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Space time is described as a continuum four-dimensional medium similar to ordinary elastic continua. Exploiting the analogy internal stress states are considered. The internal "stress" is originated by the presence of defects. The defects are described according to the typical Volterra process. The case of a point defect in an otherwise isotropic four-dimensional medium is discussed showing that the resulting metric tensor corresponds to an expanding (or contracting) universe filled up with a non-zero energy-momentum density.

In this work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach.

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

A space-time discontinuous Galerkin spectral element method is combined with two different approaches for treating problems with discontinuous solutions: (i) adding a space-time dependent artificial viscosity, and (ii) tracking the discontinuity with space-time spectral accuracy. A Picard iteration method is employed to solve nonlinear system of equations derived from the space-time DG spectral element discretization. Spectral accuracy in both space and time is demonstrated for the Burgers’ equation with a smooth solution. For tests with discontinuities, the present space-time method enables better accuracy at capturing the shock strength in the element containing shock when higher order polynomials in both space and time are used. The spectral accuracy of the shock speed and location is demonstrated for the solution of the inviscid Burgers’ equation obtained by the tracking method.

Some event horizons in space–times that are invariant under an isometric action, considered first by Carter, are called isometry horizons, especially Killing horizons. In this paper, isometry horizons in spherically symmetric space–times are considered. It is shown that these isometry horizons are all Killing horizons.

We classify all warped product space-times in three categories as (i) generalized twisted product structures, (ii) base conformal warped product structures and (iii) generalized static space-times and then we obtain the Einstein equations with the corresponding cosmological constant by which we can determine uniquely the warp functions in these warped product space-times.

The problem of classifying boundary points of space-time, for example singularities, regular points and points at infinity, is an unexpectedly subtle one. Due to the fact that whether or not two boundary points are identified or even “nearby” is dependent on the way the space-time is embedded, difficulties occur when singularities are thought of as an inherently local aspect of a space-time, as an analogy with electromagnetism would imply. The completion of a manifold with respect to a pseudo-Riemannian metric can be defined intrinsically. This was done by Scott–Szekeres via an equivalence relation, formalizing which boundary sets cover other sets. This paper works through the possibilities, providing examples to show that all covering relations not immediately ruled out by the definitions are possible.

This paper presents an investigation of the numerical computations of nonweak/strong solutions of linear and nonlinear hyperbolic and parabolic differential and partial differential equations resulting from a single conservation law using C¹p-version least squares finite element formulation (LSFEF) and C¹¹p-version space time least squares finite element formulation (STLSFEF) for stationary and time dependent processes. It is demonstrated that with this approach it is possible to compute nonweak/strong solutions in the sense that the computed solutions possess the same orders of continuity in space and time as the strong solutions and satisfy nonweak (or residual) form of the governing differential equations (GDE's). Other benefits of this approach over weak solutions are also discussed and demonstrated. Stationary and time dependent convection-diffusion and Burgers equations are used as model problems.

In this work we propose a new procedure on how to extract global information of a space-time. We consider a space-time immersed in a higher dimensional space and formulate the equations of Einstein through the Frobenius conditions of immersion. Through an algorithm and implementation into algebraic computing system we calculate normal vectors from the immersion to find the second fundamental form. We make an application for a static space-time with spherical symmetry. We solve Einstein's equations in the vacuum and obtain space-times with different topologies.

Space-time can be treated as a four-dimensional material continuum. The corresponding generally curved manifold can be thought of as having been obtained, by continuous deformation, from a flat four-dimensional Euclidean manifold. In a three-dimensional ordinary situation such a deformation process would lead to strain in the manifold. Strain in turn may be read as half the difference between the actual metric tensor and the Euclidean metric tensor of the initial unstrained manifold. On the other side we know that an ordinary material would react to the attempt to introduce strain giving rise to internal stresses and one would have correspondingly a deformation energy term. Assuming the conditions of linear elasticity hold, the deformation energy is easily written in terms of the strain tensor. The Einstein-Hilbert action is generalized to include the new deformation energy term. The new action for space-time has been applied to a Friedmann-Lemaître-Robertson-Walker universe filled with dust and radiation. The accelerated expansion is recovered, then the theory has been put through four cosmological tests: primordial isotopic abundances from Big Bang Nucleosynthesis; Acoustic Scale of the CMB; Large Scale Structure formation; luminosity/redshift relation for type Ia supernovae. The result is satisfying and has allowed to evaluate the parameters of the theory.

We investigate the topology of Schwarzschild's black holes through the immersion of this space-time in space of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.

Based on the smallest physical constant of the product of space interval, time interval, and energy, the fractal quantum gravity (FQG) theory has demonstrated that every particle or physical system consists of these smallest units in fractal structures. The general relativity is an approximation of the FQG equation when the quantum effect is negligible, while the quantum theory is an approximation of the FQG equation when the interaction between space, time, and energy is very weak or negligible. The stationary-action principle can be derived from the FQG equation. The mass range of possibly existing elementary particles and an accelerating expansion evolution model of the universe can be obtained through the FQG equation. This FQG equation satisfied almost all the requirements of a quantum gravity theory and there is no free constant needed in the FQG theory. It looks promising that the FQG theory may offer a novel way to calculate all the free constants in the Standard Model of particle physics and general relativity.

