We calculate the linearized metric perturbations in the five dimensional two-brane model of Randall and Sundrum. In a carefully chosen gauge, we write down and decouple Einstein equations for the perturbations and get the final and simple perturbative metric ansatz. This ansatz turns out

without second derivatives ’ terms when the metric ansatz is assumed to take an appropriate form.

A homogeneous Gibbons–Hawking ansatz is described, leading to 4-dimensional hyperkähler metrics with homotheties. In combination with Blaschke products on the unit disc in the complex plane, this ansatz allows one to construct infinite-dimensional families of such hyperkähler metrics that are

Abstract. It is well known that any 4-dimensional hyperkähler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons–Hawking Ansatz, from a harmonic function invariant under a Killing field on R 3. In this paper, we find all selfdual Einstein metrics of nonzero scalar

It is suggested a metric ansatz describing matter in an expanding universe, hence interpolating between the Schwarzschild metric near central bodies of mass M and the Friedman-Lemaítre-Robertson-Walker metric for large radial coordinate, given by ds 2 = Z c 2 dt 2 − 1 Z

It is suggested a metric ansatz describing matter in an expanding universe, hence interpolating between the Schwarzschild metric near central bodies of mass M and the Friedman-Lemaítre-Robertson-Walker metric for large radial coordinate, given by ds 2 = Z c 2 dt 2 − 1 Z

differential equations, due to the metric ansatz of cohomogeneity one. We identify the L 2-normalizable solution that deforms the asymptotic radius of the M theory circle.

We will show that the Nariai metric, i.e. the static spherically symmetric vacuum spacetime with a cosmological constant, admits a conformally Kerr–Schild spacetime representation. We find the vacuum solutions of the Einstein–Maxwell equations for the Nariai metric using the Horsk

of the scalar curvature for an arbitrary Kähler metric g arising from the Calabi ansatz. This suggests geometric hypotheses (which we call “σ-constancy”) to impose upon the base metric gM and Hermitian structure h in order that the scalar curvature of g be specified by solving an ODE. We show that σ

Einstein–Proca equations with respect to anholonomic frames adapted to N–connections. String corrections induced by the antisymmetric H–fields are considered. There are also proved the theorems and criteria stating a new method of constructing exact solutions with generic off–diagonal metric ansatz