Related papers: Conformal motions in plane symmetric static spacet…
This paper is devoted to the study of matter collineations of plane symmetric spacetimes (for a particular class of spacetimes) when the energy-momentum tensor is non-degenerate. There exists many interesting cases where we obtain proper…
Stationary and axisymmetric perfect-fluid metrics are studied under the assumption of the existence of a conformal Killing vector field and in the general case of differential rotation. The possible Lie algebras for the conformal group and…
A static spherically symmetric wormhole solution for conformal gravity in vacuum is found. The solution possesses a single integration constant which determines the size of the neck connecting two static homogeneous universes of constant…
A procedure to find static axially symmetric solutions to the Einstein field equations is presented. We obtained two general solutions and five particular solutions, which depend on the existence conditions for circular and $z$ direction…
Perfect fluid spacetimes admitting a kinematic self-similarity of infinite type are investigated. In the case of plane, spherically or hyperbolically symmetric space-times the field equations reduce to a system of autonomous ordinary…
Conformal Killing vectors (CKVs) preserve the spacetime metric up to a factor. Homothetic vectors and Killing vectors are special cases of CKVs. Classification of some classes of spacetimes on the basis of CKVs give interesting results…
We carry on a general study on axially symmetric, static fluids admitting a conformal Killing vector (CKV). The physical relevance of this kind of symmetry is emphasized. Next, we investigate all possible consequences derived from the…
The dynamics of pseudo-classical spinning particles in spacetime of gravitational plane waves of general polarization and harmonic profile is studied. The resulting equations of motion are solved exactly and the results are compared with…
We carry on a general study on non--static spherically symmetric fluids admitting a conformal Killing vector (CKV). Several families of exact analytical solutions are found for different choices of the CKV, in both, the dissipative and the…
The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of…
The modified theories of gravity, especially the $f(R)$ gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane symmetric solutions in the context of metric $f(R)$ gravity. We extend the work on…
We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$ for static spherically symmetric spacetimes, and write the conformal Killing gravity equations as Einstein equations augmented by this tensor. The field equations…
A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and G\"odel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally…
In numerically constructing a spacetime that has an approximate timelike Killing vector, it is useful to choose spacetime coordinates adapted to the symmetry, so that the metric and matter variables vary only slowly with time in these…
The conformal geometry of surfaces in the conformal space $\mathbf Q^n_1$ is studied. We classify the space-like surfaces in $\mathbf Q^n_1$ with vanishing conformal form up to conformal equivalence.
The solutions of generalized Killing equation have been obtained for line element with initial $t^2 \oplus so(3)$ symmetry. The coefficients of the metric $g$ corresponding to these vector fields are written down.
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
We provide a simple proof that conformally semi-symmetric spacetimes are actually semi-symmetric. We also present a complete refined classification of the semi-symmetric spacetimes.
In this essay we give an introduction to conformal symmetry, based on the example of the Yamabe operator and its use in conformal differential geometry, and in representation theory.