What are the fundamental equations of motion when we consider objects that move faster, have tinier structures, higher mass densities, higher or lower temperatures than ever studied before? Here, we emphasize the importance of studying extreme conditions and situations in science so as to uncover the basic laws of nature. One of the important extremes is extreme complexity, a necessary condition for the emergence of life.

The Andean space-time is collected in a single term: pacha, a concept which restricts the three static dimensions (length, width, and depth) and the fourth dimension that is dynamical and which corresponds to time in the same unit (kay pacha). This pacha construct, unlike the “myth of the eternal return” (from Mircea Eliade), opened the doors of entry and exit, which is evidenced by the presence of a single Quechua term that is ñawpa/ñawpan, which is both in the past and in the future. This is a structure sustained in its dynamic action by exchanges or permutations of the polysemic concepts urin and janan in their meanings: ancient and recent, natives and outsiders, obverse and reverse, visible and non-visible, left and right, and other implicit meanings.

Translator’s note: The author, taking into account his deep linguistic knowledge of Quechua, delves into relevant topics such as the infuence of the Sun on the cultural conformation of the Inca civilization (and in other words, of the Andean astronomy), taking into account that, as Steven Gullberg reminds us, the Incas proclaimed themselves to be the “children of the Sun”, whom they adored and who saw their emperor(s) as the direct descendant(s) of the Sun. At the same time, the author addresses a crucial aspect for understanding Inca astronomy and cosmology, the linguistic-cosmogonic-historical origin of their conception of space-time, where time and the three spatial dimensions of space are fused, as we see, into a single (continuum) conception, the “kay pacha”. He also addresses the combination of the “kay pacha” conception with the “ñawpa/ñawpan” and the “urin” and “janan” concepts, that overlap double meanings in the same loop: the immediate-past and the consequential or circumstantial future. Such conceptions show deep and astonishing similarity with the geometric spacetime interpretation in modern cosmology associated to the time-evolution of the Universe. The author also inserts a few statements and comments which, although the author does not focus on its relationship with modern cosmology, present points of contact with a still open problem in science: the meaning of the arrow of time.

Intuition is defined for the purposes of this analysis as: the appearance in the mind of accurate information about the external world, which can be shown to have come not through the five senses, nor through a rearrangement of stored memory contents. Forms of intuition obeying this definition have been explored scientifically under such labels as telepathy, precognition, presentiment, and remote viewing. This paper summarizes those scientific findings, and presents a few theories which have been hypothesized to explain them. Those theories are largely based in theoretical physics, including quantum non-locality, holography, and complex space-time. Related biological theories are also cited, which propose to explain how information might move from the subatomic level up into waking consciousness, for example through DNA structures or neuronal microtubules.

In this paper the mass of a universe, which began as a gravitationally closed, maximally spinning, Planck density quantum string is derived.

A universe beginning in such an initial state has been called a Super Spin Model universe. The total mass, M, of the Super Spin Model universe is shown to be a function of only four fundamental parameters ħ, c, G, e, such that: M = 4π²(ħc/G)^1/2 exp(ħc/e²).

The present paper primarily consists of a brief derivation of the above equation and a short synopsis of the Super Spin Model.

The spread spectrum technology is widely applied due to its good ability of combat multipath fading. The space-time coding technology is effective to help the wireless telecommunication system achieves both the temporal diversity and the spatial diversity. Such kind of system, adopting both code division multiple access and space-time coding, is studied. The transmitter and receiver model is put forward. Some of the performance simulation results are given.

What are the fundamental equations of motion when we consider objects that move faster, have tinier structures, higher mass densities, higher or lower temperatures than ever studied before? Here, we emphasize the importance of studying extreme conditions and situations in science so as to uncover the basic laws of nature. One of the important extremes is extreme complexity, a necessary condition for the emergence of life.

Space-time is described as a strained four-dimensional elastic continuum. The embedding of a given manifold in a higher dimensional at one allows to extend to four dimensions the usual three-dimensional theory of elastic and plastic deformations. Curvature is then described in terms of strain of the manifold and the strain tensor turns out to be the non-trivial part of the metric tensor. The global behaviour of space-time and its Robertson-Walker symmetry is described as being the consequence of a defect in the manifold. The analogy with the traditional elasticity theory suggests the introduction of an additional term in the Einstein-Hilbert action, representing the potential energy associated with the strained state. The new Lagrangian is then tested on the luminosity curve of type 1a supernovae and the accelerated expansion. The fit turns out to be slightly better than the one obtained by the ΛCDM theory and gives a value for the “bulk modulus” of space-time. The obtained value is consistent with the Newtonian limit of the theory up to the scale of galaxy clusters.

The relational-statistical approach to the nature of space-time and physical interactions is proposed.