General Relativity and Quantum Cosmology (gr-qc)

Abstract: In the framework of metric-affine gravity, we consider the role of the boundary term in Symmetric Teleparallel Gravity assuming $f(Q,B)$ models where $f$ is a smooth function of the non-metricity scalar $Q$ and the related boundary term $B$. Starting from a variational approach, we derive the field equations and compare them with respect to those of $f(Q)$ gravity in the limit of $B\to0$. It is possible to show that $f(Q,B)=f(Q-B)$ models are dynamically equivalent to $f(R)$ gravity as in the case of teleparallel $f(\tilde{B}-T)$ gravity (where $B\neq \tilde{B}$). Furtherrmore, conservation laws are derived. In this perspective, considering boundary terms in $ f(Q)$ gravity represents the last ingredient towards the Extended Geometric Trinity of Gravity where $f(R)$, $f(T,\tilde{B})$ and $f(Q,B)$ can be dealt under the same standard.

Abstract: Current searches for signals of departures from the fundamental symmetries of General Relativity using gravitational waves are largely dominated by propagation effects like dispersion and birefringence from highly dynamic sources such as coalescing binary-black holes and neutron stars. In this paper we take steps towards probing the nature of spacetime symmetries in the generation stage of gravitational waves; by using a generic effective-field theory, we solve the modified Einstein equations order-by-order for a generic source, and we write down the the first Post-Newtonian corrections, which includes contributions from the spacetime-symmetry breaking terms. Choosing as the source a system of point particles allows us to write down a simple toy solution explicitly, and we see that in contrast to General Relativity, the monopolar and dipolar contributions are non-vanishing. We comment on the detectability of such signals by the Laser Interferometer Space Antenna (LISA) space mission, which has high signal-to-noise galactic binaries (which can be modelled as point particles) well inside its predicted sensitivity band, sources which are inaccessible for current ground-based detectors, and we also discuss the possibility of going beyond the quadrupole formula and the first Post-Newtonian order, which would reveal effects which could be probed by ground-based detectors observing coalescence events.

Abstract: An effective field theory framework is used to investigate some Lorentz-violating effects on the generation of electromagnetic and gravitational waves, complementing previous work on propagation. Specifically we find solutions to a modified, anisotropic wave equation, sourced by charged or fluid matter. We derive the radiation fields for scalars, classical electromagnetic radiation, and partial results for gravitational radiation. For gravitational waves, the results show longitudinal and trace polarizations proportional to coefficients for spacetime-symmetry breaking.

Abstract: We present a rapid parameter estimation framework for compact binary coalescence (CBC) signals observed by the LIGO-Virgo-KAGRA (LVK) detector network. The goal of our framework is to enable optimal source localization of binary neutron star (BNS) signals in low latency, as well as improve the overall scalability of full CBC parameter estimation analyses. Our framework is based on the reduced order quadrature (ROQ) technique, and resolves its shortcomings by utilizing multiple ROQ bases in a single parameter estimation run. We have also developed sets of compact ROQ bases for various waveform models, IMRPhenomD, IMRPhenomPv2, IMRPhenomPv2$\_$NRTidalv2, and IMRPhenomXPHM. We benchmark our framework with hundreds of simulated observations of BNS signals by the LIGO-Virgo detector network, and demonstrate that it provides accurate and unbiased estimates on BNS source location, with a median analysis time of $6$ minutes. The median searched area is reduced by around 30$\%$ compared to estimates produced by BAYESTAR: from $21.8\,\mathrm{deg^2}$ to $16.6\,\mathrm{deg^2}$. Our framework also enables detailed parameter estimation taking into account gravitational-wave higher multipole moments, the tidal deformation of colliding objects, and detector calibration errors of amplitude and phase with the time scale of hours. Our rapid parameter estimation technique has been implemented in one of the LVK parameter estimation engines, BILBY, and is being employed by the automated parameter estimation analysis of the LVK alert system.

