Conformal vector fields of Bianchi type-I spacetimes

This paper aims to investigate Conformal Vector Fields (CVFs) of Bianchi type-I spacetimes. A set of 10-coupled Partial Differential Equations (PDEs) is obtained from the conformal Killing equations. These equations are solved by using direct integration techniques to explore the components of CVFs. Utilizing these components, we get a system of three integrability conditions. Finally, we achieve CVFs along with conformal factors for unique possibilities of unknown metric functions from the solution of these conditions. From our results, it is examined that Bianchi type-I spacetimes admit five or fifteen CVFs for specific choices of metric functions.

Mapping relativistic to ultra/non-relativistic conformal symmetries in 2D and finite $$ \sqrt{T\overline{T}} $$ deformations

The conformal symmetry algebra in 2D (Diff(S1)⊕Diff(S1)) is shown to be related to its ultra/non-relativistic version (BMS3≈GCA2) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT2, the BMS3 generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, T and $$ \overline{T} $$ T ¯ , closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS3 becomes a bona fide symmetry once the CFT2 is marginally deformed by the addition of a $$ \sqrt{T\overline{T}} $$ T T ¯ term to the Hamiltonian. The generic deformed theory is manifestly invariant under diffeomorphisms and local scalings, but it is no longer a CFT2 because its energy and momentum densities fulfill the BMS3 algebra. The deformation can also be described through the original CFT2 on a curved metric whose Beltrami differentials are determined by the variation of the deformed Hamiltonian with respect to T and $$ \overline{T} $$ T ¯ . BMS3 symmetries then arise from deformed conformal Killing equations, corresponding to diffeomorphisms that preserve the deformed metric and stress-energy tensor up to local scalings. As an example, we briefly address the deformation of N free bosons, which coincides with ultra-relativistic limits only for N = 1. Furthermore, Cardy formula and the S-modular transformation of the torus become mapped to their corresponding BMS3 (or flat) versions.

Non-Riemannian isometries from double field theory

We explore the notion of isometries in non-Riemannian geometries. Such geometries include and generalise the backgrounds of non-relativistic string theory, and they can be naturally described using the formalism of double field theory. Adopting this approach, we first solve the corresponding Killing equations for constant flat non-Riemannian backgrounds and show that they admit an infinite-dimensional algebra of isometries which includes a particular type of supertranslations. These symmetries correspond to known worldsheet Noether symmetries of the Gomis-Ooguri non-relativistic string, which we now interpret as isometries of its non-Riemannian doubled background. We further consider the extension to supersymmetric double field theory and show that the corresponding Killing spinors can depend arbitrarily on the non-Riemannian directions, leading to “supersupersymmetries” that square to supertranslations.

Pseudo null curve variations for Bishop frame in 3D semi-Riemannian manifold

In the present paper, the relation between invariants of the pseudo null curves and the variational vector fields of semi-Riemannian manifolds is introduced. After that, the Killing equations are written in terms of the Bishop curvatures along the pseudo null curve. By means of this approach, Killing equations make allow to interpret the movement of charged particles within the magnetic field. Afterwards, as an application, pseudo null magnetic curves are defined using the Killing variational vector field. The parametric representations of all pseudo null magnetic curves are determined in semi-Riemannian space form. Moreover, various examples of pseudo null magnetic curves are illustrated.

HOMOTHETIC KILLING VECTORS IN EXPANDING $\mathcal{HH}$-SPACES WITH Λ

Conformal Killing equations and their integrability conditions for expanding hyperheavenly spaces with Λ in spinorial formalism are studied. It is shown that any conformal Killing vector reduces to homothetic or isometric Killing vector. Reduction of respective Killing equation to one master equation is presented. Classification of homothetic and isometric Killing vectors is given. Type [D] ⊗ [any] is analyzed in detail and some expanding [Formula: see text] complex metrics of types [III, N] ⊗ [III, N] with Λ admitting isometric Killing vectors are found.

ISOMETRIES IN HIGHER-DIMENSIONAL CCNV SPACETIMES

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCNV spacetimes. We pay particular attention to those CCNV spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCNV spacetimes, by studying the Killing equations for the general form of the CCNV metric. In particular, we list all CCNV spacetimes allowing an additional non-spacelike isometry for all values of the light-cone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSICCNV spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.

CONFORMAL MOTIONS IN PLANE SYMMETRIC STATIC SPACE–TIMES

In this paper, conformal motions are studied in plane symmetric static space–times. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these space–times are presented. All possibilities for the existence of conformal motions in these space–times are exhausted.