Search

This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving cosmological spacetimes, aimed at both cosmologists and numerical relativists. Second, we survey the present body of work, focusing on general relativistic simulations without approximations, organised according to the cosmological history -- from cosmogenesis, through the early hot Big Bang, to the late-time evolution of universe. In both cases, we discuss the present state-of-the-art, and suggest directions in which future work can be fruitfully pursued., Comment: 42 pages, 21 figures. To be submitted to Living Reviews in Relativity. Comments welcome!

Gravitational waves can provide crucial insights about the environments in which black holes live. In this work, we use numerical relativity simulations to study the behaviour of self-interacting scalar (wave-like) dark matter clouds accreting onto isolated and binary black holes. We find that repulsive self-interactions smoothen the ``spike'' of an isolated black hole and saturate the density. Attractive self-interactions enhance the growth and result in more cuspy profiles, but can become unstable and undergo explosions akin to the superradiant bosenova that reduce the local cloud density. We quantify the impact of self-interactions on an equal-mass black hole merger by computing the dephasing of the gravitational-wave signal for a range of couplings. We find that repulsive self-interactions saturate the density of the cloud, thereby reducing the dephasing. For attractive self-interactions, the dephasing may be larger, but if these interactions dominate prior to the merger, the dark matter can undergo bosenova during the inspiral phase, disrupting the cloud and subsequently reducing the dephasing., Comment: 8 pages, 7 figures, 1 movie: https://youtu.be/ZeoMlUHknUM. Matches version published in PRD

This set of notes was designed to accompany two hours of lectures and practical exercises at the New Horizons for Psi workshop in Lisbon in July 2024 entitled "Studying fundamental fields with numerical relativity". Numerical relativity is a tool used to help understand the behaviours of metric and matter fields in dynamical, strong gravity situations. It has been used to study a range of situations involving fundamental fields, including superradiance, modified gravity, dynamical friction, dark matter accretion and early universe cosmology. The purpose of this course is to provide some background and hands-on experience in numerical relativity that will help students to better understand the possibilities provided by this tool, as well as its limitations., Comment: Comments welcome. 20 pages, 5 figures. See https://github.com/GRTLCollaboration/engrenage/wiki/New-Horizons-for-Psi-workshop for supporting material

The coefficient categories of six functor formalisms are often locally rigid, and when this is the case, the exceptional pushforward and pullback adjunctions may be defined formally. In this short note it is shown that for f a proper map resp. an open embedding the well known formulas f_! = f_* resp. f_! = f_# may likewise be deduced formally., Comment: 9 pages

This paper explores the Mechanism Design aspects of the $m$-Capacitated Facility Location Problem where the total facility capacity is less than the number of agents. Following the framework outlined by Aziz et al., the Social Welfare of the facility location is determined through a First-Come-First-Served (FCFS) game, in which agents compete once the facility positions are established. When the number of facilities is $m > 1$, the Nash Equilibrium (NE) of the FCFS game is not unique, making the utility of the agents and the concept of truthfulness unclear. To tackle these issues, we consider absolutely truthful mechanisms, i.e. mechanisms that prevent agents from misreporting regardless of the strategies used during the FCFS game. We combine this stricter truthfulness requirement with the notion of Equilibrium Stable (ES) mechanisms, which are mechanisms whose Social Welfare does not depend on the NE of the FCFS game. We demonstrate that the class of percentile mechanisms is absolutely truthful and identify the conditions under which they are ES. We also show that the approximation ratio of each ES percentile mechanism is bounded and determine its value. Notably, when all the facilities have the same capacity and the number of agents is sufficiently large, it is possible to achieve an approximation ratio smaller than $1+\frac{1}{2m-1}$. Finally, we extend our study to encompass higher-dimensional problems. Within this framework, we demonstrate that the class of ES percentile mechanisms is even more restricted and characterize the mechanisms that are both ES and absolutely truthful. We further support our findings by empirically evaluating the performance of the mechanisms when the agents are the samples of a distribution., Comment: 34 pages, 55 figures

We show that the $\infty$-category of global spaces is equivalent to the homotopy localization of the $\infty$-category of sheaves on the site of separated differentiable stacks, following a philosophy proposed by Gepner-Henriques. We further prove that this $\infty$-category of sheaves is a cohesive $\infty$-topos and that it fully faithfully contains the singular-cohesive $\infty$-topos of Sati-Schreiber., Comment: 21 pages

