Quotient space solutions of 11-dimensional supergravity

All the Freund-Rubin type solutions of the 11-dimensional supergravity with a simply connected quotient spaceG/H as the compact 7-dimensional manifold are found. Their geometries depend only on the imbedding ofHG and the Riemannian structure ofG/H. In particular, SU₃×SU₂×U₁/SU₂×U₁×U₁, Einstein solutions are discussed in detail.     

Chiral supersymmetric pp-wave solutions of IIA supergravity

We describe solutions of type IIA (N = 2, D = 10) supergravity built under the assumption of the existence of at least one residual chiral supersymmetry. Their geometry is of pp-wave type. Explicit parametrization of the metric and matter field components, in terms of Killing spinors and arbitrary functions, is provided.     

Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS–NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.     

Plane symmetric space-time of class 1

A necessary and sufficient condition for a plane symmetric space-time admitting a three-parameter group of motion to be of embedding class 1 is obtained in terms of the components of the curvature tensor.     

Axially symmetric Brans-Dicke-Maxwell solutions

Following a method of John and Goswami new solutions of coupled Brans-Dicke-Maxwell theory are generated from Zipoy's solutions in oblate and prolate spheroidal coordinates for source-free gravitational field. All these solutions become Euclidean at infinity. The asymptotic behavior and the singularity of the solutions are discussed and a comparative study made with the corresponding Einstein-Maxwell solutions. The possibility of a very large red shift from the boundary of the spheroids is also discussed.     

Axially symmetric electrovac solutions

Two classes of electrovac solutions are obtained in oblate spheroidal coordinates, which are the electromagnetic analogs of Zipoy's monopole and dipole solutions. The asymptotic behavior of the solutions is studied to gain some insight into the nature of the source of the gravitational and electromagnetic fields. A similar stationary solution of the pure gravitational field is found to belong to Papapetrou's class.     

Plane symmetric metrics associated with semi-plane symmetric electromagnetic fields in higher dimensions

Electromagnetic fields yielding plane symmetric metrics in higher-dimensional spacetimes are exhausted and classified. It is shown that these EM fields must fall into one of the following two cases: (i)F _it =F _iz =0,i=1,...,n; (ii)F_tz=0. We give the general solution to the Einstein-Maxwell equations in higher dimensions corresponding to electromagnetic fields of case (ii) withF _it =F _iz , which covers all even-dimensional spacetimes as well as a subcase of odd-dimensional spacetimes.     

Necessary and sufficient conditions for trivial solutions in supergravity

We determine the conditions necessary for a solution of the supergravity field equations with infinitesimal spin-3/2 field to be a pure gauge transformation of an Einstein vacuum field. The analysis depends on the Petrov classification of the curvature tensor and uses two-component spinor calculus. For general type I, the type II, and typeD, the necessary conditions found are also shown to be sufficient, and the explicit form of the gauge transformation can be given.Work supported in part by the Einstein Memorial Foundation.     

Axially symmetric stationary electrovac solutions

Perjes and Israel and Wilson have given independently a new class of solutions of the sourcefree Einstein-Maxwell equations, which can be interpreted as the external gravitational and electromagnetic fields of a spinning source with unit specific charge. Starting from Zipoy's solutions in oblate and prolate spheroidal coordinates for the source-free gravitational field we generate some axially symmetric stationary solutions of the source-free Einstein-Maxwell equations by using Perjes' method. All these solutions become Euclidean at infinity. The asymptotic behavior and the singularity of the solutions are studied in order to gain some insight into the nature of the source. The solution in prolate spheroidal coordinates is found to contain closed timelike lines.     

A note on supergravity solutions for partially localized intersecting branes

Using the method developed by Cherkis and Hashimoto we construct partially localized D3⊥D5(2), D4⊥D4(2) and M5⊥M5(3) supergravity solutions where one of the harmonic functions is given in an integral form. This is a generalization of the already known near-horizon solutions. The method fails for certain intersections such as D1⊥D5(1) which is consistent with the previous no-go theorems. We point out some possible ways of bypassing these results.     

A classification of compactifying solutions for d =11 supergravity

Supergravity in eleven dimensions is known to have classical solutions of the type (anti-de Sitter space-time) × (7-dimensional Einstein space). We give a list of all homogeneous 7-manifolds which admit an Einstein metric. Known solutions are reviewed, with some emphasis on the SU(3) × SU(2) × U(1) compactifications. Their topology is discussed in detail.The list includes three new solutions, with symmetry groups SU(3) × SU(2), SO(5) and SO(5) × U(1). The first solution has no supersymmetry, while the second and third yield respectively N = 1 and N = 2 supersymmetry in four dimensions. The last two solutions may be extended to solutions with nonzero internal photon curl, breaking all supersymmetry.The existence of a spin structure on homogeneous manifolds $\text{G}\text{H}$ is discussed and related to topological properties of $\text{G}\text{H}$. As an illustration, we treat the coset spaces SU(m + 1) × SU(n + 1)/SU(m) × SU(n) × U(1), which include the spaces with SU(3) × SU(2) × U(1) symmetry.     

Plane symmetric cosmologies with a synge gas and radiation

A family of plane symmetric models is obtained for a mixture of electrons, protons, and photons expanding in thermal equilibrium, characterized by two independent parameters: the initial photon/baryon number ratio in the universe and the anisotropy parameter.     

Spherically symmetric solutions in Macroscopic Gravity

Schwarzschild’s solution to the Einstein Field Equations was one of the first and most important solutions that lead to the understanding and important experimental tests of Einstein’s theory of General Relativity. However, Schwarzschild’s solution is essentially based on an ideal theory of gravitation, where all inhomogeneities are ignored. Therefore, any generalization of the Schwarzschild solution should take into account the effects of small perturbations that may be present in the gravitational field. The theory of Macroscopic Gravity characterizes the effects of the inhomogeneities through a non-perturbative and covariant averaging procedure. With similar assumptions on the geometry and matter content, a solution to the averaged field equations as dictated by Macroscopic Gravity are derived. The resulting solution provides a possible explanation for the flattening of galactic rotation curves, illustrating that Dark Matter is not real but may only be the result of averaging inhomogeneities in a spherically symmetric background.     

Axially symmetric solutions of einstein equations

Two exact axially symmetric solutions of the gravitational field equations, which depend on a number of arbitrary real constants, are derived.