Time-dependent Spacetime Research Articles

Page curve of AdS-Vaidya model for evaporating black holes

We study an evaporating black hole in the boundary conformal field theory (BCFT) model under the fully time-dependent AdS-Vaidya spacetime geometry. We introduce the time-dependent finite bath termed the effective Hawking radiation region. This is described by a nontrivial BCFT solution that acts as a time-dependent brane which we call the moving end-of-the-radiation (METR) brane that leads to a new type of Hubeny-Rangamani-Takayanagi surface. We further examine the island formulation in this particular time-dependent spacetime. The Page curve is calculated by using Holographic Entanglement Entropy (HEE) in the context of double holography.

Gravity-induced entanglement between two massive microscopic particles in curved spacetime: II. Friedmann–Lemaître–Robertson–Walker universe

In our previous work (Zhang and Shu in Eur Phys J. C 84(3):256, 2024), we have explored quantum gravity induced entanglement of masses (QGEM) in curved spacetime, observing entanglement formation between particles moving along geodesics in a Schwarzschild spacetime background. We find that long interaction time induces entanglement, even for particles with microscopic mass, addressing decoherence concerns. In this work, we build upon our previous work (Zhang and Shu 2024) by extending our investigation to a time-dependent spacetime. Specifically, we explore the entanglement induced by the mutual gravitation of massive particles in the Friedmann–Lemaître–Robertson–Walker (FLRW) universe. With the help of the phase shift and the QGEM spectrum, our proposed scheme offers a potential method for observing the formation of entanglement caused by the quantum gravity of massive particles as they propagate in the FLRW universe. Consequently, it provides insights into the field of entanglement in cosmology.

The cosmological tree theorem

A number of diagrammatic “cutting rules” have recently been developed for the wavefunction of the Universe which determines cosmological correlation functions. These leverage perturbative unitarity to relate particular “discontinuities” in Feynman-Witten diagrams (with cosmological boundary conditions) to simpler diagrams, in much the same way that the Cutkosky rules relate different scattering amplitudes. In this work, we make use of a further causality condition to derive new cutting rules for Feynman-Witten diagrams on any time-dependent spacetime background. These lead to the cosmological analogue of Feynman’s tree theorem for amplitudes, which can be used to systematically expand any loop diagram in terms of (momentum integrals of) tree-level diagrams. As an application of these new rules, we show that certain singularities in the wavefunction cannot appear in equal-time correlators due to a cancellation between “real” and “virtual” contributions that closely parallels the KLN theorem. Finally, when combined with the Bunch-Davies condition that certain unphysical singularities are absent, these cutting rules completely determine any tree-level exchange diagram in terms of simpler contact diagrams. Altogether, these results remove the need to ever perform nested time integrals when computing cosmological correlators.

Semiclassical dynamics of Hawking radiation

We consider gravity in 3+1 spacetime dimensions coupled to N scalar matter fields in a semiclassical limit where . The dynamical evolution of a black hole including the back-reaction of the Hawking radiation on the metric is formulated as an initial-value problem. The quantum stress-energy tensor is evaluated using a point-splitting regularization along spacelike geodesics. To account for the quantum entanglement of the matter fields, they are treated as a set of bilocal collective fields defined on spacelike hypersurfaces. The resulting semiclassical field equations include terms up to fourth order in derivatives that can be treated in a perturbative expansion. The formulation we arrive at should be amenable to numerical simulation of time-dependent semiclassical spacetime.

Quantum field simulator for dynamics in curved spacetime.

In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations1. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulatorof a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.

A time-dependent spacetime in f(R,T) gravity: Gravitational collapse

In this note, a time-dependent spacetime is explored in the background of [Formula: see text] gravity via the gravitational collapse of a massive star. The star is modeled by the Vaidya spacetime which is time-dependent in nature. The coupling of matter with curvature is the key feature of [Formula: see text] theory and here we have investigated its effects on a collapsing scenario. Two different types of models, one involving minimal and the other involving nonminimal coupling between matter and curvature are considered for our study. Power law and exponential functionalities are considered as examples to check the outcome of the gravitational collapse. A detailed analysis on the appearance of horizons in Vaidya spacetime is performed and its astrophysical implications are explored. Our prime objective is to explore the nature of singularities (black hole or naked singularity) that form as an end state of the collapse. Existence of outgoing radial null geodesics from the central singularity was probed and such existence implied the formation of naked singularities thus defying the cosmic censorship hypothesis. The absence of such outgoing null geodesics would imply the formation of an event horizon and the singularity formed becomes a black hole. Conditions under which such possibilities occur are derived for all the models and sub-models. Gravitational strength of the singularity is also investigated and the conditions under which we can get a strong or a weak singularity is derived. The results obtained are very interesting and may be attributed to the coupling between curvature and matter. It is seen that for nonminimal coupling there is a possibility of a globally naked singularity, whereas for a minimal coupling scenario local nakedness is the only option. It is also found that the singularity formed can be sufficiently weak in nature, which is cosmologically desirable.

