Spacetime Metric Research Articles

Timelike supersymmetric solutions of D=3 , N=4 supergravity

We study timelike supersymmetric solutions of a D=3, N=4 gauged supergravity using the Killing spinor bilinears method and prove that AdS3 is the only solution within this class. We then consider the ungauged version of this model. It is found that for this type of solution, the ungauged theory effectively truncates to a supergravity coupled to a sigma model with a two-dimensional hyperbolic target space H2, and all solutions can be expressed in terms of two arbitrary holomorphic functions. The spacetime metric is a warped product of the time direction with a two-dimensional space, and the warp factor is given in terms of the Kähler potential of H2. We show that when the holomorphic function that determines the sigma model scalar fields is not constant, the metric on the sigma model target manifold becomes part of the spacetime metric. We then look at some special choices for these holomorphic functions for which the spacetime metric and the Killing spinors are only radial dependent. We also derive supersymmetric null solutions of the ungauged model which are pp-waves on the Minkowski spacetime. Published by the American Physical Society 2025

Gravity from Pre-geometry

Abstract The gravitational interaction, as described by the Einstein–Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a formulation a ` la Yang–Mills on an SO ( 1 , 4 ) or SO ( 3 , 2 ) principal bundle and not accounting for a spacetime metric, the Einstein–Hilbert action is recovered after the identification of the effective spacetime metric and spin connection for the residual SO ( 1 , 3 ) gauge symmetry of the spontaneously broken phase—i.e. the stabiliser of the SO ( 1 , 4 ) or SO ( 3 , 2 ) gauge group. Thus, the two fundamental tenets of general relativity, i.e. diffeomorphism invariance and the equivalence principle, can arise from a more fundamental gauge principle. The two mass parameters that characterise Einstein gravity, namely the Planck mass and the cosmological constant, are likewise shown to be emergent. The phase transition from the unbroken to the spontaneously broken phase is expected to happen close to the Planck temperature. This is conjectured to be dynamically driven by a scalar field that implements a Higgs mechanism, hence providing mass to new particles, with consequences for cosmology and high-energy physics. The couplings of gravity to matter are discussed after drawing up a dictionary that interconnects pre-geometric and effective geometric quantities. In the unbroken phase where the fundamental gauge symmetry is restored, the theory is potentially power-counting renormalisable without matter, offering a novel path towards a UV completion of Einstein gravity.

Thermal Profile of Accretion Disk Around Black Hole in 4D Einstein–Gauss–Bonnet Gravity

In this study, we investigate the properties of a thin accretion disk around a static spherically symmetric black hole in 4D Einstein–Gauss–Bonnet gravity, with an additional coupling constant, α, appearing in the spacetime metric. Using the Novikov–Thorne accretion disk model, we examine the thermal properties of the disk, finding that increasing α reduces the energy, angular momentum, and effective potential of a test particle orbiting the black hole. We demonstrate that α can mimic the spin of a Kerr black hole in general relativity up to a≃ 0.23 M for the maximum value of α. Our analysis of the thermal radiation flux shows that larger α values increase the flux and shift its maximum towards the central black hole, while far from the black hole, the solution recovers the Schwarzschild limit. The impact of α on the radiative efficiency of the disk is weak but can slightly alter it. Assuming black-body radiation, we observe that the disk’s temperature peaks near its inner edge and is higher for larger α values. Lastly, the electromagnetic spectra reveal that the disk’s luminosity is lower in Einstein–Gauss–Bonnet gravity compared to general relativity, with the peak luminosity shifting toward higher frequencies, corresponding to the soft X-ray band as α increases.

