Embedding Of Spacetime Research Articles

A Variational Surface-Evolution Approach to Optimal Transport over Transitioning Compact Supports with Domain Constraints

We examine the optimal mass transport problem in Rn between densities with transitioning compact support by considering the geometry of a continuous interpolating support boundary Γ in space-time within which the mass density evolves according to the fluid dynamical framework of Benamou and Brenier. We treat the geometry of this space-time embedding in terms of points, vectors, and sets in Rn+1=R×Rn and blend the mass density and velocity as well into a space-time solenoidal vector field W|Ω→Rn+1 over a compact set Ω⊂Rn+1. We then formulate a joint optimization for W and its support using the shaped gradient of the space-time surface Γ outlining the support boundary ∂Ω. This easily accommodates spatiotemporal constraints, including obstacles or mandatory regions to visit.

Structural properties of compact stars in extended Teleparallel gravity

In this study, the structures of stars are examined using the Karmarkar condition (KC) to assess the metric components. The study also takes into account the anisotropic source of the matter distribution in the context of Modified Teleparallel Rastall Gravity (MTRG). Various values of the model parameter [Formula: see text] are tested by assuming different metric coefficients for the embedding spacetime. To calculate the involved model parameters, the Schwarzschild black hole solution is employed as an exterior solution. The stability and admissibility of the solutions obtained are demonstrated by analyzing some core properties of stellar objects, using observed data from established stellar models such as “PSRJ1416-2230”. It is worth noting that the results obtained in this study are physically feasible and acceptable.

A Dually Flat Embedding of Spacetime

A model of spacetime is presented. It has an extension to five dimensions, and in five dimensions the geometry is the dual of the Euclidean geometry w.r.t. an arbitrary positive-definite metric. Dually flat geometries are well-known in the context of information geometry. The present work explores their role in describing the geometry of spacetime. It is shown that the positive-definite metric with its flat 5-d connection can coexist with a pseudometric for which the connection is that of Levi-Civita. The 4-d geodesics are characterized by five conserved quantities, one of which can be chosen freely and is taken equal to zero in the present work. An explicit expression for the parallel transport operators is obtained. It is used to construct a pseudometric for spacetime by choosing an arbitrary possibly degenerate inner product in the tangent space of a reference point, for instance, that of Minkowski. By parallel transport, one obtains a pseudometric for spacetime, the metric connection of which extends to a 5-d connection with vanishing curvature tensor. The de Sitter space is considered as an example.

Mobility Inference on Long-Tailed Sparse Trajectory

Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel states from the raw trajectory data? How can we infer these mobility states from a single user’s trajectory information? How can we further generalize the mobility inference to the real-world trajectory data that span multiple users and are sparsely sampled over time? In this article, based on formal and rigid definitions of the stay/travel mobility, we propose a single trajectory inference algorithm that utilizes a generic long-tailed sparsity pattern in the large-scale trajectory data. The algorithm guarantees a 100% precision in the stay/travel inference with a provable lower bound in the recall metric. Furthermore, we design a transformer-like deep learning architecture on the problem of mobility inference from multiple sparse trajectories. Several adaptations from the standard transformer network structure are introduced, including the singleton design to avoid the negative effect of sparse labels in the decoder side, the customized space-time embedding on features of location records, and the mask apparatus at the output side for loss function correction. Evaluations on three trajectory datasets of 40 million urban users validate the performance guarantees of the proposed inference algorithm and demonstrate the superiority of our deep learning model, in comparison to sequence learning methods in the literature. On extremely sparse trajectories, the deep learning model improves from the single trajectory inference algorithm with more than two times of overall and F1 accuracy. The model also generalizes to large-scale trajectory data from different sources with good scalability.

Relieving string tension by making baby universes in a dynamical string tension braneworld model

String tension fundamentally determines the properties of strings; yet its value is often assigned arbitrarily, creating a fine-tuning problem. We describe a mechanism for dynamically generating string tension in a flat or almost flat spacetime, using the ‘modified measures formalism’, which in turn naturally generates a new type of stringy braneworld scenario. Such a scenario allows strings to achieve near infinite tension confining the strings to two very close expanding surfaces, but the infinite tensions also threaten to distort the near-flat embedding spacetime through large back reactions. We argue that this danger can be neutralized via the creation of a baby universe — a growing region of embedding spacetime that divorces from the ambient embedding spacetime, while our universe is still a brane separating two nearly flat spacetimes. The avoidance of a minimum length and a maximum Hagedorn temperature in the context of dynamical string tension generation is also discussed.

