Radiating black hole solutions in arbitrary dimensions

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in N-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.     

New Charged Dilaton Solutions in 2+1 Dimensions and Solutions with Cylindrical Symmetry in 3+1 Dimensions

We report a new family of solutions to Einstein-Maxwell-dilaton gravity in 2+1 dimensions and Einstein-Maxwell gravity with cylindrical symmetry in 3+1 dimensions. A set of static charged solutions in 2+1 dimensions are obtained by a compactification of charged solutions in 3+1 dimensions with cylindrical symmetry. These solutions contain naked singularities for certain values of the parameters considered. New rotating charged solutions in 2+1 dimensions and 3+1 dimensions are generated treating the static charged solutions as seed metrics and performing SL(2;R) transformations.     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Generalized Jordanian R-Matrices of Cremmer–Gervais Type

An explicit quantization is given of certain skew-symmetric solutions of the classical Yang–Baxter equation, yielding a family of R-matrices which generalize to higher dimensions the Jordanian R-matrices. Three different approaches to their construction are given: as twists of degenerations of the Shibukawa–Ueno, Yang–Baxter operators on meromorphic functions; as boundary solutions of the quantum Yang–Baxter equation; via a vertex-IRF transformation from solutions to the dynamical Yang–Baxter equation.     

Black holes in higher dimensional space-times

Black hole solutions to Einstein's equations are examined in asymptotically flat N + 1 dimensional space-times. First generalizations of Schwarzschild and Reissner-Nordstrøm solutions are examined in a discussion of static black holes in N + 1 dimensions. Then a new family of solutions is found which describe spinning black holes in higher dimensional space-times. In many respects these new solutions are similar to the familiar Kerr and Schwarzschild metrics which are recovered for N = 3. One exceptional case though is that for N ≥ 5, black holes with a fixed mass may have arbitrarily large angular momentum.     

Rotating Dilaton Solutions in 2+1 Dimensions

We report a three parameter family of solutions for dilaton gravity in 2+1 dimensions with finite mass and finite angular momentum. These solutions are obtained by a compactification of vacuum solutions in 3+1 dimensions with cylindrical symmetry. One class of solutions corresponds to conical singularities and the other leads to curvature singularities.     

Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $${\mathbb{R}^n}$$

In this paper we consider systems of coupled Schrödinger equations which appear in nonlinear optics. The problem has been considered mostly in the one-dimensional case. Here we make a rigorous study of the existence of least energy standing waves (solitons) in higher dimensions. We give: conditions on the parameters of the system under which it possesses a solution with least energy among all multi-component solutions; conditions under which the system does not have positive solutions and the associated energy functional cannot be minimized on the natural set where the solutions lie.     

Solutions of coupled KdV-type equations

We consider a family of coupled (Ito type) KdV equations in 1+1 dimensions and use Hlavatý's technique to obtain a class of explicit wave-type solutions.     

Heterotic string from a higher dimensional perspective

The (abelian bosonic) heterotic string effective action, equations of motion and Bianchi identity at order α^′ in ten dimensions, are shown to be equivalent to a higher dimensional action, its derived equations of motion and Bianchi identity. The two actions are the same up to the gauge fields: the latter are absorbed in the higher dimensional fields and geometry. This construction is inspired by heterotic T-duality, which becomes natural in this higher dimensional theory.We also prove the equivalence of the heterotic string supersymmetry conditions with higher dimensional geometric conditions. Finally, some known Kähler and non-Kähler heterotic solutions are shown to be trivially related from this higher dimensional perspective, via a simple exchange of directions. This exchange can be encoded in a heterotic T-duality, and it may also lead to new solutions.     

Relativistic Charged Star Solutions in Higher Dimensions

We present a class of relativistic solutions of the Einstein-Maxwell equations for a spherically symmetric charged static fluid sphere in higher dimensions. The interior space at t=constant considered here possess (D?1) dimensional spheroidal geometry described by a higher dimensional Vaidya-Tikekar metric. A class of new static solutions of coupled Einstein-Maxwell equations is obtained in a D-dimensional space-time by prescribing the geometry of a (D?1) dimensional hyper spheroid in hydrostatic equilibrium. The solutions of the Einstein-Maxwell field equations are employed to obtain relativistic models for charged compact stars with a suitable law for variation of electric field in terms of the charged fluid content in the interior of the sphere. The central density is found to depend on the space-time dimensions and a physically realistic model is permitted for (D≥4). The validity of both Strong Energy Condition (SEC), Weak Energy Condition (WEC) are studied for a given configuration and compactness of compact objects. We found new class of solutions with interesting stellar models where it permits a star with a core having different property than the rest which however disappears in higher dimensions. The effect of dimensions on the Electric charge of the compact object is studied. We note that the upper limit of the electric field is determined by the space-time dimensions which are determined.     

