Classical and Quantum Gravity

In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of the Hamiltonian constraint on generic basis states in the Hilbert space of quantum-reduced loop gravity. Specializing to the example of the single-vertex states, we find that the Euclidean part of the Hamiltonian bears a close formal similarity to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. Extending the formal analogy to the Lorentzian part of the Hamiltonian suggests a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part, corresponding to the scalar curvature of the spatial surfaces, is not assumed to be identically vanishing, and is represented by a non-trivial operator in the quantum theory.

Gravitational Wave (GW) signals from binary neutron star (BNS) mergers provide critical insights into the properties of matter under extreme conditions. Due to the scarcity of observational data, numerical relativity (NR) simulations are indispensable for exploring these phenomena, without replacing the need for observational confirmation. However, simulating BNS mergers is a formidable challenge, and ensuring the consistency, reliability or convergence, especially in the post-merger, remains a work in progress. In this paper we assess the performance of current BNS merger simulations by analyzing open-source GW waveforms from five leading NR codes – SACRA, BAM, THC, Whisky, and SpEC. We focus on the accuracy of these simulations and on the effect of the equation of state on waveform predictions. We first check if different codes give similar results for similar initial data, then apply two methods to calculate convergence and quantify discretization errors. Lastly, we perform a thorough investigation into the effect of tidal interactions on key frequencies in the GW spectrum. We introduce a novel quasi-universal relation for the transient post-merger time, enhancing our understanding of remnant dynamics in this region. This detailed analysis clarifies agreements and discrepancies between these leading NR codes, and highlights necessary improvements for the advanced accuracy requirements of future GW detectors.

We examine Friedmann–Lemaître–Robertson–Walker cosmology, incorporating quantum gravitational corrections through the functional renormalisation group flow of the effective action for gravity. We solve the Einstein equation with quantum improved coupling perturbatively including the case with non-vanishing classical cosmological constant (CC) which was overlooked in the literatures. We discuss what is the suitable identification of the momentum cutoff k with time scale, and find that the choice of the Hubble parameter is suitable for vanishing CC but not so for non-vanishing CC. We suggest suitable identification in this case. The energy-scale dependent running coupling breaks the time translation symmetry and then introduces a new physical scale.

In recent years there have been many studies on exactly solvable black hole mergers, based on a model by Emparan and Martínez where the mass of one black hole is blown up to infinity (Emparan and Martínez 2016 Class. Quantum Grav.33 155003). Here we replace the large black hole by a cosmological horizon, and study how it merges with a black hole in the Schwarzschild-de Sitter spacetime by considering an observer positioned at future null infinity. We describe the geometry of the horizon over time, including the role that caustics play in the merger process, and also examine the growth of the horizon area. We argue that in the limit of zero cosmological constant, the system reduces to the Emparan-Martínez Schwarzschild merger. This allows us to regularize the increase in the area during the merger, which otherwise diverges.

In their seminal 1992 paper, Bañados, Teitelboim and Zanelli (BTZ) proposed a simple charged generalization of what is now known as the spinning BTZ black hole, the proposal being that a rotating metric can be supported by a 'static vector' potential. While with such an ansatz the Einstein equations are satisfied, and the corresponding energy-momentum tensor is divergence-less, the Maxwell equations do not (due to the special degenerate form of the corresponding field strength) hold. More recently, Deshpande and Lunin have proposed a generalized 'Einstein–Maxwell' system that yields analytic rotating black holes in all odd dimensions. In this paper, we show that the original charged BTZ solution can be re-interpreted as a solution of the Deshpande–Lunin theory. Moreover, as we shall explicitly illustrate on an example of regularized conformal electrodynamics, a similar construction also works for any non-linear electrodynamics in 3-dimensions. At the same time, all these spacetimes represent self-gravitating solutions of (non-linear electrodynamics generalized) force-free electrodynamics.

Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional configuration space of a single 'atom' of geometry). Group field theory models can be seen as an extension of matrix and tensor models by additional data, and are traditionally defined through a functional integral whose perturbative expansion generates a sum over discrete geometries. More recently, some efforts have been directed towards formulations of group field theory based on a Hilbert space and operators, in particular in applications to cosmology. This is an attempt to review some of these formulations and their main ideas, to disentangle these constructions as much as possible from applications and phenomenology, and to put them into a wider context of quantum gravity research.

The unification of quantum mechanics and general relativity has long been elusive. Only recently have empirical predictions of various possible theories of quantum gravity been put to test, where a clear signal of quantum properties of gravity is still missing. The dawn of multi-messenger high-energy astrophysics has been tremendously beneficial, as it allows us to study particles with much higher energies and travelling much longer distances than possible in terrestrial experiments, but more progress is needed on several fronts. A thorough appraisal of current strategies and experimental frameworks, regarding quantum gravity phenomenology, is provided here. Our aim is twofold: a description of tentative multimessenger explorations, plus a focus on future detection experiments. As the outlook of the network of researchers that formed through the COST Action CA18108 'Quantum gravity phenomenology in the multi-messenger approach (QG-MM)', in this work we give an overview of the desiderata that future theoretical frameworks, observational facilities, and data-sharing policies should satisfy in order to advance the cause of quantum gravity phenomenology.

