The theory of evolution equations has been applied in various ways in general relativity. Following some general considerations about this, some illustrative examples of the use of ordinary differential equations in general relativity are presented. After this recent applications of Fuchsian equations are described, with particular attention to work on the structure of singularities of solution...

‎we study curvature properties of four-dimensional lorentzian manifolds with two-symmetry property‎. ‎we then consider einstein-like metrics‎, ‎ricci solitons and homogeneity over these spaces‎‎.

We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of General Relativity in four and higher dimensions, building on recent work in hep-th/0408141. We write the Einstein equations in a new form that naturally identifies the sources for such metrics. The sources live in a one-dimensional subspace and the entire metric is uniquely determined by them...

Vortex is a topological defect with a quantized winding number of the phase in superfluids and superconductors. Here, we investigate the crystallized (triangular, square, honeycomb) and amorphous vortices in rotating atomic-molecular Bose-Einstein condensates (BECs) by using the damped projected Gross-Pitaevskii equation. The amorphous vortices are the result of the considerable deviation induc...

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the sc...

Characterizing size related thermal properties of nanoclusters is challenging due to the requirement to accurately control both their average sizes and the size distributions. In this work, temperature-dependent Extended X-ray Absorption Fine Structure spectroscopy and the phenomenological bond-order-length-strength (BOLS) model were employed to investigate the size-dependent Einstein temperatu...

The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as ‘master dispersionless systems’ in four and three dimensions respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In parti...

We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N approximately 10{5} particles generated by a quantum-injected optical parametric amplifier, seeded by a single-photon belonging to an Einstein-Podolsky-Rosen entangled pair, is made to interact with a mirror-Bose-Einstein condensate (BEC) shaped as a Bragg interference structure. The overa...

We introduce and study a new type of soliton with potential Reeb vector field on Riemannian manifolds an almost paracontact structure corresponding to paracomplex structure. The special cases para-Einstein-like, para-Sasaki-like having torse-forming were considered. It was proved necessary sufficient condition for the manifold admit para-Ricci-like soliton, which is that para-Einstein-like. Exp...