Five-dimensional Minkowski Space Research Articles

A five-dimensional vacuum-defect wormhole space-time

In this study, we present a novel extension to the Klinkhamer vacuum-defect model by incorporating a fifth spatial dimension. This modification results in the formulation of a comprehensive five-dimensional wormhole space-time. Crucially, this extension preserves its classification as a vacuum solution to the field equations, thereby automatically satisfying all energy conditions. We demonstrate that this five-dimensional vacuum-defect space-time can be expressed in a pure canonical form, and thus, locally reduces to five-dimensional Minkowski space. Finally, we explore the geodesic equations in the vicinity of this five-dimensional vacuum-defect wormhole, offering insights into its intriguing properties.

Generalized Helical Hypersurface with Space-like Axis in Minkowski 5-Space

We introduce the generalized helical hypersurface having a space-like axis in five-dimensional Minkowski space. We compute the first and second fundamental form matrices, Gauss map, and shape operator matrix of the hypersurface. Additionally, we compute the curvatures of the hypersurface by using the Cayley–Hamilton theorem. Moreover, we give some relations for the mean and the Gauss–Kronecker curvatures of the hypersurface. Finally, we obtain the Laplace–Beltrami operator of the hypersurface.

Gravitational radiation from a binary system in odd-dimensional spacetime

We explore possible manifestations of an odd number of extra dimensions in gravitational radiation, which are associated with violation of Huygens' principle in flat odd-dimensional spacetime. Our setup can be regarded as the limit of an infinite compactification radius in ADD model and is not viable as realistic cosmology, but it still may be useful as a simple analytically solvable model catching certain features of more realistic scenarios. The model consists of two point masses moving inside a flat three-dimensional brane, embedded in a five-dimensional Minkowski space and interacting only through a massless scalar field localized on the same brane, while gravitational radiation is emitted into the bulk. This setup avoids the difficulties associated with taking into account the gravitational stresses binding the system, which require the cubic terms in the perturbative gravitational Lagrangian, and permits to limit ourselves to linearized theory. We calculate radiation in a linearized five-dimensional gravity generalizing the Rohrlich-Teitelboim approach to extract the emitted part of the retarded gravitational field. The source term consists of a local contribution from point particles and a non-local contribution from scalar field stresses, which is calculated using the DIRE approach to post-Newtonian expansions. In the nonrelativistic limit, we find an analog of the quadrupole formula containing an integral over the history of the particles' motion preceding the retarded time. We also show that, for an observer on the brane, the radiation contains a third polarization: the breathing mode.

A domain wall description of brane inflation and observational aspects

We consider a brane cosmology scenario by taking an inflating 3D domain wall immersed in a five-dimensional Minkowski space in the presence of a stack of N parallel domain walls. They are static BPS solutions of the bosonic sector of a 5D supergravity theory. However, one can move towards each other due to an attractive force in between driven by bulk particle collisions and resonant tunneling effect. The accelerating domain wall is a 3-brane that is assumed to be our inflating early Universe. We analyze this inflationary phase governed by the inflaton potential induced on the brane. We compute the slow-roll parameters and show that the spectral index and the tensor-to-scalar ratio are within the recent observational data.

Massless gravitons on a brane from massive gravity in five-dimensional Minkowski space

We discuss the possibility of localizing Einstein gravity on a three-brane embedded in a five-dimensional Minkowski space by giving a space-dependent mass to the graviton. We show that, with an overall fine tuning of the mass profile, it is possible to localize a massless graviton with a finite mass gap from the massive Kaluza-Klein modes. The theory does not contain ghosts and no scalar massless mode is sourced by brane matter. A massless vector mode is strongly coupled to the flux of energy-momentum into the extra dimension, so that it is not sourced as long as only brane-localized matter is considered. In the case where the mass profile has a delta-like shape the four-dimensional Planck mass $M_4$ is related to the five-dimensional one, $M_5$, by $M_4^{2}=M_5^3/m_0$, where $m_0$ is the mass of the first Kaluza-Klein mode of the graviton.

