## We theoretically investigate superradiance effects in quantum field theories in curved space-times by proposing an analogue model based on Bose--Einstein condensates subject to a synthetic vector potential.

Understanding superradiant phenomena with synthetic vector potentials in atomic Bose-Einstein condensates

## Solomon claims that this model violates both the classical energy conditions of special relativity and the quantum energy conditions of quantum field theory in curved spacetime.

Quantum Inequalities and Particle Creation in the Presence of an External, Time-Dependent Mamaev-Trunov Potential

## In this paper, we solve the Dirac Equation in curved space–time, modified by the generalized uncertainty principle, in the presence of an electromagnetic field.

Quantum gravity corrections to tunneling of spin-1/2 fermions from Kerr–Newman Black Hole

## Considering that curved space-time in coordinate or momentum representation should be curved, this paper proposes a new high-order generalized uncertainty principle by modifying the coordinate and momentum operator simultaneously, which could give a self-consistent phenomenological explanation for the existence of the minimum observable length.

Research on a new high-order generalized uncertainty principle in quantum system

## Success of S-matrix in quantum field theory in Minkowski spacetime naturally leads to the question of construction of S-matrix in a general curved spacetime.

Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate

## Due to the absence of symmetries under time and spatial translations in a general curved spacetime, the energy and momentum of matter is not conserved as it is in flat space.

Continuity equations for general matter: applications in numerical relativity

## First, we study the Weyl anomaly for a non-conformal free scalar in a four-dimensional curved spacetime.

Quantum aspects of classically conformal theories in four and six dimensions

## We consider the Weyl–Yang gauge theory of gravitation in a (4 + 3)-dimensional curved space-time within the scenario of the non-Abelian Kaluza–Klein theory for the source and torsion-free limits.

A black hole solution of higher-dimensional Weyl–Yang–Kaluza–Klein theory

## LST is non-local so it is not obvious which spaces it can be defined on; we show that holography implies that the theory cannot be put on negatively curved spaces, but only on spaces with zero or positive curvature.

Little String Theories on Curved Manifolds

## The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime.

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

## In this article, we propose a Bayesian embedded spherical topic model (ESTM) that combines both knowledge graph and word embeddings in a non-Euclidean curved space, the hypersphere, for better topic interpretability and discriminative text representations.

Combining Knowledge Graph and Word Embeddings for Spherical Topic Modeling.

## When it comes to aether, a subject rarely mentioned today, it appears to be Isaac Newton’s absolute time and space, modified to fit the Lorentz transformations and the non-Euclidean curved space of Einstein’s General Relativity.

Decrypting the Central Mystery of Quantum Mathematics:: Part 4. In What Medium Do Elementary Waves Travel?

## We study the analogy between propagation of light rays in a stationary curved spacetime and in a toroidal (meta-)material.

Optical Aharonov-Bohm effect due to toroidal moment inspired by general relativity

## We derive the Mandelstam-Tamm time-energy uncertainty relation for neutrino oscillations in a generic stationary curved spacetime.

Time-energy uncertainty relation for neutrino oscillations in curved spacetime

## In the second part we present a study first of the Kepler problem and then of the Kepler problem with additional nonlinear terms in these two curved spaces, S 3 (κ > 0) and H 3 (κ < 0).

Superintegrability on the three-dimensional spaces with curvature. Oscillator-related and Kepler-related systems on the sphere S 3 and on the hyperbolic space H 3

## At the same time, many data analysis and classification problems eventually reduce to an optimization, in which the criteria being minimized can be interpreted as the distortion associated with a mapping between two curved spaces.

A Riemannian geometric framework for manifold learning of non-Euclidean data

## X-ray quasi-periodic oscillations (QPOs) in AGN allow us to probe and understand the nature of accretion in highly curved space-time, yet the most robust form of detection (i.

Searching for energy-resolved quasi-periodic oscillations in AGN

## These effects strongly affect the destiny of observables in highly curved space– times.

Curved space equilibration vs. flat space thermalization (a short review)

## What was supposed to have happened was that matter ‘curved and warped space-time’ and when physical masses of this matter were ‘falling’ or were in orbit, they were actually following a straight line in this curved space time which created stretched holes in the ‘fabric of space-time’.

