Related papers: Coordinates are messy -- not only in General Relat…
We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their…
This thesis discusses the Newtonian limit of General Relativity for static isolated systems with compactly supported matter. We call these systems "geometrostatic" to underline their geometric nature. We introduce new quasi-local notions of…
Well-known to specialists but little-known to the wider audience is that Newtonian gravity can be understood as geodesic motion in space-time, where time is absolute and space is Euclidean. Newtonian cosmology formulated by Heckmann agrees…
The center of mass and spin for isolated sources of gravitational radiation that move at relativistic speeds are defined. As a first step, we also present these definitions in flat space. This contradicts some general wisdom given in…
We propose a definition of center of mass for asymptotically flat manifolds satisfying Regge-Teitelboim condition at infinity. This definition has a coordinate-free expression and natural properties. Furthermore, we prove that our…
The concept of mass is central to any theory of gravity. Nevertheless, defining mass in general relativity is a difficult task, and even when it can be accomplished, we still need to investigate whether the typical properties of mass in…
We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence…
A new coordinate system is defined for the Four-Body dynamical problem with general masses, having as its origin of coordinates the center of mass. The transformation from the inertial coordinate system involves a combination of a rotation…
The Newtonian approximation for the gravitational field equation should not necessarily involve admission of non-relativistic properties of the source terms in Einstein's equations: it is sufficient to merely consider the weak-field…
A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian…
We review and announce recent results on the asymptotic behavior of asymptotically Euclidean relativistic initial data sets and asymptotic foliations thereof. In particular, we discuss the geometrization of asymptotic flatness and of…
The mass contained in an arbitrary spacetime in general relativity is not well defined. However, for asymptotically flat spacetimes various definitions of mass have been proposed. In this paper I consider eight masses and show that some of…
Relativistic cosmological perturbation analyses can be made based on several different fundamental gauge conditions. In the pressureless limit the variables in certain gauge conditions show the correct Newtonian behaviors. We consider the…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center…
In this contribution, we suggest the approach that geometric concepts ought to be defined in terms of physical operations involving quantum matter. In this way it is expected that some (presumably nocive) idealizations lying deep within the…