Despite originating in science fiction, warp drives have a concrete description in general relativity, with Alcubierre first proposing a spacetime metric that supported faster-than-light travel. Whilst there are numerous practical barriers to their implementation in real life, including a requirement for negative energy, computationally, one can simulate their evolution in time given an equation of state describing the matter. In this work, we study the signatures arising from a warp drive "containment failure", assuming a stiff equation of state for the fluid. We compute the emitted gravitational-wave signal and track the energy fluxes of the fluid. Apart from its rather speculative application to the search for extraterrestrial life in gravitational-wave detector data, this work is interesting as a study of the dynamical evolution and stability of spacetimes that violate the null energy condition. Our work highlights the importance of exploring strange new spacetimes, to (boldly) simulate what no one has seen before., Comment: 12 pages, 6 figures, plus appendix. Comments welcome!

We investigate the effects of large inhomogeneities in both the inflaton field and its momentum. We find that in general, large kinetic perturbations reduce the number of e-folds of inflation. In particular, we observe that inflationary models with sub-Planckian characteristic scales are not robust even to kinetic energy densities that are sub-dominant to the potential energy density, unless the initial field configuration is sufficiently far from the minimum. This strengthens the results of our previous work. In inflationary models with super-Planckian characteristic scales, despite a reduction in the number of e-folds, inflation is robust even when the potential energy density is initially sub-dominant. For the cases we study, the robustness of inflation strongly depends on whether the inflaton field is driven into the reheating phase by the inhomogeneous scalar dynamics., Comment: 8 pages, 5 figures, 1 appendix. Comments welcome!

Vacuum decay and symmetry breaking play an important role in the fundamental structure of the matter and the evolution of the universe. In this work we study how the purely classical effect of accretion of fundamental fields onto black holes can lead to shells of symmetry restoration in the midst of a symmetry broken phase. We also show how it can catalyze vacuum decay, forming a bubble that expands asymptotically at the speed of light. These effects offer an alternative, purely classical mechanism to quantum tunnelling for seeding phase transitions in the universe., Comment: 4 pages, 4 figures, 1 movie: https://youtu.be/c2vcNoX8fVs Comments welcome!

In fluid dynamics, the Magnus effect is the force perpendicular to the motion of a spinning object as it moves through a medium. In general relativity, an analogous effect exists for a spinning compact object moving through matter, purely as a result of gravitational interactions. In this work we consider a Kerr black hole moving at relativistic velocities through scalar dark matter that is at rest. We simulate the system numerically and extract the total spin-curvature force on the black hole perpendicular to its motion. We confirm that the force scales linearly with the dimensionless spin parameter $a/M$ of the black hole up to $a/M = 0.99$, and measure its dependence on the speed $v$ of the black hole in the range $0.1 \le v \le 0.55$ for a fixed spin. Compared to previous analytic work applicable at small $v$, higher-order corrections in the velocity are found to be important: the total force is nonzero, and the dependence is not linear in $v$. We find that in all cases the total force is in the opposite direction to the hydrodynamical analogue, although at low speeds it appears to approach the expectation that the Weyl and Magnus components cancel. Spin-curvature effects may leave an imprint on gravitational wave signals from extreme mass-ratio inspirals, where the secondary black hole has a nonnegligible spin and moves in the presence of a dark matter cloud. We hope that our simulations can be used to support and extend the limits of analytic results, which are necessary to better quantify such effects in the relativistic regime., Comment: 10 pages, 6 figures

For dark matter to be detectable with gravitational waves from binary black holes, it must reach higher than average densities in their vicinity. In the case of light (wave-like) dark matter, the density of dark matter between the binary can be significantly enhanced by accretion from the surrounding environment. Here we show that the resulting dephasing effect on the last ten orbits of an equal mass binary is maximized when the Compton wavelength of the scalar particle is comparable to the orbital separation, $2\pi/\mu\sim d$. The phenomenology of the effect is different from the channels that are usually discussed, where dynamical friction (along the orbital path) and radiation of energy and angular momentum drive the dephasing, and is rather dominated by the radial force (the spacetime curvature in the radial direction) towards the overdensity between the black holes. Whilst our numerical studies limit us to scales of the same order, this effect may persist at larger separations and/or particle masses, playing a significant role in the merger history of binaries., Comment: 4 pages, 4 figures, 1 appendix, 1 movie: https://youtu.be/2VJIfqCp7D8. Matches version published in PRL