Rotating and oscillating neutron stars can give rise to long-lived Continuous Gravitational Waves (CGWs). Despite many years of searching, the detection of such a CGW signal remains elusive. In this article we describe the main astrophysical uncertainties regarding such emission, and their relation to the behaviour of matter at extremely high density. We describe the main challenges in searching for CGWs, and the prospects of detecting them using third-generation gravitational wave detectors. We end by describing some pressing issues in the field, whose resolution would help turn the detection and exploitation of CGWs into reality.

We review the status of mathematical research on the dynamical properties of relativistic fluids in cosmological spacetimes–both, in the presence of gravitational backreaction as well as the evolution on fixed cosmological backgrounds. We focus in particular on the phenomenon of fluid stabilization, which describes the taming effect of spacetime expansion on the fluid. While fluids are in general known to form shocks from regular initial data, spacetime expansion has been found to suppress this behaviour. During the last decade, various rigorous results on this problem have been put forward. We review these results, the mathematical methods involved and provide an outlook on open questions.

Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe.

The public release of data from the LIGO and Virgo detectors has enabled the identification of potential gravitational wave signals by independent teams using alternative methodologies.
In addition to the LIGO-Virgo-KAGRA (LVK) collaboration's GWTC-3 catalogue there have been several additional works claiming the detection of signals in the data from the first three observing runs.
In this paper we present an analysis of these new signals using the same analysis workflow which was used to generate the GWTC-2.1 and GWTC-3 catalogues published by the LVK, matching the analysis configuration as closely as possible, and we provide our parameter estimation results in a format comparable to those of the GWTC-3 data release \add{for 57 events not previously analysed in LVK analyses. We find our results to be broadly consistent with those published by other groups}.
We also include a discussion of the workflow developed for this analysis.

In this paper, we describe the Multi-Band Template Analysis (MBTA) search pipeline dedicated to the detection of compact binary coalescence (CBC) gravitational wave signals from the data obtained by the LIGO-Virgo-KAGRA collaboration (LVK) during the fourth observing run (O4), which started in May 2023. We give details on the configuration of the pipeline and its evolution compared to the third observing run (O3). We focus here on the configuration used for the offline results of the first part of the run (O4a), which are part of the GWTC-4 catalog (in preparation). We also give a brief summary of the online configuration and highlight some of the changes implemented or considered for the second part of O4 (O4b).

We develop and characterize a parameter estimation methodology for rotating core collapse supernovae based on the gravitational wave core bounce phase and real detector noise. Expanding on the evidence from numerical simulations for the deterministic nature of this gravitational wave emission and about the dependence on the ratio $\beta$ between rotational kinetic to potential energy, we propose an analytical model for the core bounce component which depends on $\beta$ and one phenomenological parameter. We validate the goodness of the model with a pool of representative waveforms. We use the fitting factor adopted in compact coalescing binary searches as a metric to quantify the goodness of the analytical model and the template bank generated by the model presents an average accuracy of 94.4\% when compared with the numerical simulations and is used as the basis for the work. The error for a matched filter frequentist parameter estimation of $\beta$ is evaluated. The results obtained considering real interferometric noise and a waveform at a distance of 10 kpc and optimal orientation, for one standard deviation estimation error of the rotation parameter \(\beta\) lie in the range of \(10^{-2}\) to \(10^{-3}\) as \(\beta\) increases. The results are also compared to the scenario where Gaussian recolored data is employed. The analytical model also allows for the first time, to compute theoretical minima in the error for $\beta$ for any type of estimator. Our analysis indicates that the presence of rotation would be detectable at 0.5 Mpc for third generation interferometers like CE or ET.

We investigate the properties of a charged rotating black string immersed in a Kiselev anisotropic fluid in anti-de Sitter (AdS) spacetime. The Einstein-Maxwell equations with an anisotropic stress-energy tensor and cosmological constant are analyzed and solved exactly. In this work, we calculate the Kretschmann scalar, obtaining a consistent result that agrees with the existing literature in the absence of charge and fluid. The rotating solution is obtained by applying a coordinate transformation on time and angular coordinates. The event horizon associated with specific values of the equation of state parameter $w_q$ is studied. The results show an important influence of the fluid parameters $N_{q}$ and $ w_{q}$ , the charge parameter $Q$ , and the rotation parameter $a$ on the size of the black string horizon. In addition, we determine the conditions for the existence of closed timelike curves (CTCs) and compute the conserved charges, such as mass, angular momentum, and electric charge of the black string. Utilizing the Klein-Gordon equation, we employ the quantum particle tunneling approach to obtain the probability of charged scalar particles tunneling across the event horizon. We obtain the correspondent Hawking temperature as a consequence. Furthermore, we examine the thermodynamic properties, including entropy and heat capacity, to assess the effects of the quintessence field and charge on the black string. The results include particular cases such as the Lemos black string, providing a broader view of black string configurations in AdS spacetime.