Determination of Earth’s Crust Movement at Kwoi, Kaduna State Using Gravity Method

## In this article we initiate the study of 1+ 2 dimensional wave maps on a curved space time in the low regularity setting.

Wave maps on (1+2)-dimensional curved spacetimes

## We consider the initial times of $\chi\chi\,\rightarrow\,\phi\phi$ and observe that the curved space effects promote formation of Bose-Einstein condensate of $\phi$ particles.

A mechanism for formation of Bose-Einstein condensation in cosmology.

## Even though a naive extrapolation of the linear Regge trajectory on flat space implies a violation of the Higuchi bound (a unitarity bound on the mass of higher-spin particles in de Sitter space), the curved space effects turn out to modify the trajectory to respect the bound.

String Regge trajectory on de Sitter space and implications to inflation

## The partial differential equation in curved space whose solution is the electrostatic potential A0 is obtained following Whittaker (Proc.

Three Partial Differential Equations in Curved Space and their Respective Solutions

## We establish a local monotonicity formula for mean curvature flow into a curved space whose metric is also permitted to evolve simultaneously with the flow, extending the work of Ecker (Ann Math (2) 154(2):503–525, 2001), Huisken (J Differ Geom 31(1):285–299, 1990), Lott (Commun Math Phys 313(2):517–533, 2012), Magni, Mantegazza and Tsatis (J Evol Equ 13(3):561–576, 2013) and Ecker et al.

Local energy inequalities for mean curvature flow into evolving ambient spaces

10.1038/s42005-021-00540-4

## Finally, we show that on curved surfaces, the motion of vortices and that of fractons agree; thereby opening a route to experimental study of the interplay between fracton physics and curved space.

Vortices as fractons

10.1142/S0217732321500590

## The generalized Duffin–Kemmer–Petiau (DKP) oscillator with electromagnetic interactions in the curved spacetimes is investigated.

Aharonov–Bohm effect on the generalized Duffin–Kemmer–Petiau oscillator in the Som–Raychaudhuri spacetime

10.1134/s0040577921100019

## We consider separately a case of Abelian extension, for which the RiemannHilbert equations of the dressing scheme are explicitly solvable and give an analogue of Penrose formula in the curved space.

Matrix extension of multidimensional dispersionless integrable hierarchies

10.1088/1361-6382/ac2270

## We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves.

The electromagnetic field in gravitational wave interferometers

10.1103/PhysRevE.103.013312

## The dynamics of low-energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time.

Numerical quasiconformal transformations for electron dynamics on strained graphene surfaces.

10.1016/J.IJLEO.2021.167009

## We consider the conformal transformation of electrodynamics in curved space.

Conformal electrodynamics in curved space

10.1103/PHYSREVA.103.032210

## We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected.

Complete complementarity relations in curved spacetimes

10.1016/j.physletb.2021.136429

## The speed of the graviton and photon are calculated in a curved spacetime modified by GUP, assuming that these particles have a small mass.

Bounds on GUP parameters from GW150914 and GW190521

10.17762/TURCOMAT.V12I2.1145

## The article describes how thinking about black holes as the most efficient kind of computers in the physical universe also paves the way for developing new ideas about such issues as black hole information paradox, the possibility of emulating the properties of curved space-time with the collective quantum behaviors of certain kind of condensate fluids, ideas of holographic spacetime, gravitational thermodynamics and entropic gravity, the role of quantum entanglements and non-locality in the construction of spacetime, spacetime geometry and the nature of gravitation and dark energy and dark matter, etc.

Do They Compute? Dawn of a New Paradigm based on the Information-theoretic View of Black holes, Universe and Various Conceptual Interconnections of Fundamental Physics

10.2991/ASSEHR.K.210421.061

## In this study, we extended the Brownian motion theory in a curved space-time come from a strong gravitational field on the Schwarzschild black hole.

