Five-dimensional Metrics Research Articles

A space/time interchange symmetry of rotating AdS black holes in general dimensions

We revisit the previously known local inversion symmetry of the five-dimensional Kerr-AdS metric that relates the over-rotating black hole to the under-rotating one and reinterpret it as an interchanging symmetry between time and the longitudinal angular coordinates. We generalize this to all D dimensions, including D=4, thereby enlarging the trivial linear ZN symmetry of the N=⌊(D−1)/2⌋ longitudinal angular coordinates to the nonlinearly realized ZN+1 symmetry that involves time.

Gravitational fields of axially symmetric compact objects in 5D space–time–matter gravity

In the standard Einstein’s theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space–time. In this work we present a generalization of those so called Weyl solutions to a space–time–matter metric in a five-dimensional manifold within a non-compactified Kaluza–Klein theory of gravity. The arising field equations reduce to those of vacuum Einstein’s gravity when the metric function associated to the fifth dimension is considered to be constant. The calculation of the geodesics allows to identify the existence or not of different behaviours of test particles, in orbits on a constant plane, between the two metrics. In addition, static solutions on the hypersurface orthogonal to the added dimension but with time dependence in the five-dimensional metric are also obtained. The consequences on the variation of the rest mass, if the fifth dimension is identified with it, are studied.

Gauge symmetries and isometries in higher dimensions

We study the invariance properties of five-dimensional metrics and their corresponding geodesic equations of motion. In this context a number of five-dimensional models of the Einstein–Gauss–Bonnet (EGB) theory leading to black holes, wormholes and spacetime horns arising in a variety of situations are discussed in the context of variational symmetries of which each vector field, via Noether’s theorem (NT), provides a nontrivial conservation law. In particular, it is shown that algebraic structure of isometries and the variational conservation laws of the five-dimensional Einstein–Bonnet metric extend consistently from the well-known Minkowski, de-Sitter and Schwarzschild four-dimensional spacetimes to the considered five-dimensional ones. In the equivalent five-dimensional case, the maximal algebra of kvs is fifteen with eight additional Noether symmetries. Also, whereas the constant curvature five-dimensional case leads to fifteen kvs and one additional Noether symmetry and seven plus one in the minimal case, a number of metrics of the EGB theory in five dimensions give rise to algebras isomorphic a seven-dimensional algebra of kvs and a single additional Noether symmetry.

A geometric dual of c-extremization

We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and mathcal{N} = 2 supersymmetry in one dimension. The geometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the entropy of a class of supersymmetric black holes in AdS4. We also study many specific examples of the type AdS3 × T2 × Y5, including a new family of explicit supergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dual to these solutions can arise from the compactification on T2 of certain d = 4 quiver gauge theories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, come to a negative conclusion.

Causality-violating Higgs singlets at the LHC

We construct a simple class of compactified five-dimensional metrics which admits closed timelike curves (CTCs), and derive the resulting CTCs as analytic solutions to the geodesic equations of motion. The associated Einstein tensor satisfies all the null, weak, strong and dominant energy conditions. In particular, no negative-energy ``tachyonic'' matter is required. In extra-dimensional models where gauge charges are bound to our brane, it is the Kaluza-Klein modes of gauge singlets that may travel through the CTCs. From our brane point of view, many of these Kaluza-Klein modes would appear to travel backward in time. We give a simple model in which time-traveling Higgs singlets can be produced by the LHC, either from decay of the Standard Model Higgs or through mixing with the Standard Model Higgs. The signature of these time-traveling singlets is a secondary decay vertex preappearing before the primary vertex which produced them. The two vertices are correlated by momentum conservation. We demonstrate that preappearing vertices in the Higgs singlet-doublet mixing model may well be observable at the LHC.

(4+1)-DIMENSIONAL HOMOGENEOUS ANISOTROPIC STRING COSMOLOGICAL MODELS

We present exact solutions of string cosmological models characterized by five-dimensional metrics (with four-dimensional real Lie groups as isometry groups), space independent dilaton and vanishing torsion. As an example we consider VII0⊕R model and show that it is equivalent to the (4+1)-dimensional cosmological model coupled to perfect fluid with negative deceleration parameters (accelerating universe).

