Related papers: New Superpotential in Conservation Laws in General…
We consider a classical condensed matter theory in a Newtonian framework where conservation laws \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) + \partial_i(\rho v^i v^j + p^{ij}) = 0 are related with the Lagrange…
The notions of "motion" and "conserved quantities", if applied to extended objects, are already quite non-trivial in Special Relativity. This contribution is meant to remind us on all the relevant mathematical structures and constructions…
The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual…
It is well-known that all 2d models of gravity---including theories with nonvanishing torsion and dilaton theories---can be solved exactly, if matter interactions are absent. An absolutely (in space and time) conserved quantity determines…
Considered a unified field theory approach describing matter and space (metric tensor) by means of a 3-index tensor $P^{i}_{jk}$. It is shown that if the Lagrangian has partial U(1) gauge (semi-gauge) of the type $P^{i}_{jk}->P^{i}_{jk}+a…
We find the most general, spherically symmetric solution in a special class of tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated by the superpotential method and by the Euclidean continuation…
In all 2d theories of gravity a conservation law connects the (space-time dependent) mass aspect function at all times and all radii with an integral of the matter fields. It depends on an arbitrary constant which may be interpreted as…
Recent astronomical observations verify the new scenario resulting from new conservation laws and a new relativity principle fixed either by dual properties of light or by new gravitational (G) tests and the Einstein's equivalence…
A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian…
Since some experiments have found superluminality, we assume that the particles in the universe are divided into three classes: the subluminal, luminal and superluminal particles by the speed of light, their energy-momenum relations are E2…
`Dual composition', a new method of constructing energy-preserving discretizations of conservative PDEs, is introduced. It extends the summation-by-parts approach to arbitrary differential operators and conserved quantities. Links to…
The goal of this article is to derive the reciprocity theorem, mutual energy theorem from Poynting theorem instead of from Maxwell equation. The Poynting theorem is generalized to the modified Poynting theorem. In the modified Poynting…
By employing consistent supersymmetric higher derivative terms, we show that the supersymmetric theories may have a sector where the scalar potential does no longer have the conventional form. The theories under consideration contain…
A new class of N=2 locally supersymmetric higher-derivative invariants is constructed based on logarithms of conformal primary chiral superfields. They characteristically involve a coupling to R_{\mu\nu}^2 - 1/3*R^2, which equals the…
Apart from the familiar structure firmly-rooted in the general relativistic field equations where the energy--momentum tensor has a null divergence i.e., it conserves, there exists a considerable number of extended theories of gravity…
A new representation of electromagnetic gyrokinetic Vlasov-Maxwell theory is presented in which the gyrocenter equations of motion are expressed solely in terms of the perturbed electric and magnetic fields. In this representation, the…
A unified field theory for the description of matter in a curved space is discussed. The description is based on a standard Lagrangianian formalism in a pseudo-Euclidian 4D continuum using a 3-index tensor as independent variables. The…
In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used…
An Extended Uncertainty Principle inspired Schwarzschild metric that allows for large scale modifications to gravitation is presented. At a new fundamental length scale $\Ls$, the usual black hole characteristics (horizon radius, ISCO, and…
In this Ph.D. thesis several topics in doubly special relativity are explored. The starting point of this theory is very different from other perspectives: it is not a fundamental theory, but it is considered a low energy limit of a quantum…