Effect of torsion in long-baseline neutrino oscillation experiments

In this work, we investigate the effect of curved spacetime on neutrino oscillation. In a curved spacetime, the effect of curvature on fermionic fields is represented by spin connection. The spin connection consists of a non-universal “contorsion” part which is expressed in terms of vector and axial current density of fermions. The contraction of contorsion part with the tetrad fields, which connects the internal flat space metric and the spacetime metric, is called torsion. In a scenario where neutrino travels through background of fermionic matter at ordinary densities in a curved spacetime, the Hamiltonian of neutrino oscillation gets modified by the torsional coupling constants λ21′ and λ31′. The aim of this work is to study the effect of λ21′ and λ31′ in DUNE and P2SO. In our study we, (i) discuss the effect of torsional coupling constants on the neutrino oscillation probabilities, (ii) estimate the capability of P2SO and DUNE to put bounds on these parameters and (iii) show how the physics sensitivities get modified in presence of torsion.

Dual Jet Interaction, Magnetically Arrested Flows, and Flares in Accreting Binary Black Holes

Abstract Supermassive binary black holes in galactic centers are potential multimessenger sources in gravitational waves and electromagnetic radiation. To find such objects, isolating unique electromagnetic signatures of their accretion flow is key. With the aid of three-dimensional general-relativistic magnetohydrodynamic simulations that utilize an approximate, semianalytic, superimposed spacetime metric, we identify two such signatures for merging binaries. Both involve magnetic reconnection and are analogous to plasma processes observed in the solar corona. The first, like colliding flux tubes that can cause solar flares, involves colliding jets that form an extended reconnection layer, dissipating magnetic energy and causing the two jets to merge. The second, akin to coronal mass ejection events, involves the accretion of magnetic field lines onto both black holes; these magnetic fields then twist, inflate, and form a trailing current sheet, ultimately reconnecting and driving a hot outflow. We provide estimates for the associated electromagnetic emission for both processes, showing that they likely accelerate electrons to high energies and are promising candidates for continuous, stochastic, and/or quasi-periodic higher-energy electromagnetic emission. We also show that the accretion flows around each black hole can display features associated with the magnetically arrested state. However, simulations with black hole spins misaligned with the orbital plane and simulations with larger Bondi radii saturate at lower values of horizon-penetrating magnetic flux than standard magnetically arrested disks, leading to weaker, intermittent jets owing to feedback from the weak jets or equatorial flux tubes ejected by reconnecting field lines near the horizon.

Taking the Null-Hypersurface Limit in the Parikh-Wilczek Membrane Approach

We consider subtleties of the horizon (null-hypersurface) limit in the Parikh-Wilczek Membrane Approach to Black Holes. Specifically, we refine the correspondence between the projected Einstein equations of gravity with matter and the Raychaudhuri-Damour-Navier-Stokes (RDNS) equations of relativistic hydrodynamics. For a general configuration of gravity with matter we obtain additional terms in the hydrodynamic equations, which include very specific combinations of the contracted logarithmic derivatives of a parameter (the regularization function) determining the proximity of a stretched membrane to the black hole horizon. Nevertheless, direct computations of the new terms for exact (Schwarzschild and Kerr) black hole solutions prompt the standard form of the RDNS equations, due to the non-expanding horizon property of these solutions. Therefore, the reduction of the extended RDNS equations to their classical form may be viewed as an additional consistency condition in the exact black hole solutions hydrodynamics, and may serve as a non-trivial test for various viable approximations of spacetime metrics. We compare in detail the Parikh-Wilczek Membrane Approach with the Gourgoulhon-Jaramillo method of a null-hypersurface description, as well as give the link of the obtained results to our previous work on the Kerr black holes.

QED effects on Kerr-Newman black hole shadows* *Partly supported by the National Nature Science Foundation of China (12275004)

By incorporating first-order QED effects, we explored the shadows of Kerr-Newman black holes with a magnetic charge through the numerical backward ray-tracing method. Our investigation encompassed both the direct influence of the electromagnetic field on light rays and the distortion of the background spacetime metric due to QED corrections. We found that the area of the shadow increases with the QED effect, mainly owing to the fact that the photons travel more slowly in the effective medium, making them more susceptible to being trapped by the black hole.