Brownian Motion Around Black Hole

10.1088/1361-6552/ac12a9

## Even close to 10 years after the intervention, the participants remembered several key concepts (such as curved space-time).

Long-term impact of a primary school intervention on aspects of Einsteinian physics

10.1142/S0217732321500796

## We investigate the generalized form of Duffin–Kemmer–Petiau (DKP) equation in the presence of both a position-dependent electrical field and curved spacetime for the 2-dimensional anti-de Sitter sp.

Duffin–Kemmer–Petiau equation and thermodynamic quantities

10.1088/1475-7516/2021/04/005

## Neutrino trajectories in curved spacetime as well as the particle spin evolution in dense matter of an accretion disk and in the magnetic field are accounted for exactly.

Neutrino scattering off a black hole surrounded by a magnetized accretion disk

## Our theory provides a convenient and powerful tool for investigations of radiation in curved space.

Theory of light propagation in arbitrary two-dimensional curved space

10.1140/EPJP/S13360-021-01403-1

## In this paper the Feynman Green function for Maxwell’s theory in curved space-time is studied by using the Fock–Schwinger–DeWitt asymptotic expansion; the point-splitting method is then applied, since it is a valuable tool for regularizing divergent observables.

Divergent part of the stress-energy tensor for Maxwell’s theory in curved space-time: a systematic derivation

10.1088/1402-4896/abe495

## In this paper we solve the Dirac equation with the Coulomb scalar U(r) and vector V(r) potentials and type-Mie tensor potential in curved space-time whose metric is of type ds2=(1+α2U(r))2(dt2−dr2)−r2dθ2−r2sin2θdϕ2 with spherical symmetry.

Quasi-exact solution of the Dirac equation on curved space-time with Coulomb scalar and vector potentials and Mie-type tensor potential with pseudo-spin and spin symmetries

10.22541/au.163265111.15791882/v1

## The new perturbed metric is determined over the multiplication of isolated background metric of curved space-time for two different massive sources in post-Newtonian theory.

Modified gravity over the linearized metric perturbation for two body dynamics

10.1007/jhep09(2021)035

## In curved spacetime, nonrelativistic string theory is defined by a renormalizable quantum nonlinear sigma model in background fields, following certain symmetry principles that disallow any deformation towards relativistic string theory.

Torsional deformation of nonrelativistic string theory

10.1007/978-3-030-55777-5_46

## The partial differential equation in curved space whose solution is the electrostatic potential A0 is obtained following Whittaker (Proc.

Three Partial Differential Equations in Curved Space and their Respective Solutions

10.1140/epjc/s10052-021-09215-4

## We consider scalar fields in curved space-time with local couplings and masses.

Weyl consistency conditions from a local Wilsonian cutoff

10.1016/j.cjph.2021.08.007

## This would help us to better understand some of possible applications in astrophysics and cosmology, such as the natural phenomenon of a distinctive gravitational wave signature of merging two black holes associated with curved space–time in general relativity.

Geometric transformations on a topological black hole and their applications

10.1103/PhysRevD.103.045004

## In the presence of suitable vortex flows, the density fluctuations are governed by the massive Klein-Gordon equation on a (2+1) curved spacetime, possessing an ergoregion and an event horizon.

Acoustic black-hole bombs and scalar clouds in a photon-fluid model

10.1016/J.COMPSTRUCT.2021.114577

## However, little work has been completed on the utilisation of morphing composites in the design of curved space structures, e.

Toroidal deployment of morphing cylindrical lattices

10.1016/j.nuclphysb.2020.115240

## The most common methods are to use Noether's first theorem with the 4-parameter Poincare translation, or to write the action in a curved spacetime and perform variation with respect to the metric tensor, then return to a Minkowski spacetime.

Noether and Hilbert (metric) energy-momentum tensors are not, in general, equivalent

10.1088/1742-6596/1796/1/012125

## The refractive index and curved space relation is formulated using the Riemann-Christoffel curvature tensor.

Linear and non-linear refractive indices in curved space

10.4006/0836-1398-34.1.1

## Atomic structure is described with discrete coordinates in Minkowski space, while the atom itself resides in the curved space-time continuum of the gravitational field, the background space of quantum gravity.