Abstract: Standard General Relativity assumes that, in the absence of classical matter sources, spacetime is empty. This chapter considers and analyses the new behaviours of the gravitational field that appear when one substitutes this emptiness by a reactive vacuum, stemming in particular from the idea of vacuum provided by quantum field theory. We restrict our study to spherically symmetric configurations, and take a simple free quantum scalar field as a proxy to more complicated formulations. Our analysis is split into a study of static and of dynamical configurations. Under the assumption of staticity, we find and describe the different asymptotically flat self-consistent solutions that appear when using a vacuum Renormalised Stress-Energy Tensor (RSET) as an additional source in the Einstein equations. Of particular interest is the discovery that, as opposed to standard general relativity, the new theory naturally contains static ultracompact stellar configurations which could observationally be mistaken for black holes (BHs). Then, in our study of dynamical configurations, we investigate the possibility of these same vacuum effects changing the internal gravitational processes after an initial gravitational collapse in a way which shows a path towards forming the aforementioned ultracompact configurations. This has lead us to analyse several dynamical situations seldom contemplated in the literature. Of special relevance, we find that the inner horizon that all realistic BHs should contain could inflate outwards quickly enough to meet the outer one before any appreciable Hawking evaporation has taken place.

Abstract: The Einstein Equivalence Principle (EEP) is a cornerstone of general relativity and predicts the existence of gravitational redshift. We report on new results of measuring this shift with RadioAstron (RA), a space VLBI spacecraft launched into an evolving high eccentricity orbit around Earth with geocentric distances reaching 353,000 km. The spacecraft and ground tracking stations at Pushchino, Russia, and Green Bank, USA, were each equipped with a hydrogen maser frequency standard allowing a possible violation of the predicted gravitational redshift, in the form of a violation parameter $\varepsilon$, to be measured. By alternating between RadioAstron's frequency referencing modes during dedicated sessions between 2015 and 2017, the recorded downlink frequencies can essentially be corrected for the non-relativistic Doppler shift. We report on an analysis using the Doppler-tracking frequency measurements made during these sessions and find $\varepsilon = (2.1 \pm 3.3)\times10^{-4}$. We also discuss prospects for measuring $\varepsilon$ with a significantly smaller uncertainty using instead the time-domain recordings of the spacecraft signals and envision how $10^{-7}$ might be possible for a future space VLBI mission.

Abstract: We construct novel scalarized black hole (BH) solutions beyond the general relativity (GR) framework. These scalarized BH solutions are extended from the Schwarzschild one and the non-Schwarzschild one in the pure Einstein-Weyl gravity. By studying the BH entropy and free energy, we demonstrate that the scalarized BH extending from the Schwarzschild one exhibits thermodynamically preferred. We obtain these novel solutions by directly solving the full fourth-order equations of motion. This narrows the problematic solution space obtained by commonly adopted second-order reduction to physically valid spaces. Our findings also unveil the evasion of the no-hair theorem within the realm of higher-derivative gravity.

Abstract: Quantum gravity theories predict deformations of black hole solutions relative to their classical counterparts. A model-independent approach was advocated in \cite{Binetti:2022xdi} that uses metric deformations parametrised in terms of physical quantities, such as the proper distance. While such a description manifestly preserves the invariance of the space-time under coordinate transformations, concrete computations are hard to tackle since the distance is defined in terms of the deformed metric itself. In this work, for spherically symmetric and static metrics, we provide a self-consistent framework allowing us to compute the distance function in close vicinity to the event horizon of a black hole. By assuming a minimal degree of regularity at the horizon, we provide explicit (series) expansions of the metric. This allows us to compute important thermodynamical quantities of the black hole, such as the Hawking temperature and entropy, for which we provide model-independent expressions, beyond a large mass expansion. Moreover, imposing for example the absence of curvature singularities at the event horizon leads to non-trivial consistency conditions for the metric deformations themselves, which we find to be violated by some models in the literature.