Anisotropic compact stars features using Tolman Kuchowiz and Embedding Space time in Rastall Teleparallel gravity

This study explores the stellar structures by employing Karmarkar condition Tolman Kuchowiz metric components with the anisotropic source of the matter distribution in the background of Rastall teleparallel gravity. To best of our knowledge, this is the first attempt to discuss the stellar structures in Rastall teleparallel gravity. For the embedding space–time, we ansatz the time metric co-efficient with two different values to check the effect of the model parameter n. Further, we use the Schwarzschild solution as an exterior solution to determine the unknown involved model parameters for this study. We show the stability and admissibility of the obtained solutions by investigating some core properties of the stellar objects. For the current analysis, we use the observed data of well-known stellar models like PSRJ1416-2230,Her X-1, SAX J1808.4-3658, EXO 1785-248 and SMC X-1. Finally, It is important to mention that our inquired results are physically acceptable.

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.

Isolated surfaces and symmetries of gravity

Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and paying attention to the maximal such symmetry could have important consequences to further elucidate the quantization of gravity. After establishing an algebraic off-shell derivation of the maximal closed subalgebra of the full bulk diffeomorphisms in the presence of an isolated corner, we show how to geometrically describe the latter and its embedding in spacetime, without constraining the geometry away from the corner, such as by assuming a foliation. The analysis encompasses arbitrary embedded surfaces, of generic codimensions $k$. The resulting corner algebra ${\cal A}_k$, calling $S$ the embedded surface and $M$ the bulk, is that of the group $(Diff(S)\ltimes GL(k,\mathbb{R}))\ltimes \mathbb{R}^k$. This result is independent of any dynamics or pseudo-Riemannian structure in the bulk. We then evaluate the Noether charges of ${\cal A}_2$ for Einstein-Hilbert dynamics and show that the Noether charge algebra gives a representation of the algebra ${\cal A}_2$, for finite proper distance corners in the bulk, while all other charges associated with $Diff(M)$ vanish.

The stringy origins of Galileons and their novel limit

We show generalized Galileons — a particular subclass of Horndeski gravity — arise from a consistent Kaluza-Klein reduction of the low-energy effective action of heterotic string theory to first order in α'. This suggests Horndeski theories of gravity have a string-theoretic origin. The form of the Galileonic terms is precisely fixed by parameters of the embedding spacetime, so that only a specific subset of Horndeski theories is permitted by string theory. A novel limit of the model is considered by performing a dimensionfulrescaling of α'.

Does Our Universe Conform with the Existence of a Universal Maximum Energy-Density <i>p<sub>max</sub><sup style="margin-left:-30px;">uni</sup></i>

Recent astronomical observations of high redshift quasars, dark matter-dominated galaxies, mergers of neutron stars, glitch phenomena in pulsars, cosmic microwave background and experimental data from hadronic colliders do not rule out, but they even support the hypothesis that the energy-density in our universe most likely is upper-limited by $\rho^{uni}_{max},$ which is predicted to lie between $2$ to $3$ the nuclear density $\rho_0.$ Quantum fluids in the cores of massive NSs with $\rho \approx \rho^{uni}_{max}$ reach the maximum compressibility state, where they become insensitive to further compression by the embedding spacetime and undergo a phase transition into the purely incompressible gluon-quark superfluid state. A direct correspondence between the positive energy stored in the embedding spacetime and the degree of compressibility and superfluidity of the trapped matter is proposed. In this paper relevant observation signatures that support the maximum density hypothesis are reviewed, a possible origin of $\rho^{uni}_{max}$ is proposed and finally the consequences of this scenario on the spacetime's topology of the universe as well as on the mechanisms underlying the growth rate and power of the high redshift QSOs are discussed.

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

Optical analogy of gravitational collapse and quantum tunneling of the event horizon

We present an optical method to realize the analogy of gravitational collapse by using the gradient of the refractive index system and the spacetime embedding diagram. We observe an analogy of Hawking radiation after the horizon is formed, for which the corresponding effective temperature is obtained via the transmission spectrum. We find that the effective temperature is proportional to the surface gravity, which is similar to the case in real black holes.

Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat?

The multi-messenger observations of the merger event in GW170817 did not rule out the possibility that the remnant might be a dynamically stable neutron star with $\mathcal{M}_{rm}\geq 2.69 \,\mathcal{M}_{\odot}.$ Based on this and other recent events, I argue that the universal maximum density hypothesis should be revived. Accordingly, the central densities in the cores of ultra-compact objects must be upper-limited by the critical density number $n_{cr},$ beyond which supradense nuclear matter becomes purely incompressible. Based on the spacetime-matter coupling in GR, it is shown that the topology of spacetime embedding incompressible quantum fluids with $n =n_{cr}$ must be Minkowski flat, which implies that spacetime at the background of ultra-compact objects should be of bimetric type.