Quantum gravity for dummies

10.1007/s10714-021-02828-w

## The scheme is a theory describing the dynamics of quantum fields propagating in a curved spacetime background, described by a Lorentzian manifold with a general classical metric gμν.

Particle creation in some LRS Bianchi I models

10.1093/OSO/9780198838319.003.0013

## In this chapter, which forms the central chapter of Part II, the effective action of quantum matter fields in curved spacetime is formulated in terms of functional integrals.

Quantum fields in curved spacetime: renormalization

10.1142/S0217751X21501323

## We find exact multi-instanton solutions to the self-dual Yang–Mills equation on a large class of curved spaces with [Formula: see text] isometry, generalizing the results previously found on [Formula: see text].

Exact multi-instanton solutions to self-dual Yang–Mills equation on curved spaces

10.1103/PHYSREVD.103.044051

## We investigate how pure-state Einstein-Podolsky-Rosen correlations in the internal degrees of freedom of massive particles are affected by a curved spacetime background described by extended theories of gravity.

Quantum nonlocality in extended theories of gravity

10.1007/JHEP05(2021)249

## These findings greatly extend the potential of using unitarity to bootstrap cosmological observables and to restrict the space of consistent effective field theories on curved spacetimes.

Cosmological Cutting Rules

## Quantum effects in non-inertial frames and curved space-time have been studied for decades.

Gaussian quantum information in relativistic quantum field theory for flat space-time

10.1088/1475-7516/2021/02/026

## We show that the equation of states computed in the curved spacetime of these stars depend explicitly on the metric function.

Equation of states in the curved spacetime of spherical degenerate stars

10.1007/JHEP03(2021)140

## We establish and generalize this relation to curved spaces by coupling the undeformed theory to 2d gravity.

Geometrizing $$T\overline{T}$$

10.3390/universe7050136

## They are spacetime structures that can potentially exist in curved spacetimes, so in a very wide class of gravity models.

Astrophysical Wormholes

10.3847/1538-4357/abf117

## The image polarization is determined by effects including the orientation of the magnetic field in the emitting region, relativistic motion of the gas, strong gravitational lensing by the black hole, and parallel transport in the curved spacetime.

The Polarized Image of a Synchrotron-emitting Ring of Gas Orbiting a Black Hole

10.1088/1572-9494/ac17e6

## As is well-known, it is very difficult to solve wave equations in curved space-time.

Analysis of the wave functions for accelerating Kerr-Newman metric

10.1007/JHEP09(2021)164

## In the target space, this sigma model describes classical strings propagating in a curved spacetime background, whose geometry is described by two distinct metric fields.

Strings in bimetric spacetimes

10.4236/jmp.2021.129073

## Physicists possess an intuitive awareness of Euclidian space and time and Galilean transformation, and are then challenged with Minkowski space-time and Einstein’s curved space-time.

Encoding Energy-Density as Geometry

10.1088/1361-6404/ac1abb

## String theory’s holographic QCD duality makes predictions for hadron physics by building models that live in five-dimensional (5D) curved space.

Holographic hadron masses in the language of quantum mechanics

10.1051/0004-6361/202040269

## The first one allows us to consider refractivity as spacetime curvature while the second one is used to determine the time/frequency transfers occurring in a curved spacetime.

Relativistic modeling of atmospheric occultations with time transfer functions

10.1007/JHEP09(2021)012

## We study the self-gravitating Abrikosov vortex in curved space with and with-out a (negative) cosmological constant, considering both singular and non-singular solutions with an eye to hairy black holes.

The Abrikosov vortex in curved space

10.1016/j.dark.2021.100897

## First, a generalized formalism of neutrino (spinor field) interaction with a classical scalar field in curved space-time is presented.

Distinguishing Dark Energy models with neutrino oscillations

10.1088/2633-1357/ac1725

## In practice one has to calculate the contribution of the transverse-traceless component of the metric perturbation on a curved spacetime background.