The Progenitor of the Big Bang and Its Connection to the Flatness and Acceleration of the Universe

It was argued that old and massive neutron stars end up as black objects that are made of purely incompressible superconducting gluon-quark superfluid matter (henceforth SuSu-objects). Based on theoretical investigations and numerical solving of the field equations with time-dependent spacetime topologies, I argue that a dense cluster of SuSu-objects at the background of flat spacetime that merged smoothly is a reliable candidate for the progenitor of the big bang. Here, we present and use a new time-dependent spacetime metric, which unifies the metrics of Minkowski, Schwarzschild, and Friedmann as well as a modified TOV-equation for modeling dynamical contractions of relativistic objects. Had the progenitor undergone an abrupt decay, a hadronizing front forms at its surface and starts propagating from outside-to-inside, thereby hadronizing its entire content and changing the topology of the embedding spacetime from a flat into a dynamically expanding curved one. For an observer located at the center of the progenitor, H0, the universe would be seen as isotropic and homogeneous, implying therefore that the last big bang event must have occurred in our neighborhood. For the curved spacetime re-converges into a flat one, whereas the outward-propagation topological front, which separates the enclosed curved spacetime from the exterior flat one, would appear spatially and temporally accelerating outwards. The here-presented scenario suggests possible solutions to the flatness problem, the origin of acceleration of the universe and the pronounced activities of high redshift QSOs. We anticipate that future observations by the James-Webb-Telescope to support our scenario when active QSOs with z >12 would be detected.

Quantum entanglement in inflationary cosmology

We investigate the time-dependent entanglement entropy in the AdS space with a dS boundary which represents an expanding spacetime. On this time-dependent spacetime, we show that the Ryu–Takayanagi formula, which is usually valid in the static spacetime, provides a leading contribution to the time-dependent entanglement entropy. We also study the leading behavior of the entanglement entropy between the visible and invisible universes in an inflationary cosmology. The result shows that the quantum entanglement monotonically decreases with time and finally saturates a constant value inversely proportional to the square of the Hubble constant. Intriguingly, we find that even in the expanding universes, the time-dependent entanglement entropy still satisfies the area law determined by the physical distance.

Quantum initial conditions for inflation and canonical invariance

We investigate the transformation of initial conditions for primordial curvature perturbations under two types of transformations of the associated action: simultaneous redefinition of time and the field to be quantised, and the addition of surface terms. The latter encompasses all canonical transformations, whilst the time- and field-redefinition is a distinct, non-canonical transformation since the initial and destination systems use different times. Actions related to each other via such transformations yield identical equations of motion and preserve the commutator structure. They further preserve the time-evolution of expectation values of quantum operators unless the vacuum state also changes under the transformation. These properties suggest that it is of interest to investigate vacuum prescriptions that also remain unchanged under canonical transformations. We find that initial conditions derived via minimising the vacuum expectation value of the Hamiltonian and those obtained using the Danielsson vacuum prescription are not invariant under these transformations, whereas those obtained by minimising the local energy density are. We derive the range of physically distinct initial conditions obtainable by Hamiltonian diagonalisation, and illustrate their effect on the scalar primordial power spectrum and the Cosmic Microwave Background under the just enough inflation model. We also generalise the analogy between the dynamics of a quantum scalar field on a curved, time-dependent spacetime and the gauge-invariant curvature perturbation. We argue that the invariance of the vacuum prescription obtained by minimising the renormalised stress--energy tensor should make it the preferred procedure for setting initial conditions for primordial perturbations. All other procedures reviewed in this work yield ambiguous initial conditions, which is problematic both in theory and practice.