Glitching Pulsars: Unraveling the Interactions of General Relativistic and Quantum Fields in the Strong Field Regimes

We present a modification of our previous model for the mechanisms underlying the glitch phenomena in pulsars and young neutron stars. Accordingly, pulsars are born with embryonic cores comprising of purely incompressible superconducting gluon-quark superfluid (henceforth SuSu-cores). As the ambient medium cools and spins down due to emission of magnetic dipole radiation, the mass and size of SuSu-cores are set to grow discretely with time, in accordance with the Onsager-Feynmann analysis of superfluidity. Presently, we propose that the spacetime embedding glitching pulsars is dynamical and of bimetric nature: inside SuSu-cores the spacetime must be flat, whereas the surrounding region, where the matter is compressible and dissipative, the spacetime is Schwarzschild. It is further proposed that the topological change of spacetime is derived by the strong nuclear force, whose operating length scales is found to increase with time to reach O(1) cm at the end of the luminous lifetimes of pulsars. The model presented here model is in line with the recent radio and GW observations of pulsars and NSs.

Thermodynamics of perfect fluids from scalar field theory

The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of St\"uckelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the thermodynamic variables, we find that a complete thermodynamic picture requires the four Stuckelberg fields. We show that thermodynamic stability plus the null-energy condition imply dynamical stability. We also argue that a consistent thermodynamic interpretation is not possible if any of the shift symmetries is explicitly broken.

Ashtekar-Barbero holonomy on the hyperboloid: Immirzi parameter as a cutoff for quantum gravity

In the context of the geometrical interpretation of the spin network states of Loop Quantum Gravity, we look at the holonomies of the Ashtekar-Barbero connection on loops embedded in space-like hyperboloids. We use this simple setting to illustrate two points. First, the Ashtekar-Barbero connection is not a space-time connection, its holonomies depend on the spacetime embedding of the canonical hypersurface. This fact is usually interpreted as an inconvenience, but we use it to extract the extrinsic curvature from the holonomy and separate it from the 3d intrinsic curvature. Second, we show the limitations of this reconstruction procedure, due to a periodicity of the holonomy in the Immirzi parameter, which underlines the role of a real Immirzi parameter as a cut-off for general relativity at the quantum level in contrast with its role of a mere coupling constant at the classical level.

Exact solutions for extreme black hole magnetospheres

We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classification of the subset that form highest-weight representations of the spacetime's SL(2,R) x U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2,R) highest-weight conditions lead to stationary solutions with non-trivial angular dependence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2,C) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2,C) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear currents and allows us to resum the highest-weight primaries and their SL(2,R)-descendants.

The status of modern five-dimensional gravity (A short review: Why physics needs the fifth dimension)

Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification in regard to string theory, but is misguided as applied to five-dimensional (5D) theories with a large extra dimension. Such theories smoothly embed general relativity, ensuring recovery of the latter's observational support. When the embedding of spacetime is carried out in accordance with Campbell's theorem, the resulting 5D theory naturally explains the origin of classical matter and vacuum energy. Also, constraints on the equations of motion near a high-energy surface or membrane in the 5D manifold lead to quantization and quantum uncertainty. These are major returns on the modest investment of one extra dimension. Instead of fruitless bickering about whether it is possible to "see" the fifth dimension, it is suggested that it be treated on par with other concepts of physics, such as time. The main criterion for the acceptance of a fifth dimension (or not) should be its usefulness.

Evasion paths in mobile sensor networks

Suppose that ball-shaped sensors wander in a bounded domain. A sensor does not know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. In ‘Coordinate-free coverage in sensor networks with controlled boundaries via homology', Vin de Silva and Robert Ghrist give a necessary condition, depending only on the time-varying connectivity data of the sensors, for an evasion path to exist. Using zigzag persistent homology, we provide an equivalent condition that moreover can be computed in a streaming fashion. However, no method with time-varying connectivity data as input can give necessary and sufficient conditions for the existence of an evasion path. Indeed, we show that the existence of an evasion path depends not only on the fibrewise homotopy type of the region covered by sensors but also on its embedding in spacetime. For planar sensors that also measure weak rotation and distance information, we provide necessary and sufficient conditions for the existence of an evasion path.

Asymptotic flatness and quantum geometry

We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding spacetimes, unlike the standard basis states carrying only discrete labels. The resulting quantum geometry corresponds to a nondegenerate vacuum metric, which allows a consistent realization of the asymptotic conditions on the canonical fields. Although the quantum counterpart of the classical symmetry group of conformal isometries consists only of continuous global translations, Lorentz invariance can still be recovered in an effective sense. The quantum spacetime as characterized by a gauge invariant state is shown to be made up of discrete strips at the interior, and smooth at asymptotia. The analysis here is expected to be particularly relevant for a canonical quantization of asymptotically flat gravity using kinematical states labelled by smooth geometries.