A higher-dimensional string cosmological model in a scalar-tensor theory of gravitation

A string cosmological model is obtained and presented by considering a five-dimensional Kaluza-Klein metric in the scalar-tensor theory of gravitation proposed by Brans and Dicke without taking any relation between rest energy density ρ and string tension density λ. Some physical and geometrical properties of the model are also discussed.

Casimir energy and brane stability

We investigate the role of Casimir energy as a mechanism for brane stability in five-dimensional models with the fifth dimension compactified on an S 1 / Z 2 orbifold, which includes the Randall–Sundrum two brane model (RS1). We employ a ζ -function regularization technique utilizing the Schwinger proper time method and the Jacobi theta function identity to calculate the one-loop effective potential. We show that the combination of the Casimir energies of a scalar Higgs field, the three generations of Standard Model fermions and one additional massive non-SM scalar in the bulk produces a non-trivial minimum of the potential. In particular, we consider a scalar field with a coupling in the bulk to a Lorentz violating vector particle localized to the compactified dimension. Such a scalar may provide a natural means of fine tuning needed for stabilization of the brane separation. Finally, we briefly review the possibility that Casimir energy plays a role in generating the currently observed epoch of cosmological inflation by examining a simple five-dimensional anisotropic metric.

On equations of motion for a lumped variable mass in the Kaluza‒Klein theory

Within the framework of the Kaluza-Klein theory considering cylindricity with respect to the fifth coordinate in a closed jet momentum + exhaust system, a new role of five-momentum in modeling of the external medium as an absorber of energy emitted when the rest mass changes, more exactly, when the Rogozhin reactive potential [10] newly introduced into the metric changes, is suggested for the first time. This approach allows us first, to accept automatically the Gantmakher hypothesis and second, to conserve the phase coordinates in the presence of a Hamiltonian. To solve this problem, the Gross-Perry and Kerr five-dimensional metrics are generalized.

New charged black holes in five dimensions

We obtain new stationary charged solutions of five-dimensional minimal supergravity. We first obtain purely dipole-charged solutions by extending a technique that we developed for five-dimensional Ricci-flat metrics in a previous paper, which could be viewed as being analogous to a four-dimensional construction by Demianski and Plebanski. The further introduction of electric charge is achieved by means of a solution-generating technique, which exploits the global symmetry of five-dimensional minimal supergravity reduced on a time-like direction to four dimensions. We present this procedure in detail, since it provides a particularly simple general way of adding charge to any stationary solution of five-dimensional minimal supergravity. The new charged solutions we obtain limit in special cases to black rings carrying electric and magnetic dipole charge, or to charged Myers–Perry rotating black holes. We analyze the general solutions in detail, showing that they can describe asymptotically locally flat black holes whose horizon is a lens space L(n; m) = S3/Γ(n; m). At infinity they approach Minkowski5/Γ(m; n).

Atiyah-Hitchin space in five-dimensional Einstein-Maxwell theory

We construct exact solutions to five-dimensional Einstein-Maxwell theory based on Atiyah-Hitchin space. The solutions cannot be written explicitly in a closed form, so their properties are investigated numerically. The five-dimensional metric is regular everywhere except on the location of original bolt in four-dimensional Atiyah-Hitchin base space. On each time-fixed slices, the metric, asymptotically approaches an Euclidean Taub-NUT space.

KALUZA–KLEIN SOLITONS RE-EXAMINED

In 4 + 1 gravity the assumption that the five-dimensional metric is independent of the fifth coordinate permits the extra dimension to be either spacelike or timelike. As a consequence of this, the time coordinate and the extra coordinate are interchangeable, which in turn allows the conception of different scenarios in 4D from a single solution in 5D. In this paper, we make a thorough investigation of all possible 4D scenarios, associated with this interchange, for the well-known Kramer–Gross–Perry–Davidson–Owen set of solutions. We show that there are three families of solutions with very distinct geometrical and physical properties. They correspond to different sets of values of the parameters which characterize the solutions in 5D. The solutions of physical interest are identified on the basis of physical requirements on the induced matter in 4D. We find that only one family satisfies these requirements; the other two violate the positivity of mass-energy density. The "physical" solutions possess a lightlike singularity which coincides with the horizon. The Schwarzschild black string solution as well as the zero moment dipole solution of Gross and Perry are obtained in different limits. These are analyzed in the context of Lake's geometrical approach. We demonstrate that the parameters of the solutions in 5D are not free, as previously considered. Instead, they are totally determined by measurements in 4D — namely, by the surface gravitational potential of the astrophysical phenomena, like the Sun or other stars, modeled in Kaluza–Klein theory. This is an important result which may help in observations for an experimental/observational test of the theory.

