Properties Of Spacetime Research Articles

The Penrose limit of the Weyl double copy

Abstract We embed the Penrose limit into the Weyl classical double copy. Thereby, we provide a lift of the double copy properties of plane wave spacetimes into black hole geometries and we open a novel avenue towards taking the classical double copy beyond statements about algebraically special backgrounds. In particular, the Penrose limit, viewed as the leading order Fermi coordinate expansion around a null geodesic, complements approaches leveraging asymptotic flatness such as the asymptotic Weyl double copy. Along the way, we show how our embedding of the Penrose limit within the Weyl double copy naturally fixes the functional ambiguity in the double copy for Petrov type N spacetimes. We also highlight the utility of a spinorial approach to the Penrose limit. In particular, we use this spinorial approach to derive a simple analytical expression for arbitrary Penrose limits of four-dimensional, vacuum type D spacetimes.

Studying the Properties of Spacetime with an Improved Dynamical Model of the Inner Solar System

Physical properties of the Sun (orientation of rotation axis, oblateness coefficient J2⊙, and change rate of the gravitational parameter μ˙⊙) are determined using a dynamical model describing the motion of the Sun, planets, the Moon, asteroids, and Trans-Neptunian objects (TNOs). Among the many kinds of observations used to determine the orbits and physical properties of the bodies, the most important for our study are precise interplanetary ranging data: Earth–Mercury ranges from MESSENGER spacecraft and Earth–Mars ranges from Odyssey and MRO. The findings allow us to improve the model of the Sun in modern planetary ephemerides. First, the dynamically determined direction of the Sun’s pole is ≈2° off the visible axis of rotation of the Sun’s surface, which is corroborated by present knowledge of the Sun’s interior. Second, the change rate of the Sun’s gravitational parameter is found to be smaller (in absolute value) than the nominal value derived from the estimate of mass loss through radiation and solar wind. Possible interpretations are discussed.

Quantum nature of black hole and the superposition of fermionic field

The operational framework for the superposition of spacetime is fundamentally important in developing a comprehensive description of quantum gravity (Foo et al. in Phys Rev Lett 129:181301, 2022). As a “bottom-up” unifying theory of quantum gravity, it allows us to investigate how mass superposition of spacetime influences the performance of quantum information processing. In this paper, we study how the quantum-gravitational effects produced by the mass superposition of a black hole influence the quantum coherence of fermionic fields. It is shown that the spacetime effects associated with a classical black hole lead to inevitable decoherence. Notably, compared to classical black hole spacetime scenarios, fermionic fields near a black hole with superposed masses can retain more quantum coherence. This suggests that the quantum properties of spacetime may serve as resources to mitigate coherent degradation caused by gravitational effects. The bottom-up perspective on spacetime superposition proposed in this work serves as an indication of quantum-gravitational effects and holds significant theoretical implications.

On spacetimes with a semi-symmetric recurrent metric connection

In this paper, we deal with spacetimes allowing a semi-symmetric connection whose metric tensor is recurrent. We investigate the impact of this connection on spacetimes and establish a nontrivial example. We physically explain the properties of spacetime that we obtained. Under a certain condition, we demostrate that a spacetime admitting such a connection becomes the GRW spacetime as well as the anti-de Sitter and represents the dark matter era. Finally, we scrutinize in case such a spacetime admits a Ricci soliton and generalized Ricci soliton.

Non-linear charged dS spacetime and its thermodynamics and Schottky Anomaly

Abstract In this paper, firstly, the conditions and existence region for the coexistence of the black hole and cosmological horizons in Non-linear charged dS (NLC-dS) spacetime are discussed, subsequently, the thermodynamic quantities for which the boundary conditions are satisfied in spacetime in the coexistence region of the two horizons are discussed, and the effective thermodynamic quantities in the NLC-dS spacetime in the coexistence region with two horizons are presented. Based on these, the heat capacity in the coexistence region with two horizons is addressed, the behavior of the heat capacity in the NLC-dS spacetime in the aforementioned region is found to exhibit the characteristics of Schottky specific heat. In order to investigate the intrinsic reason of the heat capacity in spacetime, regarding the two horizons in the NLC-dS spacetime as two distinct energy levels, consequently, the microscopic particles at different horizons exhibit disparate energies. Using the heat capacity relationship between the two-energy level in an ordinary thermodynamic system, the heat capacity in dS spacetime is discussed, it is observed that the behavior of the heat capacity is analogous to that of the two-energy levels in an ordinary thermodynamic system. The number of microscopic particles in the two-level system is approximated by comparing the maximum value of the heat capacity of the system with the maximum value obtained by treating the two horizons in the NLC-dS spacetime as a two-energy-level system of two distinct energies. This conclusion reflects the quantum properties of the coexistence region with two horizons in the NLC-dS spacetime. It provides a new avenue for further study of the thermodynamic properties of black holes and the quantum properties of de Sitter spacetime.

