Classical Scattering in the Covariant Two-Body Coulomb Potential

The problem of two relativistically-moving pointlike particles of constant mass is undertaken in an arbitrary Lorentz frame using the classical Lagrangian mechanics of Stückelberg, Horwitz, and Piron. The particles are assumed to interact at events along their world lines at a common world time, an invariant dynamical parameter which is not in general synchronous with the particle proper time. The Lorentz-scalar interaction is assumed to be the Coulomb potential (i.e., the inverse square spacetime potential) of the spacetime event separation. The classical orbit equations are found in 1 + 1 spacetime dimensions in the hyperbolic angle coordinates for the reduced problem. The solutions to the reduced motion in these coordinates are the spacetime generalizations of the nonrelativistic Kepler solutions. and they introduce an invariant eccentricity which is a function of other known constants of the motion for the reduced problem. Solutions compatible with physical scattering are obtained by the assumption that the eccentricity is a given function of the ratio of the particle masses.     

Rotating Kink Spacetime

A suitably chosen complex parametrization of the 3-sphere is used to construct a (3 + 1)-dimensional spacetime that is homogeneous and satisfies the various standard energy conditions. The spacetime has nonzero vorticity, closed timelike curves and is shown to possess a Finkelstein-Misner kink. Hopf projection from the 3-sphere to a 2-sphere reduces the model to a previously known toy model in lower dimensions.     

一个4+1维宇宙模型

我们讨论的4+1维宇宙模型是通常的四维时空和一个紧致的一维内禀空间的直积空间。我们假定四维时空的能量密度是以辐射为主的,而内禀子空间的能动张量是一个阶跃函数。通过求解五维的Einstein场方程得到前四维时空由de-Sitter解过渡到标准模型的辐射为主解,与此同时内禀子空间的尺度由减幅振荡过渡到为按t的负幂次收缩而趋于一常量。 关键词：     

Letter: Interpolating Between the Bose-Einstein and the Fermi-Dirac Distributions in Odd Dimensions

We consider the response of a uniformly accelerated monopole detector that is coupled to a superposition of an odd and an even power of a quantized, massless scalar field in flat spacetime in arbitrary dimensions. We show that, when the field is assumed to be in the Minkowski vacuum, the response of the detector is characterized by a Bose-Einstein factor in even spacetime dimensions, whereas a Bose-Einstein as well as a Fermi-Dirac factor appear in the detector response when the dimension of spacetime is odd. Moreover, we find that, it is possible to interpolate between the Bose-Einstein and the Fermi-Dirac distributions in odd spacetime dimensions by suitably adjusting the relative strengths of the detector's coupling to the odd and the even powers of the scalar field. We point out that the response of the detector is always thermal and we, finally, close by stressing the apparent nature of the appearance of the Fermi-Dirac factor in the detector response.     

Three-variable solution in the $$$$-dimensional null-surface formulation

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact \((2+1)\)-dimensional solution that depends nontrivially upon all three of the NSF’s intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of \((2+1)\)-dimensional general relativistic spacetimes discovered by Cavaglià.     

Equality of bulk wave functions and edge correlations in some topological superconductors: a spacetime derivation

For certain systems, the N-particle ground-state wave functions of the bulk happen to be exactly equal to the N-point spacetime correlation functions at the edge, in the infrared limit. We show why this had to be so for a class of topological superconductors, beginning with the p+ip state in D=2+1. Varying the chemical potential as a function of Euclidean time between weak and strong pairing states is shown to extract the wave function. Then a Euclidean rotation that exchanges time and space and approximate Lorentz invariance lead to the edge connection. This framework readily generalizes to other dimensions. We illustrate it with a D=3+1 example, superfluid 3He- B, and a p-wave superfluid in D=1+1. Our method works only when the particle number is not conserved, as in superconductors.     

Q-Stars in Anti de Sitter Spacetime

We study q-stars with various symmetries in anti de Sitter spacetime in 3+1 dimensions. Comparing with the case of flat spacetime, we find that the value of the field at the center of the soliton is larger when the other parameters show a more complicated behavior. We also investigate their phase space when the symmetry is local and the effect of the charge to its stability.     

Geometrodynamics vs. connection dynamics

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. We analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. We also couple varions matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. We derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, we construct constraint functions and analyze their Poisson bracket algebra. We demonstrate, whenever possible, equivalences between the theories.     

States and operators in the spacetime algebra

The spacetime algebra (STA) is the natural, representation-free language for Dirac's theory of the electron. Conventional Pauli, Dirac, Weyl, and Majorana spinors are replaced by spacetime multivectors, and the quantum - and -matrices are replaced by two-sided multivector operations. The STA is defined over the reals, and the role of the scalar unit imaginary of quantum mechanics is played by a fixed spacetime bivector. The extension to multiparticle systems involves a separate copy of the STA for each particle, and it is shown that the standard unit imaginary induces correlations between these particle spaces. In the STA, spinors and operators can be manipulated without introducing any matrix representation or coordinate system. Furthermore, the formalism provides simple expressions for the spinor bilinear covariants which dispense with the need for the Fierz identities. A reduction to2+1 dimensions is given, and applications beyond the Dirac theory are discussed.Supported by a SERC studentship.     

