Related papers: Four Dimensional Elasticity and General Relativity
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
A two-dimensional Minkowski spacetime diagram is neatly represented on a Euclidean ordinary plane. However the Euclidean lengths of the lines on the diagram do not correspond to the true values of physical quantities in spacetime, except…
The dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions are considered. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives and a second order…
We are answering the question why 4-dimensional space has the metric 1+3 by making a general argument from a certain type of equations of motion linear in momentum for any spin (except spin zero) in any even dimension d. All known free…
We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
In contrast to the traditional elastodynamic equations, a more comprehensive formulation of one dimensional (1D) elastodynamic equations is given for inhomogeneous media by using the coordinate transformation method. These modified…
In four space-time dimensions, there are good theoretical reasons for believing that General Relativity is the correct geometrical theory of gravity, at least at the classical level. If one admits the possibility of extra space-time…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
Extended Theories of Gravity can be considered a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein's Theory, is…
The special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz transformations as shown by one of us \cite{buitrago} and discussed in the…
We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in…
We investigate asymptotic symmetries in flat backgrounds of dimension higher than or equal to four. For spin two we provide the counterpart of the extended BMS transformations found by Campiglia and Laddha in four-dimensional Minkowski…
We propose a theory in electromagnetic dynamics, in which time and space are equivalent with each other and have totally twelve dimensions. Then, we solve that with realistic assumptions and find a steady state as a solution. The solution…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and…
A new formalism in general relativity with a linear response relation between perturbed Einstein tensor and the stress-energy tensor is presented. Basic concepts are borrowed from statistical physics and theory of stochastic processes by…
An effective theory of gravity in the infrared is proposed, which involves the determinant of the metric relative to the determinant of a prior metric taken to be that of Minkowski spacetime. This effective theory can be interpreted as a…
Careful analysis of parametrized variational principles in mechanics and field theory leads to a generalization of Einstein theory that includes a cosmological stress tensor. This generalization also follows by restricting variations of the…
We explore models with emergent gravity and metric by means of numerical simulations. A particular type of two-dimensional non-linear sigma-model is regularized and discretized on a quadratic lattice. It is characterized by lattice…
We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and…