Height-function-based 4D reference metrics for hyperboloidal evolution

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications.

Exactly solvable non-unitary time evolution in quantum critical systems I: effect of complex spacetime metrics

Abstract In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal (2021 arXiv:2105.10161) and Witten (2021 arXiv:2111.06514) on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including the entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibit universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

Non-degenerate metrics, hypersurface deformation algebra, non-anomalous representations and density weights in quantum gravity

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions.

A Riemannian geometric approach for timelike and null spacetime geodesics

The geodesic motion in a Lorentzian spacetime can be described by trajectories in a 3-dimensional Riemannian metric. In this article we present a generalized Jacobi metric obtained from projecting a Lorentzian metric over the directions of its Killing vectors. The resulting Riemannian metric inherits the geodesics for asymptotically flat spacetimes including the stationary and axisymmetric ones. The method allows us to find Riemannian metrics in three and two dimensions plus the radial geodesic equation when we project over three different directions. The 3-dimensional Riemannian metric reduces to the Jacobi metric when static, spherically symmetric and asymptotically flat spacetimes are considered. However, it can be calculated for a larger variety of metrics in any number of dimensions. We show that the geodesics of the original spacetime metrics are inherited by the projected Riemannian metric. We calculate the Gaussian and geodesic curvatures of the resulting 2-dimensional metric, we study its near horizon and asymptotic limit. We also show that this technique can be used for studying the violation of the strong cosmic censorship conjecture in the context of general relativity.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

Exploring the possibility of testing the no-hair theorem with Minkowski-deformed regular hairy black holes via photon rings

In this paper, we investigate the optical appearance of a regular static spherically symmetric hairy black hole within the context of Minkowski deformation governed by the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. This black hole describes a hairy black hole with geometric deformations in the radial and temporal metric components, parameterized by α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. The optical appearance of the black hole, illuminated by a static thin accretion disk in three toy emission function models, exhibits distinctive shadows and photon rings. Our findings reveal that for static spherically symmetric hairy Minkowski-deformed regular black holes, the event horizon radius rh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_h$$\\end{document}, photon sphere radius rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ph}$$\\end{document}, critical impact parameter bph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ph}$$\\end{document}, and innermost stable circular orbit radius risco\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{isco}$$\\end{document} all have a positive correlation with α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. These parameters affect the null geodesic trajectories, shadows, and the optical appearance of the photon rings illuminated by a static thin accretion disk around the black hole. Utilizing this, we obtained the optical appearance of this black hole when observed in the forward direction of the optical and geometric thin accretion disk models. In all three models, the radius of the photon ring images also shows a positive correlation with the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Therefore, under the static spherically symmetric hairy Minkowski-deformed regular black hole, there is no degeneracy of photon rings dependent on the parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}. Theoretically, this allows for the distinction of different spacetime metrics of hairy Minkowski-deformed regular black holes, providing a potential method for testing the no-hair theorem through future observations of black hole photon rings.

The Asymptotic Expansion of the Spacetime Metric at the Event Horizon

AbstractHawking’s local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degenerate Killing horizon. In this paper, we prove that the full asymptotic expansion of any smooth vacuum metric at a non-degenerate Killing horizon is determined by the geometry of the horizon. This gives a new perspective on the black hole uniqueness conjecture. In spacetime dimension 4, we also prove an existence theorem: Given any non-degenerate horizon geometry, Einstein’s vacuum equations can be solved to infinite order at the horizon in a unique way (up to isometry). The latter is a gauge invariant version of Moncrief’s classical existence result, without any restriction on the topology of the horizon. In the real analytic setting, the asymptotic expansion is shown to converge and we get well-posedness of this characteristic Cauchy problem.

