Related papers: Coordinates are messy -- not only in General Relat…
The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy-momentum is now regarded as \emph{quasi-local} (associated with a closed…
We consider the Newtonian limit of the theory based on the Lagrangian L = R + \sum a_k R \Box^k R. The gravitational potential of a point mass turns out to be a combination of Newtonian and Yukawa terms. For sixth-order gravity the…
After a brief summary of the Newton-Cartan theory in a form which emphasizes its close analogy to general relativity, we illustrate the theory with selective applications in cosmology. The geometrical formulation of this nonrelativistic…
In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear…
The gravitational couplings of matter are studied in the presence of Lorentz and CPT violation. At leading order in the coefficients for Lorentz violation, the relativistic quantum hamiltonian is derived from the gravitationally coupled…
Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by…
The models of New General Relativity have recently got attention of research community, and there are some works studying their dynamical properties. The formal aspects of this investigation have been mostly restricted to the primary…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity…
We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican…
Recent studies have thrown up a big enigma. On the one hand they point to satellite galaxies rotating faster than they should with the usual theory. On the other hand they also go against explanation of Newtonian gravity with dark matter.…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
The Classical Newtonian problem of describing the free motions of N gravitating bodies which form an isolated system in free space has been considered. It is well known from the Poincares Dictum that the problem is not exactly solvable.…
A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics…
We give a definition of mass for conformally compactifiable initial data sets. The asymptotic conditions are compatible with existence of gravitational radiation, and the compactifications are allowed to be polyhomogeneous. We show that the…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…
It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting…
In standard general relativity the universe cannot be started with arbitrary initial conditions, because four of the ten components of the Einstein's field equations (EFE) are constraints on initial conditions. In the previous work it was…