Abstract The exploration of the surrounding world and the universe is an important theme in the legacy of humankind. The detection of gravitational waves is adding a new dimension to this grand effort. What are the fundamental physical laws governing the dynamics of the universe? What is the fundamental composition of the universe? How has the universe evolved in the past and how will it evolve in the future? These are the basic questions that press for answers. The space-based gravitational wave detector TianQin will tune in to gravitational waves in the millihertz frequency range ( $$10^{-4}$$ 10 - 4 –1 Hz, to be specific), opening a new gravitational wave spectrum window to explore many of the previously hidden sectors of the universe. TianQin will discover many astrophysical systems, populating the universe at different redshifts: some will be of new types that have never been detected before, some will have very high signal-to-noise ratios, and some will have very high parameter estimation precision. The plethora of information collected will bring us to new fronts on which to search for the breaking points of general relativity, the possible violation of established physical laws, the signature of possible new gravitational physics and new fundamental fields, and to improve our knowledge on the expansion history of the universe. In this white paper, we highlight the advances that TianQin can bring to fundamental physics and cosmology.
Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).
The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems. Current ground-based very-long-baseline interferometry (VLBI) arrays like the EHT and proposed future extensions like the next-generation Event Horizon Telescope will greatly enhance the capabilities of black-hole imaging interferometry. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that future mm/sub-mm VLBI developments will enable.
While the early literature on black holes focused on event horizons, subsequently it was realized that their teleological nature makes them unsuitable for many physical applications both in classical and quantum gravity. Therefore, over the past two decades, event horizons have been steadily replaced by quasi-local horizons which do not suffer from teleology. In numerical simulations event horizons can be located as an ‘after thought’ only after the entire space-time has been constructed. By contrast, quasi-local horizons naturally emerge in the course of these simulations, providing powerful gauge-invariant tools to extract physics from the numerical outputs. They also lead to interesting results in mathematical GR, providing unforeseen insights. For example, for event horizons we only have a qualitative result that their area cannot decrease, while for quasi-local horizons the increase in the area during a dynamical phase is quantitatively related to local physical processes at the horizon. In binary black hole mergers, there are interesting correlations between observables associated with quasi-local horizons and those defined at future null infinity. Finally, the quantum Hawking process is naturally described as formation and evaporation of a quasi-local horizon. This article focuses on the dynamical aspects of quasi-local horizons in classical general relativity, emphasizing recent results and ongoing research.
The first direct measurement of gravitational waves by the LIGO and Virgo collaborations has opened up new avenues to explore our Universe. This white paper outlines the challenges and gains expected in gravitational-wave searches at frequencies above the LIGO/Virgo band. The scarcity of possible astrophysical sources in most of this frequency range provides a unique opportunity to discover physics beyond the Standard Model operating both in the early and late Universe, and we highlight some of the most promising of these sources. We review several detector concepts that have been proposed to take up this challenge, and compare their expected sensitivity with the signal strength predicted in various models. This report is the summary of a series of workshops on the topic of high-frequency gravitational wave detection, held in 2019 (ICTP, Trieste, Italy), 2021 (online) and 2023 (CERN, Geneva, Switzerland).
This article provides an overview of the current state of machine learning in gravitational-wave research with interferometric detectors. Such applications are often still in their early days, but have reached sufficient popularity to warrant an assessment of their impact across various domains, including detector studies, noise and signal simulations, and the detection and interpretation of astrophysical signals. In detector studies, machine learning could be useful to optimize instruments like LIGO, Virgo, KAGRA, and future detectors. Algorithms could predict and help in mitigating environmental disturbances in real time, ensuring detectors operate at peak performance. Furthermore, machine-learning tools for characterizing and cleaning data after it is taken have already become crucial tools for achieving the best sensitivity of the LIGO–Virgo–KAGRA network. In data analysis, machine learning has already been applied as an alternative to traditional methods for signal detection, source localization, noise reduction, and parameter estimation. For some signal types, it can already yield improved efficiency and robustness, though in many other areas traditional methods remain dominant. As the field evolves, the role of machine learning in advancing gravitational-wave research is expected to become increasingly prominent. This report highlights recent advancements, challenges, and perspectives for the current detector generation, with a brief outlook to the next generation of gravitational-wave detectors.
Fundamental constants are a cornerstone of the physical laws. Any constant varying in space and/or time would signal a violation of local position invariance and be associated with a violation of the universality of free fall, and hence of the weak equivalence principle. It will reflect the existence of new degrees of freedom that couple to standard matter. Thus, testing for the stability of fundamental constants is of utmost importance for our understanding of gravity and for characterizing the domain of validity of General Relativity. Besides, it opens an independent window on dark matter and dark energy. As a consequence, thanks to the active development of experiments and of their accuracy, fundamental constants have become a key player in our search for physics beyond the standard model of and beyond General Relativity. This review details the roles of the fundamental constants in the laws of physics and in the construction of the International System of units. Then, the relations between constants, tests of the local position invariance and of the universality of free fall are exposed, as well as the construction of field theories that account for "varying constants". Then, the main experimental and observational constraints are described. It details the basics of each system, its dependence with respect to the primary parameters the variation of which can be constrained from observations, the known systematics effects and the most recent constraints. It also describes how these primary parameters can be related to the fundamental constants and the model-dependencies. Both time and space variation are considered. Given the huge increase of data and constraints, a general scheme to present experimental and observational results and to construct a collaborative data base that will be more efficient for the community and allow for better traceability, is proposed.