Shadow of rotating black holes surrounded by dark fluid with Chaplygin-like equation of state and constraints from EHT results

Abstract The present work is devoted to testing spacetime properties around black holes surrounded by a dark fluid that are candidates for dark energy, which can be described by the Chaplygin-like equation of state through its shadow. To do this, we first study the horizon structure of the black hole and its shadow. Then, we obtain a rotating black hole solution in the presence of a dark fluid using the generalized Newman-Janis algorithm and study the effects of the black hole spin and the fluid parameters on the black hole horizons. Also, we obtain the shadow cast of the rotating black hole using celestial coordinates and have shown that the presence of the dark fluid causes an increase in shadow size. Moreover, we also obtain constraints on the spin and black hole charge together with the dark fluid parameters using the shadow size of supermassive black holes Sagittarius A* and M87* from Event Horizon Telescope observations. Finally, we also investigate the energy emission rate of the charged black hole surrounded by a Chaplygin-like dark fluid compared to both rotating and nonrotating cases.

Localization–delocalization transition for light particles in turbulence

Small bubbles in fluids rise to the surface due to Archimede's force. Remarkably, in turbulent flows this process is severely hindered by the presence of vortex filaments, which act as moving potential wells, dynamically trapping light particles and bubbles. Quantifying the statistical weights and roles of vortex filaments in turbulence is, however, still an outstanding experimental and computational challenge due to their small scale, fast chaotic motion, and transient nature. Here we show that, under the influence of a modulated oscillatory forcing, the collective bubble behavior switches from a dynamically localized to a delocalized state. Additionally, we find that by varying the forcing frequency and amplitude, a remarkable resonant phenomenon between light particles and small-scale vortex filaments emerges, likening particle behavior to a forced damped oscillator. We discuss how these externally actuated bubbles can be used as a type of microscopic probe to investigate the space-time statistical properties of the smallest turbulence scales, allowing to quantitatively measure physical characteristics of vortex filaments. We develop a superposition model that is in excellent agreement with the simulation data of the particle dynamics which reveals the fraction of localized/delocalized particles as well as characteristics of the potential landscape induced by vortices in turbulence. Our approach paves the way for innovative ways to accurately measure turbulent properties and to the possibility to control light particles and bubble motions in turbulence with potential applications to oceanography, medical imaging, drug/gene delivery, chemical reactions, wastewater treatment, and industrial mixing.

Emergence of negative mass in general relativity

We investigate a symmetric traversable wormhole model, integrating Einstein’s gravitational coupling phantom field and a nonlinear electromagnetic field. This work indicates the emergence of negative ADM mass within a specific parameter range, coinciding with distinct alterations in the wormhole’s spacetime properties. Despite violating the Null Energy Condition (NEC) and other energy conditions, the solution exhibits unique characteristics in certain energy-momentum tensor components, potentially accounting for the manifestation of negative mass.

Observation of thermal transport close to diffusive in a weak long-ranged Fermi-Pasta-Ulam-Tsingou-type model

We explore thermal transport in a one-dimensional Fermi-Pasta-Ulam-Tsingou-type (FPUT-type) system with long-range (LR) interactions. In such a system, the harmonic part of the potential is nearest-neighbor coupled, while the strength of the quartic part of the potential between two lattice sites decays as a power σ of the inverse of their distance, demonstrating the LR feature of the system. The relevant strong LR model (0≤σ≤1) has been considered in detail in our recent study [Xiong and Wang, ], and here, we focus on the weak LR regime (1≤σ≤3). We show that the thermal transport behaviors in this regime are quite unexpected. We discovered a subregime (1≤σ≤1.5) wherein the thermal transport behaviors are very close to diffusive. This suggests that even a momentum-conserving system with appropriate LR interactions can still exhibit normal heat conduction. By meticulously analyzing the space-time scaling properties of equilibrium heat correlations, we also determine the center of this diffusive thermal transport at approximately σ≃1.25. These discoveries, together with our prior results, provide a comprehensive understanding of thermal transport of this kind of LR-FPUT-type model. Published by the American Physical Society 2024

