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We investigate the kinematics of deformations in two and three dimensional media by explicitly solving (analytically) the evolution equations (Raychaudhuri equations) for the expansion, shear and rotation associated with the deformations.…
We examine conditions on a (compact metrizable) space $X$ such that for any space $Y$ and closed subspace $Z$, the set of continuous functions from $Z$ to $X$ which extend to $Y$ is either open or closed in the set of continuous functions…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
Swimming in curved spacetimes is a phenomenon whereby free bodies in curved spacetimes are able to propel themselves by performing cyclic internal motions. When originally proposed, it was further suggested that, in the limit of fast…
The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial value problem for a zero-rest-mass field with…
The accelerating Friedmann flat universe, filled with an ideal fluid with a linear (oscillating) inhomogeneous equation of state (EoS) depending on time, is reviewed. The equations of motions are solved. It is shown that in some cases there…
It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…
We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are…
We study relativistically expanding electromagnetic fields of cylindrical geometry. The fields emerge from the side surface of a cylinder and are invariant under translations parallel to the axis of the cylinder. The expansion velocity is…
We report a symmetry property of the Einstein-Friedmann equations for spatially flat Friedmann-Lema\^itre-Robertson-Walker universes filled with a perfect fluid with any constant equation of state. The symmetry transformations form a…
In this note we provide a direct proof of the complete classification of conformally flat isoparametric submanifolds of Euclidean space.
Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e.,…
Many professional physicists do not fully understand the implications of the Einstein equivalence principle of general relativity. Consequently, many are unaware of the fact that special relativity is fully capable of handling accelerated…
We present the scientific motivation for future space tests of the equivalence principle, and in particular the universality of free fall, at the $10^{-17}$ level or better. Two possible mission scenarios, one based on quantum technologies,…
Timescales spanning 24 orders of magnitude smaller than one second can be studied experimentally, and each range is packed with different physical phenomena. This rich range of timescales offers a great context for an innovative…
In this essay we wish to seek a unifying thread between the basic forces. We propose that there exists a universal force which is shared by all that physically exists. Universality is characterized by the two properties: (i) universal…
From the equivalence principle, one gets the strength of the gravitational effect of a mass $M$ on the metric at position r from it. It is proportional to the dimensionless parameter $\beta^2 = 2GM/rc^2$, which normally is $<< 1$. Here $G$…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
The foundation of continuum elasticity theory is based on two general principles: (i) the force felt by a small volume element from its surrounding acts only through its surface (the Cauchy principle, justified by the fact that interactions…