Algebraic symmetries of the observables on the sky: Variable emitters and observers

In this paper we prove a number of exact relations between optical observables, such as trigonometric parallax, position drift, and the proper motion of a luminous source, in addition to the variations of redshift and the viewing angle. These relations are valid in general relativity for any spacetime, and they are of potential interest for astrometry and precise cosmology. They generalize the well-known Etherington’s reciprocity relation between the angular diameter distance and the luminosity distance. Similar to the Etherington’s relation, they hold independently of the spacetime metric, the positions, and the motions of a light source or an observer. We show that those relations follow from the symplectic property of the bilocal geodesic operator, i.e., the geometric object that describes the light propagation between two distant regions of a spacetime. The set of relations we present is complete in the sense that no other relations between those observables should hold, in general. In the meantime, we develop the mathematical machinery of the bilocal approach to light propagation in general relativity and its corresponding Hamiltonian formalism. Published by the American Physical Society 2024

Analytical solutions to Einstein field equations for spherically symmetric anisotropic matter: a comparative study using Tolman VII metric potential

In this paper, we present analytical solutions to the Einstein field equations for spherically symmetric anisotropic matter distributions using the well-established Tolman VII metric potential, chosen for its strong physical and mathematical foundations. Our solutions are derived using three distinct approaches: the vanishing complexity factor condition (VCC), the embedding class I condition (ECC), and the conformally flat condition (CFC). We conduct a comprehensive comparative analysis of these three approaches. By ensuring a smooth match between the interior spacetime metric and the exterior Schwarzschild metric, and applying the condition of vanishing radial pressure at the boundary, we determine the model parameters. We graphically assess the model’s stability by examining conditions such as causality, the adiabatic index, equations of state, and the generalized Tolman–Oppenheimer–Volkov (TOV) equation, considering the forces acting within the system. Additionally, the effects of anisotropy on the stars’ physical characteristics are investigated through graphical representations.

Schwarzschild spacetime in fractal dimensions: Deflection of light, supermassive black holes and temperature effects

In this paper, we construct a Schwarzschild metric in the fractal dimension based on fractal calculus, and we study the deflection of light near the sun. It was observed that the new fractal spherically symmetric spacetime metric may describe supermassive black holes, which have been detected through various astronomical observations such as SDSS. We have discussed the deflection of light by the gravitational field of the sun. It was observed that the total deflection of light is affected by the fractal dimension. To estimate the numerical value of the fractal dimension, we have used the 2004[Formula: see text]analysis of almost 2 million VLBI observations of 541 radio sources made by 87 VLBI sites, which estimates the factor [Formula: see text] based on PNN formalism. It was observed that the fractal dimension is roughly less than unity. However, our analysis showed that large bending gravity gives fractal dimensions lower than unity to some extent. We also gave a naïve idea about the emission thermal Unruh process in fractal dimension. It was observed that both the temperature and the entropy of black holes are affected by the fractal dimension, and that for low numerical values, the entropy of the black hole is enhanced.

Rotational influence on fermions within negative curvature wormholes

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.

Generalized Bach solitons on (κ,μ)′-almost-Kenmotsu manifolds and its applications in perfect fluid spacetimes

The principal aim of this paper is to find the expression of *-Bach tensors on [Formula: see text]-almost-Kenmotsu manifolds. It is shown that if the metric of a [Formula: see text]-almost-Kenmotsu manifold admits a generalized closed *-Bach soliton, then the metric is *-Bach flat under certain restrictions. We also prove that the metric of a generalized gradient *-Bach soliton on a [Formula: see text]-almost-Kenmotsu manifold is *-Bach flat, for a soliton function which is invariant under the Reeb vector field. Further, we characterize generalized *-Bach solitons with trace-free *-Bach tensors on [Formula: see text]-almost-Kenmotsu manifolds and results are verified by an example. As an application of these solitons, we study generalized almost-Bach solitons whose metrics are associated with the Lorentzian metric of the perfect fluid spacetimes.

What no one has seen before: gravitational waveforms from warp drive collapse

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.