In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective canonical models. While the main purpose is to test models obtained in Loop Quantum Gravity, the criterion is not limited to those physical systems and may be applied to any canonically formulated modified theory of gravity. The approach here is hence not that of finding an effective model, but rather to examine a given one represented by a quantum corrected Hamiltonian. Specifically, we will apply the criterion to spherically symmetric spacetimes in vacuum with inverse triad and holonomy modifications that arise as a consequence of the loop quantization procedure. It is found that, in addition to the initial modifications of the Hamiltonian, quantum corrections of the classical metric itself are needed as well in order to obtain generally covariant models. A comparison with recent alternative criteria is included in the discussion.

In this article we examine a Hamiltonian constraint operator governing the dynamics of simple quantum states, whose graph consists of a single six-valent vertex, in quantum-reduced loop gravity. To this end, we first derive the action of the Hamiltonian constraint on generic basis states in the Hilbert space of quantum-reduced loop gravity. Specializing to the example of the single-vertex states, we find that the Euclidean part of the Hamiltonian bears a close formal similarity to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. Extending the formal analogy to the Lorentzian part of the Hamiltonian suggests a possible modified definition of the Hamiltonian constraint for loop quantum cosmology, in which the Lorentzian part, corresponding to the scalar curvature of the spatial surfaces, is not assumed to be identically vanishing, and is represented by a non-trivial operator in the quantum theory.

The public release of data from the LIGO and Virgo detectors has enabled the identification of potential gravitational wave signals by independent teams using alternative methodologies.
In addition to the LIGO-Virgo-KAGRA (LVK) collaboration's GWTC-3 catalogue there have been several additional works claiming the detection of signals in the data from the first three observing runs.
In this paper we present an analysis of these new signals using the same analysis workflow which was used to generate the GWTC-2.1 and GWTC-3 catalogues published by the LVK, matching the analysis configuration as closely as possible, and we provide our parameter estimation results in a format comparable to those of the GWTC-3 data release \add{for 57 events not previously analysed in LVK analyses. We find our results to be broadly consistent with those published by other groups}.
We also include a discussion of the workflow developed for this analysis.

We examine Friedmann–Lemaître–Robertson–Walker cosmology, incorporating quantum gravitational corrections through the functional renormalisation group flow of the effective action for gravity. We solve the Einstein equation with quantum improved coupling perturbatively including the case with non-vanishing classical cosmological constant (CC) which was overlooked in the literatures. We discuss what is the suitable identification of the momentum cutoff k with time scale, and find that the choice of the Hubble parameter is suitable for vanishing CC but not so for non-vanishing CC. We suggest suitable identification in this case. The energy-scale dependent running coupling breaks the time translation symmetry and then introduces a new physical scale.

In recent years there have been many studies on exactly solvable black hole mergers, based on a model by Emparan and Martínez where the mass of one black hole is blown up to infinity (Emparan and Martínez 2016 Class. Quantum Grav.33 155003). Here we replace the large black hole by a cosmological horizon, and study how it merges with a black hole in the Schwarzschild-de Sitter spacetime by considering an observer positioned at future null infinity. We describe the geometry of the horizon over time, including the role that caustics play in the merger process, and also examine the growth of the horizon area. We argue that in the limit of zero cosmological constant, the system reduces to the Emparan-Martínez Schwarzschild merger. This allows us to regularize the increase in the area during the merger, which otherwise diverges.

In their seminal 1992 paper, Bañados, Teitelboim and Zanelli (BTZ) proposed a simple charged generalization of what is now known as the spinning BTZ black hole, the proposal being that a rotating metric can be supported by a 'static vector' potential. While with such an ansatz the Einstein equations are satisfied, and the corresponding energy-momentum tensor is divergence-less, the Maxwell equations do not (due to the special degenerate form of the corresponding field strength) hold. More recently, Deshpande and Lunin have proposed a generalized 'Einstein–Maxwell' system that yields analytic rotating black holes in all odd dimensions. In this paper, we show that the original charged BTZ solution can be re-interpreted as a solution of the Deshpande–Lunin theory. Moreover, as we shall explicitly illustrate on an example of regularized conformal electrodynamics, a similar construction also works for any non-linear electrodynamics in 3-dimensions. At the same time, all these spacetimes represent self-gravitating solutions of (non-linear electrodynamics generalized) force-free electrodynamics.