Higher-dimensional topological dS black hole with a nonlinear source and its thermodynamics and phase transitions

In this paper, the higher-dimensional topological dS black hole with a nonlinear source (HDTNS) is considered. First, we obtain the thermodynamic quantities of the (n+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n+1$$\\end{document})-dimensional topological dS black hole, which satisfy the first law of thermodynamics. Second, based on the effective thermodynamic quantities and Maxwell’s equal-area law method, we explore the phase equilibrium for the HDTNS. The boundary of the two-phase coexistence region in the Peff0-Teff0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\ extrm{eff}^{0}-T_\ extrm{eff}^{0}$$\\end{document} diagram is obtained. The critical thermodynamic quantities as well as the horizon potential are also investigated. Furthermore, we analyze the effect of parameters (the spacetime dimension n and the ratio of two horizon radii x=r+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$x= {r_{+}}$$\\end{document}/rc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {r_{c}}$$\\end{document}) on the boundary of the two-phase coexistence region and study the latent heat of phase transition for this system, which corresponds to the Clapeyron equation. The results indicate that the phase transition in HDTNS spacetime is analogous to that in a van der Waals (vdW) fluid system, which is determined by electrical potential at the horizon. These results help to understand the fundamental properties of black holes. A more intuitive and profound understanding of gravity is gained by studying the thermodynamic properties of different spacetimes. They provide a theoretical basis for an in-depth study of the classical and quantum properties of de Sitter spacetime and its evolution.

Probing black holes in a dark matter spike of M87 using quasinormal modes

Dark matter density can be significantly enhanced by the supermassive black hole at the galactic center, leading to a structure called dark matter spike. Dark matter spike may change the spacetime properties of black holes that constitute deviations from GR black holes. Based on these interesting background, we construct a set of solutions of black holes in a dark matter spike under the Newtonian approximation and full relativity. Combining the mass model of M87, we study the quasinormal modes of black holes in the scalar field and axial gravitational perturbation, then compared them with Schwarzschild black hole. Besides, the impacts of dark matter on the quasinormal mode of black holes have been studied in depth. In particular, in the axial gravitational perturbation, our results show that the impacts of dark matter spike on the quasinormal mode of black holes can reach up to 10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-4}$$\\end{document}. These new features from quasinormal mode of black holes under the Newtonian approximation and full relativity may provide some help for the establishment of the final dark matter model, and provide a new thought for the indirect detection of dark matter.

Scalar curvature for metric spaces: Defining curvature for quantum gravity without coordinates

Geometrical properties of spacetime are difficult to study in nonperturbative approaches to quantum gravity like causal dynamical triangulations (CDT), where one uses simplicial manifolds to define the gravitational path integral, instead of Riemannian manifolds. In particular, in CDT one only relies on two mathematical tools, a distance measure and a volume measure. In this paper, we define a notion of scalar curvature, for metric spaces endowed with a volume measure or a random walk, without assuming nor using notions of tensor calculus. Furthermore, we directly define the Ricci scalar, without the need of defining and computing the Riemann or the Ricci tensor . For this, we make use of quantities, like the surface of a geodesic sphere, or the return probability of scalar diffusion processes, that can be computed in these metric spaces, as in a Riemannian manifold, where they receive scalar curvature contributions. Our definitions recover the classical results of scalar curvature when the sets are Riemannian manifolds. We propose two methods to compute the scalar curvature in these spaces, and we compare their features in natural implementations in discrete spaces. The defined generalized scalar curvatures are easily implemented on discrete spaces, like graphs. We present the results of our definitions on random triangulations of a 2D sphere and plane. Additionally, we show the results of our generalized scalar curvatures on the quantum geometries of 2D CDT, where we find that all our definitions indicate a flat ground state of the gravitational path integral. Published by the American Physical Society 2024

Constraints on quantum spacetime-induced decoherence from neutrino oscillations

We investigate the implications of decoherence induced by quantum spacetime properties on neutrino oscillation phenomena. We develop a general formalism where the evolution of neutrinos is governed by a Lindblad-type equation and we compute the oscillation damping factor for various models that have been proposed in the literature. Furthermore, we discuss the sensitivity to these effects of different types of neutrino oscillation experiments, encompassing astrophysical, atmospheric, solar, and reactor neutrino experiments. By using neutrino oscillation data from long-baseline reactors and atmospheric neutrino observations, we establish stringent constraints on the energy scale governing the strength of the decoherence induced by stochastic metric fluctuations, amounting to, respectively, EQG≥2.6×1034 GeV and EQG≥2.5×1055 GeV. Published by the American Physical Society 2024

