Higher Dimensional Einstein-Maxwell Theory Research Articles

Exact dynamical black hole solutions in five or higher dimensions

We construct new classes of the dynamical black hole solutions in five or higher dimensional Einstein–Maxwell theory, coupled to a dilaton field, in the presence of an arbitrary cosmological constant. The dilaton field interacts non-trivially with the Maxwell field, as well as the cosmological constant, with two arbitrary coupling constants. The solutions are non-stationary, and almost conformally regular everywhere. To construct the solutions, we use the four-dimensional Bianchi type IX geometry, as the base space. We find three different classes of solutions, based on the values of the coupling constants. We notice that our solutions could be asymptotically de-Sitter, anti-de-Sitter or flat. We find the relevant quantities of the solutions, and discuss the properties of the solutions.

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.

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 solutions to Einstein–Maxwell theory on Eguchi–Hanson space

In this paper, we construct explicit analytical exact solutions to the six and higher-dimensional Einstein–Maxwell theory. In all solutions, a subspace of the metric is the Eguchi–Hanson space where the metric functions are completely determined in terms of known analytical functions. Moreover, we find the solutions can be extended from nonstationary exact solutions to Einstein–Maxwell theory with cosmological constant. We show that the solutions are asymptotically expanding patches of de Sitter space–time.

New class of exact solutions in Einstein-Maxwell-dilaton theory

We find new solutions to the five-dimensional Einstein-Maxwell-dilaton theory with cosmological constant where the dilaton field couples to the electromagnetic field as well as to the cosmological term with two different coupling constants. The five-dimensional spacetime is non-stationary and is a conformally regular spacetime, everywhere. Both the dilaton field and the electromagnetic field depends on time and two spatial directions. The cosmological constant takes positive, negative or zero value, depending on the value of coupling constant. We study the physical properties of the spacetime and show that the solutions are unique in five dimensions and can't be uplifted to higher-dimensional Einstein-Maxwell theory or Einstein gravity in presence of cosmological constant. Moreover, we construct new solutions to the theory where both coupling constants are equal.

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.

SIX-DIMENSIONAL BRANEWORLD COSMOLOGY

We derive the brane cosmological solutions in the six-dimensional Einstein-Maxwell-dilaton theory, via dimensional reduction from the higher-dimensional Einstein-Maxwell theory. Two extra dimensions are compactified by a magnetic flux and two codimension-two branes are located at the boundaries. All the cosmological solutions approach an attractor in the later times. The attractor represents a simple power-law inflationary Universe whose power is simply given by the dilatonic coupling in the theory. Then, we discuss the properties of our solutions and deduce the cosmological implications.

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.

Higher-dimensional Einstein-Maxwell theory with inflation

It is shown how an inflationary universe can be realized in the context of higher-dimensional Einstein-Maxwell theory. As an explicit example, we present here the cosmological applications of the eight-dimensional Einstein-Maxwell theory. For $n=\ifmmode\pm\else\textpm\fi{}m$, where $n$ and $m$ are integers representing monopole charges in monopole configurations on ${S}^{2}\ifmmode\times\else\texttimes\fi{}{S}^{2}$, we find an inflation phase.