Stationary axisymmetric solutions of five-dimensional gravity

We consider stationary axisymmetric solutions of general relativity that asymptote to five-dimensional Minkowski space. It is known that this system has a hidden symmetry. We identify an SO(2, 1) subgroup of this symmetry group that preserves the asymptotic boundary conditions. We show that the action of this subgroup on a static solution generates a one-parameter family of stationary solutions carrying angular momentum. We conjecture that by repeated applications of this procedure one can generate all stationary axisymmetric solutions starting from static ones. As an example, we derive the Myers–Perry black hole starting from the Schwarzschild solution in five dimensions.

An Infinite Number of Stationary Soliton Solutions to the Five-Dimensional Vacuum Einstein Equation

We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2,2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical.

Supersymmetric AdS5 solutions of M-theory

We analyse the most general supersymmetric solutions of D = 11 supergravity consisting of a warped product of five-dimensional anti-de Sitter space with a six-dimensional Riemannian space M6, with 4-form flux on M6. We show that M6 is partly specified by a one-parameter family of four-dimensional Kähler metrics. We find a large family of new explicit regular solutions where M6 is a compact, complex manifold which is topologically a 2-sphere bundle over a four-dimensional base, where the latter is either (i) Kähler–Einstein with positive curvature, or (ii) a product of two constant-curvature Riemann surfaces. After dimensional reduction and T-duality, some solutions in the second class are related to a new family of Sasaki–Einstein spaces which includes . Our general analysis also covers warped products of five-dimensional Minkowski space with a six-dimensional Riemannian space.

Elementary particles in a curved space. II

This is an attempt to develop conventional, contemporary, elementary-particle physics in a Riemannian space of constant curvature. We study the global structure of the 3 + 2 de Sitter space, which we take to mean the covering space of the hyperboloid $y_{0}^{}{}_{}{}^{2}\ensuremath{-}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{y}}}^{2}+y_{5}^{}{}_{}{}^{2}={\ensuremath{\rho}}^{\ensuremath{-}1}$ in a five-dimensional Minkowski space. This space is not periodic in time. A causal structure is shown to exist and the commutation relations between free fields are shown to be causal. Elementary massive particles are associated with a class of irreducible representations of the universal covering group of SO(3, 2) for which the Hamiltonian has a discrete spectrum with a lower (positive) bound. A detailed study is made of the wave functions in "momentum space" and in configuration space. Free quantum fields are introduced with the help of a discrete set of creation and destruction operators and the commutator [${\ensuremath{\varphi}}_{0}(x), {\ensuremath{\varphi}}_{0}({x}^{\ensuremath{'}})$] is calculated. An appendix describes what we think is an interesting way to realize irreducible representations of the "discrete series."

On representations of the inhomogeneous de Sitter group and equations in five-dimensional Minkowski space

This paper is a continuation and elaboration of our brief notice [1] where some approach to the variable-mass problem was proposed. Here we have found a definite realization of irreducible representations of the inhomogeneous group P(1, n), the group of translations and rotations in (1 + n)-dinsional Minkowski space, in two classes (when P o 2 − P k 2 > 0 and P o 2 − P k 2 < 0). All P(1, n)-invariant equations of the Schrödinger-Foldy type are written down. Some equations of physical interpretation of the quantal scheme based on the inhomogeneous de Sitter group P(1, 4) are discussed. The analysis of the Dirac and Kemmer-Duffin type equations in the P(1. 4) scheme is carried out. A concrete realization of representations of the algebra P(1, 4) connected with this equations, is obtained. The transformations of the Foldy-Wouthuysen type for this equations are found. It is shown that in the P(1, 4) scheme of the Kemmer-Duffin type equation describes a fermion multiplet like the nucleon-antinucleon.