Dimensional Einstein-Maxwell Theory Research Articles

Kaluza–Klein tower and bubble nucleation in six dimensional Einstein–Maxwell theory

We study the implication of the distance and the cobordism conjecture on the 6-dimensional Einstein–Maxwell theory compactified on S2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S^2$$\\end{document}. In this toy model, the radion potential is stabilized by the conspiracy of the curvature of S2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S^2$$\\end{document} and the flux through S2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S^2$$\\end{document} parametrized by f, and uplifted by the positive 6-dimensional cosmological constant parametrized by λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}. When λ=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =0$$\\end{document}, the radion is stabilized at the anti-de Sitter (AdS) vacuum, which cannot be interpolated to the Minkowski vacuum since the Kaluza–Klein (KK) tower descends from UV in the vanishing limit of the 4-dimensional cosmological constant. For nonzero λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} which realizes the metastable de Sitter (dS) vacuum, as well as the AdS and the Minkowski vacuum, such an obstruction can be found provided the combination f2λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f^2\\lambda $$\\end{document} is fixed and the limit λ→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda \\rightarrow 0$$\\end{document} is taken. Moreover, the 6-dimensional Einstein–Maxwell theory allows the transition between vacua through the nucleation of the bubble. In this case, the values of the 4-dimensional cosmological constant inside and outside the bubble are different as f is changed at the bubble wall, while λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} remains unchanged. Regarding the AdS vacuum with the vanishing curvature radius as the ‘nothing’, we find that the transition from the metastable dS vacuum to the nothing is not prevented by the descent of the KK tower since f2λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f^2\\lambda $$\\end{document} is not fixed.

Stability of topological solitons, and black string to bubble transition

We study the existence of smooth topological solitons and black strings as locally-stable saddles of the Euclidean gravitational action of five dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein background of four dimensional Minkowski with an S1. We compute the off-shell gravitational action in the canonical ensemble with fixed boundary data corresponding to the asymptotic radius of S1, and to the electric and magnetic charges that label the solitons and black strings. We show that these objects are locally-stable in large sectors of the phase space with varying lifetime. Furthermore, we determine the globally-stable phases for different regimes of the boundary data, and show that there can be Hawking-Page transitions between the locally-stable phases of the topological solitons and black strings. This analysis demonstrates the existence of a large family of globally-stable smooth solitonic objects in gravity beyond supersymmetry, and presents a mechanism through which they can arise from the black strings.

Bianchi IX geometry and the Einstein–Maxwell theory

We construct numerical solutions to the higher-dimensional Einstein–Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We find the solutions as superposition of two functions, which one of them can be found numerically. We show that the solutions in any dimensions, are almost regular everywhere, except a singular point. We find that the solutions interpolate between the two exact analytical solutions to the higher dimensional Einstein–Maxwell theory, which are based on Eguchi–Hanson type I and II geometries. Moreover, we construct the exact cosmological solutions to the theory, and study the properties of the solutions.

Orbifold black holes

We construct a regular black hole solution on the orbifold {mathbb C}^{n}/{mathbb Z}_{n} in the (2n+1)-dimensional Einstein–Maxwell theory. The event horizon is S^{2n-1}/{mathbb Z}_{n}.

Building (1+1) holographic superconductors in the presence of non-linear Electrodynamics

In the framework of the gauge/gravity duality, and in particular of the AdS3/CFT2 correspondence, we study one-dimensional superconductors analysing the dual (1+2)-dimensional gravity in the presence of the Einstein-power-Maxwell non-linear Electrodynamics. In the probe limit we compute the critical temperature of the transition as a function of the mass of the scalar field. The computation is performed analytically employing the Rayleigh-Ritz variational principle. The comparison with a power Maxwell field in higher dimensions as well as with the (1+3)-dimensional Einstein-Maxwell theory for two-dimensional superconductors is made as well.

No static bubbling spacetimes in higher dimensional Einstein–Maxwell theory

We prove that any asymptotically flat static spacetime in higher dimensional Einstein–Maxwell theory must have no magnetic field. This implies that there are no static soliton spacetimes and completes the classification of static non-extremal black holes in this theory. In particular, these results establish that there are no asymptotically flat static spacetimes with non-trivial topology, with or without a black hole, in Einstein–Maxwell theory.

Exact helicoidal and catenoidal solutions in five- and higher-dimensional Einstein-Maxwell theory

We present several new exact solutions in five and higher dimensional Einstein-Maxwell theory by embedding the Nutku instanton. The metric functions for the five-dimensional solutions depend only on a radial coordinate and on two spatial coordinates for the six and higher dimensional solutions. The six and higher dimensional metric functions are convoluted-like integrals of two special functions. We find that the solutions are regular almost everywhere and some spatial sections of the solution describe wormhole handles. We also find a class of exact and nonstationary convoluted-like solutions to the Einstein-Maxwell theory with a cosmological constant.

Exact convoluted solutions in higher-dimensional Einstein-Maxwell theory

We construct two classes of exact solutions to six and higher dimensional Einstein-Maxwell theory in which the metric functions can be written as convolution-like integrals of two special functions. The solutions are regular everywhere and show a bolt structure on a single point in any dimensionality. Moreover, we find the exact nonstationary solutions to the Einstein-Maxwell theory with positive cosmological constant. We show that the cosmological solutions are expanding patches in asymptotically de Sitter spacetime.

