed from the Holst term in tetrad variables using covariant phase space methods. We highlight that they originate from an exact 3-form in the tetrad symplectic potential that has no analogue in metric variables. Hence there exists a choice of the tetrad symplectic potential that sets the dual charges to zero. This observation relies on the ambiguity of the covariant phase space methods. To shed more light on the dual contributions, we use the Kosmann variation to compute (quasi-local) Hamiltonian charges for arbitrary diffeomorphisms. We obtain a formula that illustrates comprehensively why the dual contribution to the Hamiltonian charges: (i) vanishes for exact isometries and asymptotic symmetries at spatial infinity; (ii) persists for asymptotic symmetries at future null infinity, in addition to the usual BMS contribution. Finally, we point out that dual gravitational charges can be equally derived using the Barnich-Brandt prescription based on cohomological methods, and that the same considerations on asymptotic symmetries apply. 

Abstract: We propose a new approach to find magnetically-dominated force-free magnetospheres around highly spinning black holes, relevant for models of astrophysical jets. Employing the near-horizon extreme Kerr (NHEK) limit of the Kerr black hole, any stationary, axisymmetric and regular force-free magnetosphere reduces to the same attractor solution in the NHEK limit with null electromagnetic field strength. We use this attractor solution as the universal starting point for perturbing away from the NHEK region in the extreme Kerr spacetime. We demonstrate that by going to second order in perturbation theory, it is possible to find magnetically dominated magnetospheres around the extreme Kerr black hole. Furthermore, we consider the near-horizon near-extreme Kerr (near-NHEK) limit that provides access to a different regime of highly spinning black holes. Also in this case we find a novel force-free attractor, which can be used as the universal starting point for a perturbative construction of force-free magnetospheres. Finally, we discuss the relation between the NHEK and near-NHEK attractors.  

Abstract: We consider force-free magnetospheres around the extreme Kerr black hole. In this case there is no known exact analytic solution to force free electrodynamics which is stationary, axisymmetric and magnetically-dominated. However, any stationary, axisymmetric and regular force-free magnetosphere in extreme Kerr black hole approaches the same attractor solution in the near-horizon extreme Kerr (NHEK) limit with null electromagnetic field. We show that by moving away from the attractor solution in the NHEK region, one finds magnetically-dominated solutions in the extreme Kerr black hole with finite angular momentum outflow. This result is achieved using a perturbative analysis up to the second order. 

Abstract: Asymptotically flat spacetimes admit both supertranslations and Lorentz transformations as asymptotic symmetries. Furthermore, they admit super-Lorentz transformations, namely superrotations and superboosts, as outer symmetries associated with super-angular momentum and super-center-of-mass charges. In this paper, we present comprehensively the flux-balance laws for all such BMS charges. We distinguish the Poincaré flux-balance laws from the proper BMS flux-balance laws associated with the three relevant memory effects defined from the shear, namely, the displacement, spin and center-of-mass memory effects. We scrutinize the prescriptions used to define the angular momentum and center-of-mass. In addition, we provide the exact form of all Poincar\'e and proper BMS flux-balance laws in terms of radiative symmetric tracefree multipoles. Fluxes of energy, angular momentum and octupole super-angular momentum arise at 2.5PN, fluxes of quadrupole supermomentum arise at 3PN and fluxes of momentum, center-of-mass and octupole super-center-of-mass arise at 3.5PN. We also show that the BMS flux-balance laws lead to integro-differential consistency constraints on the radiation-reaction forces acting on the sources. Finally, we derive the exact form of all BMS charges for both an initial Kerr binary and a final Kerr black hole in an arbitrary Lorentz and supertranslation frame, which allows to derive exact constraints on gravitational waveforms produced by binary black hole mergers from each BMS flux-balance law. 

Abstract: Varying the gravitational Lagrangian produces a boundary contribution that has various physical applications. It determines the right boundary terms to be added to the action once boundary conditions are specified, and defines the symplectic structure of covariant phase space methods. We study general boundary variations using tetrads instead of the metric. This choice streamlines many calculations, especially in the case of null hypersurfaces with arbitrary coordinates, where we show that the spin-1 momentum coincides with the rotational 1-form of isolated horizons. The additional gauge symmetry of internal Lorentz transformations leaves however an imprint: the boundary variation differs from the metric one by an exact 3-form. On the one hand, this difference helps in the variational principle: gluing hypersurfaces to determine the action boundary terms for given boundary conditions is simpler, including the most general case of non-orthogonal corners. On the other hand, it affects the construction of Hamiltonian surface charges with covariant phase space methods, which end up being generically different from the metric ones, in both first and second-order formalisms. This situation is treated in the literature gauge-fixing the tetrad to be adapted to the hypersurface or introducing a fine-tuned internal Lorentz transformation depending non-linearly on the fields. We point out and explore the alternative approach of dressing the bare symplectic potential to recover the value of all metric charges, and not just for isometries. Surface charges can also be constructed using a cohomological prescription: in this case we find that the exact 3-form mismatch plays no role, and tetrad and metric charges are equal. This prescription leads however to different charges whether one uses a first-order or second-order Lagrangian, and only for isometries one recovers the same charges. 