Dirac quasinormal modes of Born-Infeld black hole spacetimes

Quasinormal modes (QNMs) for massless and massive Dirac perturbations of Born-Infeld black holes (BHs) in higher dimensions are investigated. Solving the corresponding master equation in accordance with hypergeometric functions and the QNMs are evaluated. We discuss the relationships between QNM frequencies and spacetime dimensions. Meanwhile, we also discuss the stability of the Born-Infeld BH by calculating the temporal evolution of the perturbation field. Both the perturbation frequencies and the decay rate increase with increasing dimension of spacetime n. This shows that the Born-Infeld BHs become more and more unstable at higher dimensions. Furthermore, the traditional finite difference method is improved, so that it can be used to calculate the massive Dirac field. We also elucidate the dynamic evolution of Born-Infeld BHs in a massive Dirac field. Because the number of extra dimensions is related to the string scale, there is a relationship between the spacetime dimension n and the properties of Born-Infeld BHs that might be advantageous for the development of extra-dimensional brane worlds and string theory.     

Black Hole Hair in Higher Dimensions

We study the property of matter in equilibrium with a static, spherically symmetric black hole in D- dimensional spacetime. It requires that this kind of matter has an equation of state ω≡pr/ρ = -n/（n ＋ 2k）, k, n ∈ N （where n 〉 1 corresponds to a mixture of vacuum matter and ＂hair＂ matter）, which seems to be independent of D. However, when we associate this result with specific models, we find that these hairy black holes can live only in some special dimensional spacetime： （i） D = 2 ＋ 2k/n while the black hole is surrounded by cosmic strings, which requires D is even or D ∈ N, depending on the value of n, this is consistent with some important results in superstring theory, it might reveal the relation between cosmic string and superstring in another aspect; （ii） the black hole can be surrounded by linear dilaton field only in 4-dimensional spacetime. In both cases, D = 4 is special. We also present some examples of such hairy black holes in higher dimensions, including a toy model with negative energy density.     

On analytic formulas of Feynman propagators in position space

We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in(3+1)-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary(D+1)-dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in(D+l)-dimensional spacetime and the scalar Feynman propagators in(D+1)-,(D-1)-and(D+3)-dimensional spacetimes.     

Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

We review the relation between AdS spacetime in 1 $+$ 2 dimensions and the BTZ black hole (BTZbh). Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZbh. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZbh. In order to make this we use the correspondence introduced in algebraic holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism.     

Symmetry and Integrability in the Classical Model of Zitterbewegung

We extended the Barut’s classical model of zitterbewegung from 3+1 dimensional spacetime into 2+1 and 1+1 dimensional spacetimes and discussed the symmetry and integrability properties of the model in 2+1, 1+1 and 3+1 dimensions. In these cases, the free particle current or the velocity of the particle can be decomposed as a constant convection current and polarization currents.     

Dimension in a Radiative Stellar Atmosphere

Dimensional scales are examined in an extended 3 + 1 Vaidya atmosphere surrounding a Schwarzschild source. At one scale, the Vaidya null fluid vanishes and the spacetime contains only a single spherical 2-surface. Both of these behaviors can be addressed by including higher dimensions in the spacetime metric.     

Curved traversable wormholes in (3+1)-dimensional spacetime

We present the general method of constructing curved traversable wormholes in (3+1)-d spacetime and proceed to thoroughly discuss the physics of a zero tidal force metric without cross-terms. The (3+1)-d solution is compared with the recently studied lower-dimensional counterpart, where we identify that the much richer physics—involving pressures and shear forces of the mass-energy fluid supporting the former—is attributed to the mixing of all three spatial coordinates. Our (3+1)-d universe is the lowest dimension where such nontrivial terms appear. An explicit example, the static zero tidal force (3+1)-d catenary wormhole is analysed and we show the existence of a geodesic through it supported locally by non-exotic matter, similar to the (2+1)-d version. A key difference is that positive mass-energy is used to support the entire (3+1)-d catenary wormhole, though violation of the null energy condition in certain regions is inevitable. This general approach of first constructing the geometry of the spacetime and then using the field equations to determine the physics to support it has the potential to discover new solutions in general relativity or to generalise existing ones. For instance, the metric of a time-evolving inflationary wormhole with a conformal factor can actually be geometrically constructed using our method.     

Higher Dimensional Spherically Symmetric Expanding Wormholes in Einstein’s Gravity

We present (n+1)-dimensional expanding structures in a cosmological background. Due to the expansion of spacetime the throat of wormholes enlarge with time. These solutions are examined in the Einstein’s framework. A general linear relation between diagonal elements of an anisotropic energy-momentum tensor is assumed and the spherically symmetric structures are obtained. Solutions include naked singularity and expanding wormholes in an open universe. The traversibility of wormhole solutions is explored and we find that they are basically traversable. Finally, we consider the corresponding energy-momentum tensor properties and specially take into account the standard energy conditions.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Vacuum in a strong magnetic field as a hyperbolic metamaterial

As demonstrated by Chernodub, vacuum in a strong magnetic field behaves as Abrikosov vortex lattice in a type-II superconductor. We investigate electromagnetic behavior of vacuum in this state and demonstrate that vacuum behaves as a hyperbolic metamaterial. If the magnetic field is constant, low frequency extraordinary photons experience this medium as a (3+1) Minkowski spacetime in which the role of time is played by the spatial z coordinate. Variations of the magnetic field curve this spacetime, and may lead to formation of "electromagnetic black holes." Since hyperbolic metamaterials behave as diffractionless "perfect lenses," and large enough magnetic fields probably existed in the early Universe, the demonstrated hyperbolic behavior of early vacuum may have imprints in the large scale structure of the present-day Universe.