Quaternionic generalization of telegraph equations

Using non-commutative spacetime quaternion algebra, we represent the generalization of one-dimensional and three-dimensional telegraph equations, which are widely applied to consider the propagation of an electromagnetic signal in communication lines, as well as to describe particle diffusion and heat transfer. It is shown that the system of telegraph equations can be represented in compact form as a single quaternion equation taking into account the spacetime properties of physical quantities. The distinctive features of the one-dimensional and three-dimensional telegraph equations are discussed.

Interacting chiral form field theories and TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-like flows in six and higher dimensions

In this paper we initiate the study of six-dimensional non-linear chiral two-form gauge theories as deformations of free chiral two-form gauge theories driven by stress-tensor TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-like flows. To lay the background for this study, we elaborate on the relationship between different Lagrangian formulations of duality-invariant p-form theories and corresponding TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-like flows in various dimensions. To this end we propose a new formulation which (i) is a generalization of the four-dimensional construction by Ivanov, Nurmagambetov and Zupnik (INZ) and (ii) turns into the PST formulation upon integrating out an auxiliary self-dual field. We elucidate space-time covariant properties of the PST formulation by clarifying and making use of its relation to the INZ-type formulation and to a so-called “clone” construction.

Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the Ψ0 and Ψ4 Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for Ψ0 and Ψ4, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society 2024

Multiscale analysis of the space-time properties in incompressible wall-bounded turbulence

Multiscale analysis of the space-time properties in incompressible wall-bounded turbulence

Antipersistent energy-current correlations in strong long-ranged Fermi-Pasta-Ulam-Tsingou-type models.

We study heat transfer in one-dimensional Fermi-Pasta-Ulam-Tsingou-type systems with long-range (LR) interactions. The strength of the LR interaction between two lattice sites decays as a power σ of the inverse of their distance. We focus on the strong LR regime (0≤σ≤1) and show that the thermal transport behaviors are remarkably nuanced. Specifically, we observe that the antipersistent (negative) energy current correlation in this regime is intricately dependent on σ, displaying a nonmonotonic variation. Notably, a significant qualitative change occurs at σ_{c}=0.5, where with respect to other σ values the correlation shows a minimum negative value. Furthermore, our findings also demonstrate that within the long-time range considered, these antipersistent correlations will eventually vanish for certain σ>0.5. The underlying mechanisms behind these intriguing phenomena are related to the crossover of two diverse space-time scaling properties of equilibrium heat correlations and the various scattering processes of phonons and discrete breathers.

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole in general relativity coupled to nonlinear electrodynamics, which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric black hole spacetime. Later, we obtain the rotating black hole solution using the Newman–Janis algorithm and determine the event horizon properties of the black hole. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating black hole. Also, we analyze the photon sphere around the novel black hole and its shadow using celestial coordinates. We obtain that an increase of the black hole spin and charge as well as nonlinear electrodynamics field nonlinearity parameters causes an increase in the distortion parameter of the black hole shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the black hole charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive black holes Sgr A* and M87*. Finally, the emission rate of black hole evaporation through Hawking radiation is also studied.

Splitting the spacetime: a systematic analysis of foliation dependence in cosmic averaging

It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries.In a cosmological context this is sometimes referred to as the averaging problem.At the heart of this problem in relativity is the non-uniqueness of the choice of foliation within which the statistical properties of the local spacetime are quantified,which can lead to ambiguity in the formulated average theory. This has led to debate in the literature on how to best construct and view such a coarse-grained hydrodynamic theory.Here, we address this ambiguity by performing the first quantitative investigation of foliation dependence in cosmological spatial averaging. Starting from the aim of constructing slicing-independent integral functionals (volume, mass, entropy, etc.) as well as average functionals (mean density, average curvature, etc.) defined on spatial volume sections, we investigate infinitesimal foliation variations and derive results on the foliation dependence of functionals and on extremal leaves.Our results show that one may only identify fully foliation-independent integral functionals in special scenarios, requiring the existence of associated conserved currents.We then derive bounds on the foliation dependence of integral functionals for general scalar quantities under finite variations within physically motivated classes of foliations.Our findings provide tools that are useful for quantifying, eliminating or constraining the foliation dependence in cosmological averaging.