EVH black hole solutions with higher derivative corrections

We analyze the effect of higher derivative corrections to the near horizon geometry of the extremal vanishing horizon (EVH) black hole solutions in four dimensions. We restrict ourselves to a Gauss–Bonnet correction with a dilation dependent coupling in an Einstein–Maxwell-dilaton theory. This action may represent the effective action as it arises in tree level heterotic string theory compactified to four dimensions or the K3 compactification of type II string theory. We show that EVH black holes, in this theory, develop an AdS₃ throat in their near horizon geometry.     

The string theory landscape: a tale of two hydras

String theory is the leading theoretical approach to finding a consistent quantum theory that unifies gravity with the other three forces. However, the theory is only consistent in ten dimensions. In order for string theory to describe observable physics, the six extra dimensions must be sufficiently small to be unobservable. Originally it was hoped that there would only be one consistent way of doing this, but now it is realized that this problem may have as many as 10⁵⁰⁰ possible solutions. I describe where this number comes from and the approaches, both statistical and anthropic, taken in dealing with this superfluity of solutions.     

Dirac field in topologically massive gravity

We consider a Dirac field coupled minimally to the Mielke–Baekler model of gravity and investigate cosmological solutions in three dimensions. We arrive at a family of solutions which exists even in the limit of vanishing cosmological constant.     

Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations

We study a family of generalized slope limiters in two dimensions for Runge–Kutta discontinuous Galerkin (RKDG) solutions of advection-diffusion systems. We analyze the numerical behavior of these limiters applied to a pair of model problems, comparing the error of the approximate solutions, and discuss each limiter’s advantages and disadvantages. We then introduce a series of coupled p-enrichment schemes that may be used as standalone dynamic p-enrichment strategies, or may be augmented via any in the family of variable-in-p slope limiters presented.     

Critical dimension in the black-string phase transition

In spacetimes with compact dimensions, there exist several black object solutions including the black hole and the black string. They may become unstable depending on their relative size and the length scales in the compact dimensions. The transition between these solutions raises puzzles and addresses fundamental questions such as topology change, uniquenesses, and cosmic censorship. Here, we consider black strings wrapped over the compact circle of a d-dimensional cylindrical spacetime. We construct static nonuniform strings around the marginally stable uniform string. First, we compute the instability mass for a large range of dimensions and find that it follows an exponential law gamma(d), where gamma<1 is a constant. Then we determine that there is a critical dimension, d(*)=13, such that for dd(*) it is, surprisingly, of higher order.     

Stainless super p-branes

The elementary and solitonic supersymmetric p-brane solutions to supergravity theories form families related by dimensional reduction, each headed by a maximal (‘stainless’) member that cannot be isotropically dimensionally oxidized into higher dimensions. We find several new families, headed by stainless solutions in various dimensions D ⩽ 9. In some cases, these occur with dimensions (D, p) that coincide with those of descendants of known families, but since the new solutions are stainless, they are necessarily distinct. The new stainless supersymmetric solutions include a 6-brane and a 5-brane in D = 9, a string in D = 5, and particles in all dimensions 5 ⩽ D ⩽ 9.     

The Boulware–Deser class of spacetimes radiates

We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.     

Experimental Test for Extra Dimensions in Kaluza–Klein Gravity

5D Kaluza–Klein gravity has several nonasymptotically flat solutions which generally, possess both electric and magnetic charges. In this paper we suggest that these solutions can act as quantum virtual handles (wormholes) in spacetime foam models. In the presence of a sufficently large, external electric and/or magnetic field it may be possible to inflate these solutions from a quantum to a classical state. This effect would lead to a possible experimental signal for higher dimensions in multidimensional gravity.     

Composite S-Brane Solutions on the Product of Ricci-Flat Spaces

A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields and antisymmetric forms is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. The solutions depend on charge densities of branes, their dimensions and intersections, dilatonic couplings and the number of dilatonic fields.     

Local structure of the self-focusing singularity of the nonlinear Schrödinger equation

For the cubic Schrödinger equation in two dimensions we construct a family of singular solutions by perturbing slightly the dimension d = 2 tod > 2.