Mimetic black holes

In this paper, we look for the vacuum static spherically symmetric solution in the mimetic gravity scenario based on the conformal invariance principle. The trivial solution is a stealth Schwarzschild black hole with scalar hair where the mimetic field does not contribute to the background. However, a solution with two naked singularities shows up when the mimetic scalar field contributes to the background. We show that one of these singularities is the same as the singularity at the center of standard Schwarzschild black hole while the other appears due to caustics formation. However, we construct the mimetic black hole solution by gluing the exterior static spherically symmetric solution to a time-dependent anisotropic spacetime describing the interior of the black hole. It is shown that these two solutions match continuously on the surface of the apparent horizon. Some physical properties of the corresponding mimetic black holes are discussed.

A Novel Energy-conserving Scheme for Eight-dimensional Hamiltonian Problems

Abstract We design a novel, exact energy-conserving implicit nonsymplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to one of the phase-space variables is discretized by the average of eight Hamiltonian difference terms. Such a discretization form is a second-order approximation to the Hamiltonian gradient. It is shown numerically via simulations of a Fermi–Pasta–Ulam-β system and a post-Newtonian conservative system of compact binaries with one body spinning that the newly proposed method has extremely good energy-conserving performance, compared to the Runge–Kutta; an implicit midpoint symplectic method, and extended phase-space explicit symplectic-like integrators. The new method is advantageous over very long times and for large time steps compared to the state-of-the-art Runge–Kutta method in the accuracy of numerical solutions. Although such an energy-conserving integrator exhibits a higher computational cost than any one of the other three algorithms, the superior results justify its use for satisfying some specific purposes on the preservation of energies in numerical simulations with much longer times, e.g., obtaining a high enough accuracy of the semimajor axis in a Keplerian problem in the solar system or accurately grasping the frequency of a gravitational wave from a circular orbit in a post-Newtonian system of compact binaries. The new integrator will be potentially applied to model time-varying external electromagnetic fields or time-dependent spacetimes.

Holographic complexity in Vaidya spacetimes. Part I

We examine holographic complexity in time-dependent Vaidya spacetimes with both the complexity=volume (CV) and complexity=action (CA) proposals. We focus on the evolution of the holographic complexity for a thin shell of null fluid, which collapses into empty AdS space and forms a (one-sided) black hole. In order to apply the CA approach, we introduce an action principle for the null fluid which sources the Vaidya geometries, and we carefully examine the contribution of the null shell to the action. Further, we find that adding a particular counterterm on the null boundaries of the Wheeler-DeWitt patch is essential if the gravitational action is to properly describe the complexity of the boundary state. For both the CV proposal and the CA proposal (with the extra boundary counterterm), the late time limit of the growth rate of the holographic complexity for the one-sided black hole is precisely the same as that found for an eternal black hole.

Symmetry of Brans-Dicke gravity as a novel solution-generating technique

A symmetry of Brans-Dicke gravity in (electro-)vacuo or in the presence of conformally invariant matter is presented and used as a solution-generating technique starting from a known solution as a seed. This novel technique is applied to generate, as examples, new spatially homogeneous and isotropic cosmologies, a 3-parameter family of spherical time-dependent spacetimes conformal to a Campanelli-Lousto geometry, and a family of cylindrically symmetric geometries.

Modified <i> f(R)</i> Gravity and Thermodynamics of Time-Dependent Wormholes at Event Horizon

In the context of modified $f(R)$ gravity theory, we study time-dependent wormhole spacetimes in the radiation background. In this framework, we attempt to generalize the thermodynamic properties of time-dependent wormholes in $f(R)$ gravity. Finally, at event horizon, the rate of change of total entropy has been discussed.

Temperature and thermodynamic structure of Einstein’s equations for a cosmological black hole

It is expected that the cosmological black holes are the closest realistic solutions of gravitational theories and they evolve with time. Moreover, the natural way of defining thermodynamic entities for the stationary ones is not applicable in the case of a time dependent spacetime. Here we confine our discussion within the Sultana-Dyer metric which is a cosmological black hole solution of Einstein's gravity. In literature, there exists two expressions of horizon temperature -- one is time dependent and the other does not depend on time. To single out the correct one we find the temperature by studying the Hawking effect in the tunnelling formalism. This leads to time dependent structure. After identifying the correct one, the Einstein's equations are written on the horizon and we show that this leads to the first law of thermodynamics. In this process the expressions for horizon entropy and energy, obtained earlier by explicit calculations, are being used. This provides the evidence that Einstein's equations have thermodynamic structure even for a cosmological black hole spacetime. Moreover, this study further clarifies the correctness of the expressions for the thermodynamic quantities; like temperature, entropy and internal energy.

On shape dependence of holographic entanglement entropy in AdS4/CFT3

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.

