Related papers: Spacetime with prescribed hidden symmetry
The hedgehog ansatz for spherically symmetric spacetimes in self-gravitating nonlinear sigma models and Skyrme models is revisited and its generalization for non-spherically symmetric spacetimes is proposed. The key idea behind our…
Symmetries of spacetimes with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in an axially symmetric spacetime with null dust field in which at…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic…
We study the group properties and the similarity solutions for the constraint conditions of anti-self-dual null K\"{a}hler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply the theory of Lie…
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…
Dynamical black holes in the non-perturbative regime are not mathematically well understood. Studying approximate symmetries of spacetimes describing dynamical black holes gives an insight into their structure. Utilising the property that…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
A symmetric tensor field on a Riemannian manifold is called Killing field if the symmetric part of its covariant derivative is equal to zero. There is a one to one correspondence between Killing tensor fields and first integrals of the…
In this paper we show that the equation of motion of a massless scalar particle near the black hole (BH) horizon in the Schwarzschild-deSitter (SdS) spacetime enjoys a hidden conformal symmetry when the two horizons satisfy a quadratic…
The relations between the hidden symmetries of the six-dimensional pseudo-Euclidean space with signature (+++ -- ) and the conserved quantum characteristics of elementary particles is established. The hidden symmetries are brought out by…
The paper studies non-Lie symmetry of the Klein-Gordon-Fock equation (KGF) in $(p+q)$-dimensional Minkowsky space. Full set of symmetry operators for the $n$-order KGF equation was explicitly calculated for arbitrary $n<\infty$ and $p+q…
In the differential geometry of certain F-structures, the role of W-curvature tensor is very well known. A detailed study of this tensor has been made on the spacetime of general relativity. The spacetimes satisfying Einstein field…
The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially…
Stationary and axially symmetric space-times play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum sub-class of these space-times is known as Weyl's class, and contains the…
Every Killing tensor field on the space of constant curvature and on the complex projective space can be decomposed into the sum of symmetric tensor products of Killing vector fields (equivalently, every polynomial in the velocities…
The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma-model metric are either coinciding or…
In this paper we have introduced a new symmetry property of spacetime which is named as semiconformal curvature collineation, and its relationship with other known symmetry properties has been established. This new symmetry property of the…
We present a new method for constructing conformal Yano-Killing tensors in five-di\-men\-sio\-nal Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors,…
We initiate the rigorous study of classification in quasi-metric spaces. These are point sets endowed with a distance function that is non-negative and also satisfies the triangle inequality, but is asymmetric. We develop and refine a…