Related papers: Approximate spacetime symmetries and conservation …
A definition is suggested for affine symmetry tensors, which generalize the notion of affine vectors in the same way that (conformal) Killing tensors generalize (conformal) Killing vectors. An identity for these tensors is proved, which…
Symmetries concerning the ordinary coordinate spacetime and internal spacetime are discussed. A possible unification model of electroweak, strong and gravitational interactions is briefly described.
We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions.…
There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar\'{e} gauge theory and…
The integrals of the motion associated with conformal Killing vectors of a curved space-time with an additional electromagnetic background are studied for massive particles. They involve a new term which might be non-local. The difficulty…
The "conformal mass prescriptions" were used recently to calculate the mass of spacetimes in higher dimensional and higher curvature theories of gravity. These definitions are closely related to Komar integrals for spacetimes that are…
We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global…
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…
In this paper, conformal motions are studied in plane symmetric static spacetimes. The general solution of conformal Killing equations and the general form of the conformal Killing vector for these spacetimes are presented. All…
Working in a semi-classical setting, we consider solutions of the Einstein equations that exhibit light trapping in finite time according to distant observers. In spherical symmetry, we construct near-horizon quantities from the assumption…
The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
The most general form of non-static plane symmetric space-times is considered to study proper curvature collineations by using the rank of the 6X6 Riemann matrix and direct integration techniques. Studying proper curvature collineations in…
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler's third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a…
All diagonal proper Bianchi I space-times are determined which admit certain important symmetries. It is shown that for Homotheties, Conformal motions and Kinematic Self-Similarities the resulting space-times are defined explicitly in terms…
The conventional role of spacetime geometry in the description of gravity is pointed out. Global Poincar$\acute{\mbox{e}}$ symmetry as an inner symmetry of field theories defined on a fixed Minkowski spacetime is discussed. Its extension to…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
Local nonlinear approximations to the growth of cosmic perturbations are developed, resulting in relations, at a given epoch, between the peculiar velocity and gravity fields and their gradients. Only the equation of motion is approximated,…
In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependend co-ordinate transformations naturally leads to the…
The intention of our paper is to provide a pedagogical application of geometric algebra to a particularly well-investigated system: We formulate the geometric and dynamical properties of Friedmann-Robertson-Walker spacetimes within the…