Search for Ultralight Scalar Dark Matter from Pulsar Timing

AbstractWe perform a Bayesian analysis of pulsar-timing residuals from the NANOGrav pulsar-timing array to search for a specific form of stochastic narrow-band signal produced by oscillating gravitational potential (Gravitational Potential Background) in the Galactic halo. Such oscillations arise in models of warm dark matter composed of an ultralight massive scalar field (m ≃ 10−23 eV). The propagation of an electromagnetic signal from a pulsar through the time-dependent spacetime will leave an imprint in the pulsar timing, much like a gravitational wave. From the physical point of view, this is the classical Sachs-Wolfe effect. A distinctive feature of the pulsar-timing residuals due to GBP produced by a variable scalar field is that the amplitude of the TOA residuals should be independent of the pulsar location in the sky. In the monochromatic approximation, the stringent upper limit (95% C.L.) on the variable gravitational potential amplitude is found to be (Ψc<1.14 × 10−15), corresponding to the characteristic strain hc = 2$\sqrt{3}$Ψc < 4 × 10−15 at f=1.75 × 10−8 Hz. In the narrow-band approximation, the upper limit of this background energy density is ΩGPB < 1.27 × 10−9 at f=1.75 × 10−8 Hz. These limits are an order of magnitude higher than the expected signal amplitude assuming all Galactic dark matter is made of such scalar particles. The applied analysis of the pulsar-timing residuals can be used to search for any narrow-band stochastic signals with different correlation properties. As a by-product, parameters of the red noise present in four NANOGrav pulsars were found.

Unitarity and ultraviolet regularity in cosmology

Quantum field theory in curved space-times is a well developed area in mathematical physics which has had important phenomenological applications to the very early universe. However, it is not commonly appreciated that on time dependent space-times ---including the simplest cosmological models--- dynamics of quantum fields is not unitary in the standard sense. This issue is first explained with an explicit example and it is then shown that a generalized notion of unitarity does hold. The generalized notion allows one to correctly pass to the Schr\"odinger picture starting from the Heisenberg picture used in the textbook treatments. Finally, we indicate how these considerations can be extended from simple cosmological models to general globally hyperbolic space-times

Experimental quantum cosmology in time-dependent optical media

It is possible to construct artificial spacetime geometries for light by using intense laser pulses that modify the spatiotemporal properties of an optical medium. Here we theoretically investigate experimental possibilities for studying spacetime metrics of the form . By tailoring the laser pulse shape and medium properties, it is possible to create a refractive index variation that can be identified with . Starting from a perturbative solution to a generalized Hopfield model for the medium described by an , we provide estimates for the number of photons generated by the time-dependent spacetime. The simplest example is that of a uniformly varying that therefore describes the Robertson–Walker metric, i.e. a cosmological expansion. The number of photon pairs generated in experimentally feasible conditions appears to be extremely small. However, large photon production can be obtained by periodically modulating the medium and thus resorting to a resonant enhancement similar to that observed in the dynamical Casimir effect. Curiously, the spacetime metric in this case closely resembles that of a gravitational wave. Motivated by this analogy, we show that a periodic gravitational wave can indeed act as an amplifier for photons. The emission for an actual gravitational wave will be very weak but should be readily observable in the laboratory analogue.

Classical radiation by free-falling charges in de Sitter spacetime

We study the classical radiation emitted by free-falling charges in de Sitter spacetime coupled to different kinds of fields. Specifically we consider the cases of the electromagnetic field, linearized gravity and scalar fields with arbitrary mass and curvature coupling. Given an arbitrary set of such charges, there is a generic result for sufficiently late times which corresponds to each charge being surrounded by a field zone with negligible influence from the other charges. Furthermore, we explicitly find a static solution in the static patch adapted to a charge (implying no energy loss by the charge) which can be regularly extended beyond the horizon to the full de Sitter spacetime, and show that any other solution decays at late times to this one. On the other hand, for non-conformal scalar fields the inertial observers naturally associated with spatially flat coordinates will see a non-vanishing flux far from the horizon, which will fall off more slowly than the inverse square of the distance for sufficiently light fields (m^2 + \xi R < 5H^2/4) and give rise to a total integrated flux that grows unboundedly with the radius. This can be qualitatively interpreted as a consequence of a classical parametric amplification of the field generated by the charge due to the time-dependent background spacetime. Most of these results do not hold for massless minimally coupled scalar fields, whose special behavior is analyzed separately.