Abstract: We define the mass and current multipole moments for an arbitrary theory of gravity in terms of canonical Noether charges associated with specific residual transformations in canonical harmonic gauge, which we call multipole symmetries. We show that our definition exactly matches Thorne’s mass and current multipole moments in Einstein gravity, which are defined in terms of metric components. For radiative configurations, the total multipole charges — including the contributions from the source and the radiation — are given by surface charges at spatial infinity, while the source multipole moments are naturally identified by surface integrals in the near-zone or, alternatively, from a regularization of the Noether charges at null infinity. The conservation of total multipole charges is used to derive the variation of source multipole moments in the near-zone in terms of the flux of multipole charges at null infinity. 

Abstract: Near-maximally spinning black holes display conformal symmetry in their near-horizon region, which is therefore the locus of critical phenomena. In this paper, we revisit the Novikov–Thorne accretion thin disc model and find a new self-similar radiation-dominated solution in the extremely high spin regime. Motivated by the self-consistency of the model, we require that matter flows at the sound speed at the innermost stable circular orbit (ISCO). We observe that, when the disc pressure is dominated by radiation at the ISCO, which occurs for the best-fitting Novikov–Thorne model of GRS 1915+105, the Shakura–Sunyaev viscosity parameter can be expressed in terms of the spin, mass accretion rate and radiative efficiency. We quantitatively describe how the exact thin disc solution approaches the self-similar solution in the vicinity of the ISCO and for increasing spins.

Abstract: The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincaré group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system. 

Abstract: The explicit solution for a Kerr-Newman black hole immersed in an external magnetic field, sometimes called the Melvin-Kerr-Newman black hole, has been derived by Ernst and Wild in 1976. In this paper, we clarify the first law and Smarr formula for black holes in a magnetic field. We then define the unique mass which is integrable and reduces to the Kerr-Newman mass in the absence of magnetic field. This defines the thermodynamic potentials of the black hole. Quite strikingly, the mass coincides with the standard Christodoulou-Ruffini mass of a black hole as a function of the entropy, angular momentum and electric charge. 

Abstract: Analytical solutions to force-free electrodynamics around black holes are fundamental for building simple models of accretion disk and jet dynamics. We present a (nonexhaustive) classification of complex highest-weight solutions to the force-free equations in the near-horizon region of the extremal Kerr black hole. Several classes of real magnetically dominated or null solutions, either axisymmetric or nonaxisymmetric, are described which admit finite energy and angular momentum with respect to the asymptotically flat observer. Subtleties related to the velocity of light surface in the near-horizon region are discussed.

Abstract: We describe some key astrophysical processes driving the formation and evolution of black hole binaries of different nature, from stellar-mass to supermassive systems. In the first part, we focus on the mainstream channels proposed for the formation of stellar mass binaries relevant to ground-based gravitational wave detectors, namely the field and the dynamical scenarios. For the field scenario, we highlight the relevant steps in the evolution of the binary, including mass transfer, supernovae explosions and kicks, common envelope and gravitational wave emission. For the dynamical scenario, we describe the main physical processes involved in the formation of star clusters and the segregation of black holes in their centres. We then identify the dynamical processes leading to binary formation, including three-body capture, exchanges and hardening. The second part of the notes is devoted to massive black hole formation and evolution, including the physics leading to mass accretion and binary formation. Throughout the notes, we provide several step-by-step pedagogical derivations, that should be particularly suited to undergraduates and PhD students, but also to gravitational wave physicists interested in approaching the subject of gravitational wave sources from an astrophysical perspective. 

Abstract: This thesis deals with two classes of space-time symmetries: emergent symmetries in the near-horizon region of rapidly rotating Kerr black holes and residual gauge symmetries. The main aim of the thesis is to investigate consequences and effects of these symmetries on black holes and gravitational radiation. The first class of symmetries is exploited to address questions of astrophysical relevance for force-free magnetospheres, thin accretion discs, and strong magnetic fields around Kerr black holes. We investigate how the dynamics of electromagnetic and matter fields is constrained by global conformal symmetries of the near-horizon geometry. In the context of force-free electrodynamics, we find exact solutions and classify them according to the highest weight representation of the isometry group. We introduce novel criteria to distinguish physical solutions and deduce bounds on conformal weights of electromagnetic fields. For thin accretion discs, within the Novikov-Thorne model, new properties arise in the high spin regime of the Kerr black hole. We find a novel self-similar solution and we explain the critical behaviour of the observables by symmetry arguments. Afterwards, we study an exact analytic solution to the Einstein-Maxwell theory. It describes a black hole immersed in a strong magnetic field and it shares the same near-horizon geometry of extreme Kerr black holes. We compute its total conserved mass by means of the covariant phase space formalism and study its thermodynamics. The second class of symmetries is considered in order to provide a new definition of gravitational multipole moments by means of Noether charges and by adopting the covariant phase space formalism. We show that such a definition in terms of Noether charges reproduces multipole moments in General Relativity. We propose to apply it to an arbitrary generally covariant metric theory of gravity.