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, organised according to the cosmological history—from cosmogenesis, through the early hot Big Bang, to the late-time evolution of the universe. We discuss the present state-of-the-art, and suggest directions in which future work can be fruitfully pursued.
This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.
The Event Horizon Telescope (EHT) Collaboration recently published the first images of the supermassive black holes in the cores of the Messier 87 and Milky Way galaxies. These observations have provided a new means to study supermassive black holes and probe physical processes occurring in the strong-field regime. We review the prospects of future observations and theoretical studies of supermassive black hole systems with the next-generation Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of the existing EHT array. These enhancements will open up several previously inaccessible avenues of investigation, thereby providing important new insights into the properties of supermassive black holes and their environments. This review describes the current state of knowledge for five key science cases, summarising the unique challenges and opportunities for fundamental physics investigations that the ngEHT will enable.
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.
In the recent years, primordial black holes (PBHs) have emerged as one of the most interesting and hotly debated topics in cosmology. Among other possibilities, PBHs could explain both some of the signals from binary black hole mergers observed in gravitational wave detectors and an important component of the dark matter in the Universe. Significant progress has been achieved both on the theory side and from the point of view of observations, including new models and more accurate calculations of PBH formation, evolution, clustering, merger rates, as well as new astrophysical and cosmological probes. In this work, we review, analyse and combine the latest developments in order to perform end-to-end calculations of the various gravitational wave signatures of PBHs. Different ways to distinguish PBHs from stellar black holes are emphasized. Finally, we discuss their detectability with LISA, the first planned gravitational-wave observatory in space.
This review aims at providing an extensive discussion of modern constraints relevant for dense and hot strongly interacting matter. It includes theoretical first-principle results from lattice and perturbative QCD, as well as chiral effective field theory results. From the experimental side, it includes heavy-ion collision and low-energy nuclear physics results, as well as observations from neutron stars and their mergers. The validity of different constraints, concerning specific conditions and ranges of applicability, is also provided.
The discovery of the first pulsar in a binary star system, the Hulse–Taylor pulsar, 50 years ago opened up an entirely new field of experimental gravity. For the first time it was possible to investigate strong-field and radiative aspects of the gravitational interaction. Continued observations of the Hulse–Taylor pulsar eventually led, among other confirmations of the predictions of general relativity (GR), to the first evidence for the reality of gravitational waves. In the meantime, many more radio pulsars have been discovered that are suitable for testing GR and its alternatives. One particularly remarkable binary system is the Double Pulsar, which has far surpassed the Hulse–Taylor pulsar in several respects. In addition, binary pulsar-white dwarf systems have been shown to be particularly suitable for testing alternative gravitational theories, as they often predict strong dipolar gravitational radiation for such asymmetric systems. A rather unique pulsar laboratory is the pulsar in a hierarchical stellar triple, that led to by far the most precise confirmation of the strong-field version of the universality of free fall. Using radio pulsars, it could be shown that additional aspects of the Strong Equivalence Principle apply to the dynamics of strongly self-gravitating bodies, like the local position and local Lorentz invariance of the gravitational interaction. So far, GR has passed all pulsar tests with flying colours, while at the same time many alternative gravity theories have either been strongly constrained or even falsified. New telescopes, instrumentation, timing and search algorithms promise a significant improvement of the existing tests and the discovery of (qualitatively) new, more relativistic binary systems.
Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt–Deser–Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Configurations are treated where the absolute values of the spin vectors can be considered constant. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to d-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up. The conservative spin-dependent dynamics finds explicit presentation in Hamiltonian form through next-to-next-to-leading-order spin–orbit and spin1–spin2 couplings and to leading-order in the cubic and quartic in spin interactions. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin–orbit and spin1–spin2 couplings. The most important historical issues get pointed out.
To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence—require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the multipolar-post-Minkowskian approximation scheme, merged to the standard post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational-wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin–spin) on the equations of motion and gravitational-wave energy flux and waveform.
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs' main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.
We describe here how planetary ephemerides are built in the framework of General Relativity and how they can be used to test alternative theories. We focus on the definition of the reference frame (space and time) in which the planetary ephemeris is described, the equations of motion that govern the orbits of solar system bodies and {electromagnetic waves}. After a review on the existing planetary and lunar ephemerides, we summarize the results obtained considering full modifications of the ephemeris framework with direct comparisons with the observations of planetary systems, with a specific attention for the PPN formalism. We then discuss other formalisms such as Einstein-dilaton theories, the massless graviton and MOND. The paper finally concludes on some comments and recommendations regarding misinterpreted measurements of the advance of perihelia.
We review recent developments in Jackiw–Teitelboim gravity. This is a simple solvable model of quantum gravity in two dimensions (that arises e.g. from the s-wave sector of higher dimensional gravity systems with spherical symmetry). Due to its solvability, it has proven to be a fruitful toy model to analyze important questions such as the relation between black holes and chaos, the role of wormholes in black hole physics and holography, and the way in which information that falls into a black hole can be recovered.