Cold planar horizons are floppy

Extremal planar black holes of four dimensional Einstein-Maxwell theory with a negative cosmological constant have an AdS$_2 \times \R^2$ near horizon geometry. We show that this near horizon geometry admits a deformation to a two parameter family of extremal geometries with inhomogeneous, spatially periodic horizons. At a linear level, static inhomogeneous perturbations of AdS$_2 \times \R^2$ decay towards the horizon and thus appear irrelevant under the holographic RG flow. However we have found numerically that nonlinear effects lead to inhomogeneous near horizon geometries. A consequence of these observations is that an arbitrarily small periodic deformation of the boundary theory at nonzero charge density does not flow to AdS$_2 \times \R^2$ in the IR, but rather to an inhomogeneous horizon. These results shed light on existing numerical studies of low temperature periodically modulated black holes and also offer a new mechanism for holographic metal-insulator crossovers or transitions.

Attractors and first order formalism in five dimensions revisited

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five-dimensional rotating black object potential depending on Taub-Newman-Unti-Tamburino, electric and magnetic charges as well as on all the scalar and gauge fields, is investigated. The first order formalism in $d=5$ is constructed and analyzed. We derive a general expression defining the fake superpotential which is valid for all charge configurations. An explicit expression for the fake superpotential is constructed, for all very special geometries, in the case of vanishing Taub-Newman-Unti-Tamburino charge. We carry out an analogous construction in the very special geometries corresponding to ${t}^{3}$ and $stu$ models, for the most general charge configurations. The attractor flows and horizon values of all fields are given.

Charged rotating black holes in higher-dimensional (A)dS gravity

We present numerical evidences for the existence of rotating black holes in $d$-dimensional Einstein-Maxwell theory with a cosmological constant and for an odd number of dimensions. The metric used possesses $(d+1)/2$ Killing vectors and the black holes have $(d\ensuremath{-}1)/2$ equal angular momenta. The Schwarzschild-like coordinate system used clearly reveals the influence of the electromagnetic field on the vacuum black holes where analytic expressions are available. The domain of existence of the charged rotating black holes is then characterized for both signs of the cosmological constant. The generic solutions are specified by their event horizon and by two additional parameters: the magnetic field and the angular velocity at the horizon. The dependence of several physical quantities---surface gravity, mass, angular momentum, etc.---is studied as a function of these parameters; Smarr-like relations are derived.

On the smoothness of static multi-black hole solutions of higher dimensional Einstein–Maxwell theory

Previous work has shown that static multi-black hole solutions of higher dimensional Einstein–Maxwell theory do not possess smooth horizons. We show that the lack of smoothness is worse than previously demonstrated. We consider solutions describing multiple black holes on a common axis. In five dimensions, the metric is generically twice, but not three times, continuously differentiable at the horizon. The Maxwell field is generically continuous, but not differentiable, at the horizon. In more than five dimensions, the metric is once, but not twice, continuously differentiable, and there is a parallely propagated curvature singularity at the horizon. The Maxwell field strength is again continuous, but not differentiable, at the horizon.

Charged–rotating black holes and black strings in higher dimensional Einstein–Maxwell theory with a positive cosmological constant

We present arguments for the existence of charged, rotating black holes in d = 2N + 1 dimensions, with d ⩾ 5 with a positive cosmological constant. These solutions possess both a regular horizon and a cosmological horizon of spherical topology and have N equal-magnitude angular momenta. They approach asymptotically the de Sitter-spacetime background. The counterpart equations for d = 2N + 2 are investigated, by assuming that the fields are independent of the extra dimension y, leading to black string solutions. These solutions are regular at the event horizon. The asymptotic form of the metric is not of the de Sitter-type and exhibits a naked singularity at finite proper distance.

Thin shell wormholes in higher dimensional Einstein–Maxwell theory

We construct thin shell Lorentzian wormholes in higher dimensional Einstein-Maxwell theory applying the ' Cut and Paste ' technique proposed by Visser. The linearized stability is analyzed under radial perturbations around some assumed higher dimensional spherically symmetric static solution of the Einstein field equations in presence of Electromagnetic field. We determine the total amount of exotic matter, which is concentrated at the wormhole throat.

Solutions of (2+1)-dimensional Einstein-Maxwell theory with parasupersymmetry

Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle are obtained. The solutions correspond to the static spacetime of a locally constant curvature in its spatial part and a constant magnetic field of a magnetic monopole together with a deficit of angle at the location of the point mass. The quantum mechanics of a point particle in these spacetimes in the absence of an angular deficit are solved algebraically both relativistically and nonrelativistically. It is also shown that these two-dimensional Hamiltonians have the degeneracy group of $\mathrm{GL}(2,c)$ type and parasupersymmetry of arbitrary order or shape invariance, which originated from an $\mathrm{SO}(4,c)$ group.

Classical stability of direct products of spheres in gravitational systems

Abstract Classical stability of Einstein spaces S d 1 ×⋯×S d n ( d j ⩾ 2) against all fluctuations is investigated in euclidean gravity with a cosmological constant. It is shown that S d is classically stable, while S d 1 ×⋯× S d n ( n ⩾ 2) is classically unstable. As a generalization of this analysis it is proved that a compact Einstein space B 1 ×⋯× B n ( n ⩾ 2) which is a direct product of each Einstein space is classically unstable. Non-Einstein spaces M 2 × S 4 (M 2 × S 2 × S 2 ) are also considered in six- dimensional Einstein-Maxwell theory and are shown to be classically stable (unstable).