On the Lichnerowicz operator in traversable wormhole spacetimes

10.1209/0295-5075/134/50008

## First, the Klein-Gordon equation and Hamilton-Jacobi equation of bosons that are corrected by Lorentz symmetry violation theory in curved space-time are obtained.

Lorentz symmetry violation and accurate correction of bosons Hawking tunneling radiation for a stationary axisymmetric black hole

10.13111/2066-8201.2021.13.1.5

## Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures.

Gravitational waves on Earth and their warming effects

10.1093/OSO/9780198838319.003.0015

## First, the minimal subtraction renormalization group in curved space is formulated.

The renormalization group in curved space

10.24912/STUPA.V3I1.10907

## This points are applied in the forms of open and flexible spaces for exploration, easy access to green open spaces, spaces that suits the ergonomics of children, special corners that invoke children’s sense of place, the use of natural colours and curved spaces, and the use of soft materials and gardening to stimulate children’s sense of touch.

PENERAPAN METODE DESAIN ARSITEKTUR BERDASARKAN PERILAKU PADA PROYEK RUMAH EDUKASI-BERMAIN ANAK DI PLUIT

10.1088/1674-1056/abe300

## This condition is introduced according to the definition of the position operator in curved space.

Introducing the general condition for an operator in curved space to be unitary

10.1007/JHEP09(2021)105

## For our predictions, we trace curvilinear rays to the line of sight using the full set of equations from Hamiltonian optics for a dispersive medium in curved spacetime.

Radio line properties of axion dark matter conversion in neutron stars

10.20944/PREPRINTS202105.0586.V1

## We overcome this obstacle by using the equivalence principle for electric energy and describe a curved spacetime of fluid nature.

New Results in Quantum Thermodynamics

10.29322/IJSRP.11.04.2021.P11250

## What was supposed to have happened was that matter ‘curved and warped space-time’ and when physical masses of this matter were ‘falling’ or were in orbit, they were actually following a straight line in this curved space time which created stretched holes in the ‘fabric of space-time’.

Determination of Earth’s Crust Movement at Kwoi, Kaduna State Using Gravity Method

10.1103/PhysRevD.104.044057

## We set up a model of an electric charge where the noninvertible metric phase of first order gravity supercedes the point charge singularity in a curved spacetime.

Finite model of an electric charge

10.1093/OSO/9780198838319.003.0012

## Spontaneous symmetry breaking in curved space is shown to provide the induced gravity action with a cosmological constant.

Classical fields in curved spacetime

10.1016/J.FMRE.2021.06.014

## Understanding the effect of curvature and topological frustration on self-assembly yields insight into the mechanistic details of the ordering of identical subunits in curved spaces, such as the assembly of viral capsids, growth of solid domains on vesicles, and the self-assembly of molecular monolayers.

Entropy-driven self-assembly of tethered Janus nanoparticles on a sphere

10.1139/cjp-2020-0510

## Objects move along the geodesics in the curved space-time.

Derivation of general relativistic gravitational potential energy using principle of equivalence and gravitational time dilation

10.1103/PHYSREVB.103.064506

## To this end, we gauge the internal global symmetries of the theory on curved space by introducing the background gauge fields and spatial metric so as to expose a hidden local symmetry known as nonrelativistic diffeomorphism.

Hall viscosity in the A phase of superfluid He3

10.4006/0836-1398-34.3.397

## We discuss a theory in which symmetry between electricity and magnetism comes forward at the level of a grand unification mathematical logic as the defined symmetry between gravity and magnetogravity within the same allgravity responsible for all that in a curved space-time.

An allgravity as a grand unification of forces

## Starting from the wave equation with a non-zero space curvature, a generalized coordinate-independent expression for the evolution of a light beam on a curved space is derived.

Propagation and transformation of a light beam on a curved surface.

10.1093/OSO/9780198864899.001.0001

## In addition, it provides a (hopefully short) preparation for the student to be able to conduct research in a variety of topics in theoretical physics; with particular emphasis on physics in curved spacetime backgrounds.