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

The Information Retrieval in Software Engineering (IRSE) track aims to develop solutions for automated evaluation of code comments in a machine learning framework based on human and large language model generated labels. In this track, there is a binary classification task to classify comments as useful and not useful. The dataset consists of 9048 code comments and surrounding code snippet pairs extracted from open source github C based projects and an additional dataset generated individually by teams using large language models. Overall 56 experiments have been submitted by 17 teams from various universities and software companies. The submissions have been evaluated quantitatively using the F1-Score and qualitatively based on the type of features developed, the supervised learning model used and their corresponding hyper-parameters. The labels generated from large language models increase the bias in the prediction model but lead to less over-fitted results., Comment: Overview Paper of the Information Retrieval of Software Engineering Track at the Forum for Information Retrieval, 2023

GRFolres is an open-source code for performing simulations in modified theories of gravity, based on the publicly available 3+1D numerical relativity code GRChombo. Note: Submitted for review in the Journal of Open Source Software; Comments welcome; The code can be found at https://github.com/GRChombo/GRFolres

The pump and dump scheme is a form of market manipulation attack in which coordinated actors drive up the price of an asset in order to sell at a higher price. Due in part to a lack of enforcement, these schemes are widespread within the cryptocurrency marketplace, but the negative impact of these events on the coins they target is not yet fully understood. Drawing upon a novel dataset of pump events extracted from Telegram channels, an order of magnitude larger than the nearest comparable dataset in the literature, we explore the differing tactics of pumping channels and the long-term impact of pump and dump schemes across 765 coins. We find that, despite a short-term positive impact in some cases, the long-term impact of pump and dump schemes on the targeted assets is negative, amounting to an average 30% relative drop in price a year after the pump event.

Many important theorems in differential topology relate properties of manifolds to properties of their underlying homotopy types -- defined e.g. using the total singular complex or the \v{C}ech nerve of a good open cover. Upon embedding the category of manifolds into the $\infty$-topos $\mathbf{Diff}^\infty$ of differentiable sheaves one gains a further notion of underlying homotopy type: the shape of the corresponding differentiable sheaf. In a first series of results we prove using simple cofinality and descent arguments that the shape of any manifold coincides with many other notions of underlying homotopy types such as the ones mentioned above. Our techniques moreover allow for computations, such as the homotopy type of the Haefliger stack, following Carchedi. This leads to more refined questions, such as what it means for a mapping differential sheaf to have the correct shape. To answer these we construct model structures as well as more general homotopical calculi on the $\infty$-category $\mathbf{Diff}^\infty$ (which restrict to its full subcategory of $0$-truncated objects,$\mathbf{Diff}^\infty_{\leq 0}$) with shape equivalences as the weak equivalences. These tools are moreover developed in such a way so as to be highly customisable, with a view towards future applications, e.g. in geometric topology. Finally, working with the $\infty$-topos $\mathbf{Diff}^0$ of sheaves on topological manifolds, we give new and conceptual proofs of some classical statements in algebraic topology. These include Dugger and Isaksen's hypercovering theorem, and the fact that the Quillen adjunction between simplicial sets and topological spaces is a Quillen equivalence., Comment: 100 pages, 1 figure

Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In principle, such modifications may affect the principal part of the operator in the resulting elliptic equations, and so further complicate the already highly non-linear, coupled constraints that apply to the initial data in numerical relativity simulations of curved spacetimes. However, since these are effective field theories, we expect the additional curvature terms to be small, which motivates treating them simply as an additional source in the constraints, and iterating to find a solution to the full problem. In this work we implement and test a modification to the CTT/CTTK methods of solving the constraints for the case of the most general four derivative, parity invariant scalar-tensor theory, and show that solutions can be found in both asymptotically flat/black hole and periodic/cosmological spacetimes, even up to couplings of order unity in the theory. Such methods will allow for numerical investigations of a much broader class of initial data than has previously been possible in these theories, and should be straightforward to extend to similar models in the Horndeski class., Comment: 9 pages, 4 figures, comments welcome!