Abstract: In a recent series of papers, new exact analytical solutions to field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been displayed. This work is currently extended to the case of differentially rotating irrotational fluids. The results are presented in a new series of papers considering, in turn, a perfect fluid source, arXiv:2305.11565 [gr-qc], as well as the three anisotropic pressure cases already studied in the rigidly rotating configuration. The axially directed pressure case has already been developed in arXiv:2307.07263. Here, a fluid with an azimuthally directed pressure is considered. A general method for generating the corresponding new mathematical solutions to the field equations when the ratio $h=$pressure/energy density varies with the radial coordinate is proposed, and a class of solutions exemplifying this recipe is derived. Then, the case where $h=const.$ is solved. It splits into two subclasses depending on the value of $h$. The mathematical and physical properties of these three classes are analyzed which provides some constraints on $h$, different for each class and subclass. Their matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed. A comparison with the rigidly rotating fluid case is provided.

Abstract: In this paper, the structure of a dark matter halo can be well described by the mass model of M87 and the Einasto profile for the cold dark matter model, i.e., $\rho_{\text{halo}} (r)=\rho_e \exp ( -2 \alpha ^{-1} ((r/r_e)^\alpha -1 ) )$ [J. Wang et al., Nature, 585, 39-42 (2020)]. Under these conditions, we construct a solution of a static spherically symmetric black hole in a dark matter halo. Then, using the Newman-janis algorithm, we extend this static solution to the case of rotation, and obtain a solution for the Kerr-like black hole. We prove that this solution of the Kerr-like black hole is indeed a solution to the Einstein field equations. Finally, taking M87 as an example, we study and analyze some physical properties of this Kerr-like black hole, and then compare them with the Kerr black hole. These research results for the black hole in a dark matter halo may indirectly provide an effective method for detecting the existence of dark matter.

Abstract: We consider a class of three parameter static and axially symmetric metrics that reduce to the Janis-Newman-Winicour (JNW) and $ \gamma$-metrics in certain limits of the parameters. We obtain rotating form of the metrics that are asymptotically flat, stationary and axisymmetric. In certain values of the parameters, the solutions represent the rotating JNW metric, rotating $ \gamma$-metric and Bogush-Gal'tsov (BG) metric. The singularities of rotating metrics are investigated. Using the light-ring method, we obtain the quasi normal modes (QNMs) related to rotating metrics in the eikonal limit. Finally, we investigate the precession frequency of a test gyroscope in the presence of the rotating metrics.

Abstract: Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can comprehensively address the quantum-to-classical transition problem in the leading order of curvature perturbations. To this end, we test spatial bipartitions of quadratic systems for the interplay between three different signatures of classical behavior : i) decoherence, ii) peaking of the Wigner function about classical trajectories, and iii) relative suppression of non-commutativity in observables. We extract these signatures from the covariance matrix of a multi-mode Gaussian state and address them primarily in terms of entanglement entropy and log-classicality. Through a phase-space stability analysis of spatial sub-regions via their reduced Wigner function, we ascertain that the underlying cause for the dominance of classicality signatures is the occurrence of gapped inverted mode instabilities. While the choice of conjugate variables enhances some of these signatures, decoherence studied via entanglement entropy is the stronger and more reliable condition for classicality to emerge. We demonstrate the absence of decoherence, which preempts a quantum-to-classical transition of scalar fluctuations in an expanding background in $(1+1)$-dimensions using two examples : i) a Tanh-like expansion and ii) a de-Sitter expansion. We then extend the analysis to leading order fluctuations in $(3+1)-$dimensions to show that a quantum-to-classical transition occurs in the de-Sitter expansion and discuss the relevance of our analysis in distinguishing cosmological models.

Abstract: We investigate the effects of external torsion fields on ideal gases and Fermi gases, and derive a macroscopic quantity, which we call torsion susceptibility. We first consider the Dirac fermions in the Riemann-Cartan spacetime minimally coupled to the background torsion and electromagnetic fields. After applying the Foldy-Wouthuysen transformation, Hamiltonian of a spin-1/2 particle in weak field limit is obtained. The coupling of spin and spatial components of axial torsion vector has a Zeeman-like effect, which removes the degeneracy of energy levels and splits the energy levels with respect to the spin. We calculate the macroscopic effects of the spin-torsion coupling on ideal gases, which satisfying the Boltzmann distribution, and Fermi gases, which satisfying the Fermi-Dirac distribution. The torsion susceptibility of ideal gases is inversely proportional to the temperature and is constant in Fermi gases.