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The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
Generalised geometry studies structures on a d-dimensional manifold with a metric and 2-form gauge field on which there is a natural action of the group SO(d,d). This is generalised to d-dimensional manifolds with a metric and 3-form gauge…
We give a local parametric description of all holomorphic hypersurfaces in complex Euclidean and projective spaces with constant index of relative nullity, together with applications. This is a complex analogue to the parametrization for…
The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r = 0$. The radial…
In this article we consider the low regularity well-posedness of the surface quasi-geostrophic (SQG) front equation. Recent work on other quasilinear models, including the gravity water waves system and nonlinear waves, have demonstrated…
We construct convex bodies that can be "captured by nets." More precisely, for each dimension $n \geq 2$, we construct a family of Riemannian $n$-spheres, each with a stable geodesic net, which is a stable 1-dimensional integral varifold.…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space one can naturally introduce two Gauss maps and Weierstrass representation. In this paper we investigate their global geometry systematically. The…
Energy is at best defined quasilocally in general relativity. Quasilocal energy definitions depend on the conditions one imposes on the boundary Hamiltonian, i.e., how a finite region of spacetime is "isolated". Here, we propose a method to…
The traditional description of black holes in terms of event horizons is inadequate for many physical applications, especially when studying black holes in non-stationary spacetimes. In these cases, it is often more useful to use the…
The quantum geometry arising in Loop Quantum Gravity has been known to semi-classically lead to generalizations of length-geometries. There have been several attempts to interpret these so called twisted geometries and understand their role…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
This article explores the overall geometric manner in which human beings make sense of the world around them by means of their physical theories; in particular, in what are nowadays called pregeometric pictures of Nature. In these, the…
A consistent quantum theory of gravity has remained elusive ever since the emergence of General Relativity and Quantum Field Theory. Attempts to date have not yielded a candidate that is either free from problematic theoretical…
A family of quasilocal mass definitions that includes as special cases the Hawking mass and the Brown-York ``rest mass'' energy is derived for spacelike 2-surfaces in spacetime. The definitions involve an integral of powers of the norm of…
General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…
Geometric momentum is the appropriate momentum for a particle constrained to move on a curved surface, which depends on the extrinsic curvature and leads to observable effects, and curvature-induced quantum potentials appear for a…
During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and…
We describe a theory amalgamating quantum theory and general relativity through the identification of a continuous 4-dimensional spacetime arena constructed from the substructures of a generalised multi-dimensional form for proper time. In…