GRDzhadzha is an open-source code for relativistic simulations of matter fields on curved spacetimes that admit an analytic description (e.g. stationary black holes). It is based on the publicly available 3+1D numerical relativity code GRChombo. Such a description is valid where the density of the matter is small compared to the curvature scale of the spacetime, which is the case for many physical scenarios - for example, dark matter environments. The approach offers significant savings on memory and speed compared to running full numerical relativity simulations, since the metric variables and their derivatives are calculated analytically, and therefore are not evolved or stored on the grid. This brief paper introduces the code and gives details of some applications for which it has already been used., Comment: Submitted for review in the Journal of Open Source Software; Comments welcome; The code can be found at https://github.com/GRChombo/GRDzhadzha.git

If we imagine rewinding the universe to early times, the scale factor shrinks and the existence of a finite spatial volume may play a role in quantum tunnelling effects in a closed universe. It has recently been shown that such finite volume effects dynamically generate an effective equation of state that could support a cosmological bounce. In this work we extend the analysis to the case in which a (homogeneous) anisotropy is present, and identify a criteria for a successful bounce in terms of the size of the closed universe and the properties of the quantum field., Comment: 9 pages, 5 figures, minor changes, version accepted for publication in Physical Review D

Quadratic theories of gravity with second order equations of motion provide an interesting model for testing deviations from general relativity in the strong gravity regime. However, they can suffer from a loss of hyperbolicity, even for initial data that is in the weak coupling regime and free from any obvious pathology. This effect has been studied in a variety of cases including isolated black holes and binaries. Here we explore the loss of hyperbolicity in spin-induced scalarization of isolated Kerr black holes in a scalar-Gauss-Bonnet theory of gravity, employing the modified CCZ4 formulation that has recently been developed. We find that, as in previous studies, hyperbolicity is lost when the scalar field and its gradients become large, and identify the breakdown in our evolutions with the physical modes of the purely gravitational sector. We vary the gauge parameters and find the results to be independent of their value. This, along with our use of a different gauge formulation to previous works, supports the premise that the loss of hyperbolicity is dominated by the physical modes. Since scalar-Gauss-Bonnet theories can be viewed as effective field theories (EFTs), we also examine the strength of the coupling during the evolution. We find that at the moment when hyperbolicity is lost the system is already well within the regime where the EFT is no longer valid. This reinforces the idea that the theories should only be applied within their regime of validity, and not treated as complete theories in their own right., Comment: 23 pages, 10 figure, 1 table

We develop a modified CCZ4 formulation of the Einstein equations in $d+1$ spacetime dimensions for general relativity plus a Gauss-Bonnet term, as well as for the most general parity-invariant scalar-tensor theory of gravity up to four derivatives. We demonstrate well-posedness for both theories and provide full expressions for their implementation in numerical relativity codes. As a proof of concept, we study the so-called ``stealth-scalarisation'' induced by the spin of the remnant black hole after merger. As in previous studies using alternative gauges we find that the scalarisation occurs too late after merger to impact on the tensor waveform, unless the parameters are finely tuned. Naively increasing the coupling to accelerate the growth of the scalar field risks a breakdown of the effective field theory, and therefore well-posedness, as the evolution is pushed into the strongly coupled regime. Observation of such an effect would therefore rely on the detection of the scalar radiation that is produced during scalarisation. This work provides a basis on which further studies can be undertaken using codes that employ a moving-punctures approach to managing singularities in the numerical domain. It is therefore an important step forward in our ability to analyse modifications of general relativity in gravitational wave observations., Comment: Version accepted for publication in PRD

We use numerical simulations of scalar field dark matter evolving on a moving black hole background to confirm the regime of validity of (semi-)analytic expressions derived from first principles for both dynamical friction and momentum accretion in the relativistic regime. We cover both small and large clouds (relative to the de Broglie wavelength of the scalars), and light and heavy particle masses (relative to the BH size). In the case of a small dark matter cloud, the effect of accretion is a non-negligible contribution to the total force on the black hole, even for small scalar masses. We confirm that this momentum accretion transitions between two regimes (wave- and particle-like) and we identify the mass of the scalar at which the transition between regimes occurs., Comment: 11 pages, 5 figures. Minor corrections and references added to match published version

We study the non-perturbative evolution of inflationary fluctuations during preheating using fully non-linear general-relativistic field-theory simulations. We choose a single-field inflationary model that is consistent with observational constraints and start the simulations at the end of inflation with fluctuations both in the field and its conjugate momentum. Gravity enhances the growth of density perturbations, which then collapse and virialize, forming long-lived stable oscillon-like stars that reach compactnesses $\mathcal{C}\equiv GM/R \sim 10^{-3}-10^{-2}$. We find that $\mathcal{C}$ increases for larger field models, until it peaks due to the interplay between the overdensity growth and Hubble expansion rates. Whilst gravitational effects can play an important role in the formation of compact oscillons during preheating, the objects are unlikely to collapse into primordial black holes without an additional enhancement of the initial inflationary fluctuations., Comment: 7 pages. 4 figures. Movie: https://youtu.be/vTl9agMfPB0. Matches version published in PRD