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The 'anholonomic frame' method (see gr-qc/0005025, gr-qc/0001060 and hep-th/0110250) is applied for constructing new classes of exact solutions of vacuum Einstein equations with off-diagonal metrics in 4D and 5D gravity. We examine several…

All purely bosonic supersymmetric solutions of minimal gauged supergravity in five dimensions are classified. The solutions fall into two classes depending on whether the Killing vector constructed from the Killing spinor is time-like or…

The squashed and stretched 7-dimensional internal metric preserving U(1) x U(1) x U(1)_R symmetry possesses an Einstein-Kahler 2-fold which is a base manifold of 5-dimensional Sasaki-Einstein L^{p, q, r} space. The r(transverse to the…

Eleven-dimensional supergravity has a non-relativistic variant obtained by taking a limit associated with the M2 brane. Consistency of this non-relativistic supergravity requires constraints. There is one choice of constraints which keeps…

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We analytically construct families of type IIB supergravity backgrounds in ten dimensions in which the four-dimensional metric is time dependent, while the six-dimensional internal space is an arbitrary compact Calabi-Yau manifold (with no…

Let $P$ be a Poisson structure on a finite-dimensional affine real manifold. Can $P$ be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach -- with respect to all affine Poisson…

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by…

Modified gravity theories (MGTs) have long been studied as alternatives to general relativity (GR) and the standard Lambda CDM cosmological model. For example, exponential f(R) models often yield better fits to observational data,…

We show that the recent work of Lee [23] implies existence of a large class of new singularity-free strictly static Lorentzian vacuum solutions of the Einstein equations with a negative cosmological constant. This holds in all space-time…

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Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian…

Solitonic solution-generating methods are powerful tools to construct nontrivial black hole solutions of the higher-dimensional Einstein equations systematically. In five dimensions particularly, the solitonic methods can be successfully…

In ungauged supergravity theories, the no-force condition for BPS states implies the existence of stable static multi-centered solutions. The first solutions to Einstein-Maxwell theory with a positive cosmological constant describing an…

We present a new two-parameter family of solutions of Einstein gravity with negative cosmological constant in 2+1 dimensions. These solutions are obtained by squashing the anti-de Sitter geometry along one direction and posses four Killing…

For an infinitesimal deformation of a Riemannian manifold, we prove that the scalar, vector, and tensor modes in decompositions of perturbations of the metric tensor, the scalar curvature, the Ricci tensor, and the Einstein tensor decouple…

We consider $n+1$ dimensional smooth Riemannian and Lorentzian spaces satisfying Einstein's equations. The base manifold is assumed to be smoothly foliated by a one-parameter family of hypersurfaces. In both cases---likewise it is usually…

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics,…

We formulate the full bosonic SL(5) exceptional field theory in a coordinate-invariant manner. Thereby we interpret the 10-dimensional extended space as a manifold with $\mathrm{SL}(5)\times\mathbb{R}^+$-structure. We show that the algebra…