RICCI FLOWS AND SOLITONIC pp-WAVES

We find exact solutions describing Ricci flows of four-dimensional pp-waves nonlinearly deformed by two-/three-dimensional solitons. Such solutions are parametrized by five-dimensional metrics with generic off-diagonal terms and connections with nontrivial torsion which can be related, for instance, to antisymmetric tensor sources in string gravity. There are defined nontrivial limits to four-dimensional configurations and the Einstein gravity.

Space-time matter inflation

We study a model of power-law inflationary inflation using the space-time-matter theory of gravity for a five-dimensional canonical metric that describes an apparent vacuum. In this approach the expansion is governed by a single scalar (neutral) quantum field. In particular, we study the case where the power of expansion of the universe is p⪢1. This kind of model is more successful than others in accounting for galaxy formation.

Remarks on a five-dimensional Kaluza-Klein theory of the massive Dirac monopole

The Gross-Perry-Sorkin spacetime, formed by the Euclidean Taub-NUT space with the time trivially added, is the appropriate background of the Dirac magnetic monopole without an explicit mass term. One remarks that there exists a very simple five-dimensional metric of spacetimes carrying massive magnetic monopoles that is an exact solution of the vacuum Einstein equations. Moreover, the same isometry properties as the original Euclidean Taub-NUT space are preserved. This leads to an Abelian Kaluza-Klein theory whose metric appears as a combinations between the Gross-Perry-Sorkin and Schwarzschild ones. The asymptotic motion of the scalar charged test particles is discussed, now by accounting for the mixing between the gravitational and magnetic effects.

The universe as a five-dimensional black hole

We show the geometrical equivalence of two five-dimensional metrics, one describing a cosmology which smoothly embeds the standard Friedmann-Robertson-Walker-Lemaitre models, and another describing an object which topologically is a black hole. The solutions can be interpreted using either membrane or induced-matter theory. We outline the main physics, wherein the horizon of the black hole is connected to a big bounce in the cosmology, which may in turn be connected to a phase change in the vacuum.

Properties of some five-dimensional Einstein metrics

The volumes, spectra and geodesics of a recently constructed infinite family of five-dimensional inhomogeneous Einstein metrics on the two S3 bundles over S2 are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics Tp,1. The geodesic flow is shown to be completely integrable, in fact both the Hamilton–Jacobi and the Laplace equation separate. As an application of these results, we compute the zeta function of the Laplace operator on Tp,1 for large p. We discuss the spectrum of the Lichnerowicz operator on symmetric transverse tracefree second rank tensor fields, with application to the stability of Freund–Rubin compactifications and generalized black holes.

Large-Scale Two-Dimensional Quantum Fluctuations of Five-Dimensional and Four-Dimensional Space-Time Metrics

Large-scale two-dimensional quantum fluctuations of five-dimensional space-time metric are constructed and the effect of the fluctuations on the nested four-dimensional worlds is studied. In doing so, the fluctuations affect not all four-dimensional worlds but only a part of them. The energy-momentum tensor of four-dimensional space-time has a physical form both in the absence and in the presence of fluctuations; it means that the fluctuations can be realized by real matter. A spatial region occupied by the fluctuations constructed in this work can be infinitely large and the fluctuations can occur during a long period of time. Therefore, we refer to these fluctuations as large-scale fluctuations.

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the “splitting” of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure “constant” and the Thomson cross section are also discussed.

Fresh Inflation from Five-Dimensional Vacuum State

I study fresh inflation from a five-dimensional vacuum state, where the fifth dimension is constant. In this framework, the universe can be seen as inflating in a four-dimensional FRW metric embedding in a five-dimensional metric. Finally, the experimental data $n_s=1$ are consistent with $(p+\rho_t)/\rho_t \simeq1/3$ in the fresh inflationary scenario.