In this work we introduce a criterion for testing general covariance in effective quantum gravity theories. It adapts the analysis of invariance under general spacetime diffeomorphisms of the Einstein-Hilbert action to the case of effective canonical models. While the main purpose is to test models obtained in Loop Quantum Gravity, the criterion is not limited to those physical systems and may be applied to any canonically formulated modified theory of gravity. The approach here is hence not that of finding an effective model, but rather to examine a given one represented by a quantum corrected Hamiltonian. Specifically, we will apply the criterion to spherically symmetric spacetimes in vacuum with inverse triad and holonomy modifications that arise as a consequence of the loop quantization procedure. It is found that, in addition to the initial modifications of the Hamiltonian, quantum corrections of the classical metric itself are needed as well in order to obtain generally covariant models. A comparison with recent alternative criteria is included in the discussion.

A Wick rotation in the lapse (not in time) is introduced that interpolates between Riemannian and Lorentzian metrics on real manifolds admitting a codimension-one foliation. The definition refers to a fiducial foliation but covariance under foliation changing diffeomorphisms can be rendered explicit in a reformulation as a rank one perturbation. Applied to scalar field theories a Lorentzian signature action develops a positive imaginary part thereby identifying the underlying complex metric as 'admissible'. This admissibility is ensured in non-fiducial foliations in technically distinct ways also for the variation with respect to the metric and for the Hessian. The Hessian of the Wick rotated action is a complex combination of a generalized Laplacian and a d'Alembertian, which is shown to have spectrum contained in a wedge of the upper complex half plane. Specialized to near Minkowski space the induced propagator differs from the one with the Feynman $i\epsilon$ prescription and on Friedmann-Lemaître backgrounds the difference to a Wick rotation in time is illustrated.

We provide a characterisation of the Kerr spacetime close to future null infinity using the asymptotic characteristic initial value problem in a conformally compactified spacetime. Stewart's gauge is used to set up the past-oriented characteristic initial value problem. By a theorem of M. Mars characterising the Kerr spacetime, we provide conditions for the existence of an asymptotically timelike Killing vector on the development of the initial data by demanding that the spacetime is endowed with a Killing spinor. The conditions on the characteristic initial data ensuring the existence of a Killing spinor are, in turn, analysed. Finally, we write the conditions on the initial data in terms of the free data in the characteristic initial value problem. As a result, we characterise the Kerr spacetime using only a section of future null infinity and its intersection with an outgoing null hypersurface.

Third generation ground-based gravitational wave detectors are proposing the use of cryogenics. The low-temperature regime will require a cooling-down system capable of removing heat from test masses and maintaining its low temperature. The present study analyzes the Newtonian noise introduced by rotating impellers used in a cooling-down system with sub-cooled nitrogen circulating in a loop. In order to calculate this noise, a computational model was developed and the results were compared to the LIGO Voyager and Cosmic Explorer design sensitivity curves. For a system using two impellers having three blades each, the model shows that this Newtonian noise is always below the sensitivity curve if their distance to the test mass center is greater than 2.3 m for LIGO Voyager and 2.4 m for Cosmic Explorer. In addition, our calculations showed zero noise values for specific impeller's locations, depending on the blade number. This revealed a new region where it is possible to minimize the noise.

We construct an effective cosmological spin-foam model for a $(2+1)$ dimensional spatially flat Universe, discretized on a cubical lattice, containing both space- and time-like regions. Our starting point is the recently proposed coherent state spin-foam model for (2+1) Lorentzian quantum gravity. The full amplitude is assumed to factorize into single vertex amplitudes with boundary data corresponding to Lorentzian 3-frusta. A stationary phase approximation is performed at each vertex individually, where the inverse square root of the Hessian determinant serves as a measure for the effective path integral. Additionally, a massive scalar field is coupled to the geometry, and we show that its mass renders the partition function convergent. For a single 3-frustum with time-like struts, we compute the expectation value of the bulk strut length and show that it generically agrees with the classical solutions and that it is a discontinuous function of the scalar field mass. Allowing the struts to be space-like introduces causality violations, which drive the expectation values away from the classical solutions due to the lack of an exponential suppression of these configurations. This is a direct consequence of the semi-classical amplitude only containing the real part of deficit angles, in contrast with the Lorentzian Regge action used in effective spin-foams. We give an outlook on how to evaluate the partition function on an extended discretization including a bulk spatial slice. This serves as a foundation for future investigations of physically interesting scenarios such as a quantum bounce or the viability of massive scalar field clocks. Our results demonstrate that the effective path integral in the causally regular sector serves as a viable quantum cosmology model, but that the agreement of expectation values with classical solutions is tightly bound to the path integral measure.