Covariant Physics

10.1016/j.aop.2021.168648

## We introduced a generalized Maxwell-Higgs model in a (3 + 1) isotropic spacetime, and we found their stationary solutions using the BPS approach in curved spacetime.

Compact-like vortices in isotropic curved spacetime

10.1016/J.CAG.2021.04.002

## Virtual-reality simulations of curved space are most effective and most fun when presented as a game (for example, curved-space billiards), so the user not only has something to see in the curved space, but also has something fun to do there.

Body coherence in curved-space virtual reality games

10.3389/fphy.2021.655857

## In the low energy regime, the secondary notions of spacetime and of matter would then emerge as approximate representations of the abstract correlators, namely, in the form of Feynman rules on curved spacetime.

Replacing the Notion of Spacetime Distance by the Notion of Correlation

10.1142/S0217732321400034

## Besides Schrödinger Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schrödinger equation, where impact of the fractional Laplacian is discussed.

Fractional Schrödinger equation in gravitational optics

10.1142/S021773232150139X

## We investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter Ω(x) of Weyl transformation satisfies a constraint ✷Ω = 0 in a curved space-time.

Quadratic gravity and restricted Weyl symmetry

10.1016/j.cagd.2021.102002

## Discrete exterior calculus (DEC) offers a coordinate–free discretization of exterior calculus especially suited for computations on curved spaces.

A simple and complete discrete exterior calculus on general polygonal meshes

10.1088/1757-899X/1038/1/012084

## In this work, the RBF (Radial Basis Function) method has been presented as a capable technology that can morph the flat mesh electronic data to a curved space which can be further used for analysis purposes.

Modeling flexible/curved PCBs using RBF mesh morphing

10.1142/S0219887821501541

## Therefore, our method of finding the QNMs can be used for other curved spacetimes that obey the same boundary conditions.

Quasinormal modes of dS and AdS black holes: Feedforward neural network method

10.1088/1361-6382/ab0a97 10.1088/1361-6382/abc522

## We probe the effect of diffeomorphism symmetry on the critical exponents values for massive O(N) λφ4 scalar field theories in curved spacetime.

Diffeomorphism symmetry effect on the O(N ) universality class

10.20944/PREPRINTS202105.0406.V1

## The various authors in past have considered the 2D and 4D flat generalization of Misner space, but in the present work, we have considered the curved spacetime generalzations of 4D Misner space, and is asymptotically flat radially.

Type II Vacuum Spacetime Admitting Closed Timelike Curves

10.1088/1361-648X/ac0a1a

## The effect of many-body interaction in curved space is studied based on the extended Bose–Hubbard model on hyperbolic lattices.

Quantum phase transitions of interacting bosons on hyperbolic lattices

10.1088/1361-6382/abf97f

## In this work, in the context of modified gravity, a curved spacetime analogous to the ‘canonical acoustic black hole (CABH)’ is constructed.

Gravitational analog of the canonical acoustic black hole in Einstein–scalar–Gauss–Bonnet theory

10.1080/24748706.2021.1914881

## Therefore, despite being an overall smaller device than the original PASCAL implant, the grasp on the mitral valve leaflets may encase more leaflet surface area around the curved spacer, distributing tension across the captured leaflet tissue and minimizing leaflet trauma.

First-in-Human Experience of Transcatheter Mitral Valve Repair With the PASCAL Ace Implant System

10.1140/EPJP/S13360-021-01117-4

## Formulating the theory of QGIFs, a set of fundamental geometric, probability and quantum concepts, and methods of computation, are reconsidered for curved spacetime and (relativistic) phase spaces.

Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows

10.1093/OSO/9780198864899.003.0006

## We discuss mechanics in curved spacetime backgrounds, gravitational time dilation, the motion of free particles, geodesics.

Physics in Curved Spacetime

10.1088/1475-7516/2021/08/028

## The total deflection angle is defined by the difference between the sum of internal angles of two triangles; one of the triangles lies on curved spacetime distorted by a gravitating body and the other on its background.

The optical geometry definition of the total deflection angle of a light ray in curved spacetime