The proposed third-generation gravitational-wave detectors Einstein Telescope will have a triangular design that consists of three colocated interferometers. Summing the strain outputs from interferometers cancel any signal and resultant signal-free stream is known as null stream. in fixed subspace observation space telescope where no can exist. In this paper, we establish decomposition into co...

Let $(g, X)$ be a K\"ahler-Ricci soliton on complex manifold $M$. We prove that if the K\"ahler $(M, g)$ can immersed into definite or indefinite space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein rational multiple $c$.

In this paper we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure-radiation type and that it restricts the spacetimes to Petrov types N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with...

For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as affine holonomy of such a connection. We give an example of an ambient connectio...

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl’s construction is generalized here to arbitrary dimension D ≥ 4. The general solution of the D-dimensional vacuum Einstein equations that admits D− 2 orthogonal com...

Motivated by the search for a Hamiltonian formulation of Einstein equations of gravity which depends in a minimal way on choices of coordinates, nor on a choice of gauge, we develop a multisymplectic formulation on the total space of the principal bundle of orthonormal frames on the 4-dimensional space-time. This leads quite naturally to a new theory which takes place on 10-dimensional manifold...

We relate the Bohr-Sommerfeld conditions established in λ-microlocal analysis to formal deformation quantization of symplectic manifolds by classifying star products adapted to some Lagrangian sub-manifold L, i.e. products preserving the classical vanishing ideal IL of L up to IL-preserving equivalences.