Related papers: General Relativity and Geodesy
According to General Relativity, as distinct from Newtonian gravity, motion under gravity is treated by a theory that deals, initially, only with test particles. At the same time, satellite measurements deal with extended bodies. We discuss…
Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over…
In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…
Geodesic deviation is the most basic manifestation of the influence of gravitational fields on matter. We investigate geodesic deviation within the framework of Regge calculus, and compare the results with the continuous formulation of…
The introduction of General Relativity (GR) in 1915 revolutionized our understanding of gravity, but over time, its limitations in explaining phenomena like dark energy, dark matter, and quantum gravity have motivated alternative theories.…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
The GRACE and GRACE-FO missions have provided an unprecedented quantification of large-scale changes in the water cycle. However, it is still an open problem of how these missions' data sets can be referenced to a ground truth. Meanwhile,…
This paper introduces new definitions of common geodetic measures on a planetary surface (namely surface area, path length, and mean value or other statistical parameters of a surface function) that are not based on a datum such as a…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
Modified gravity theories have been suggested to address the limitations of general relativity, each exhibiting differences, particularly in their strong-field limits. Nonetheless, there lacks effective means to distinguish or test these…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant…
Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to…
A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using…
According to the Einstein's theory of relativity, the passage of time changes in a gravitational field. On earth, raising a clock by one centimetre increases its tick rate by 1.1 parts in 10$^{18}$, enabling optical clocks to perform…
The general relativistic gravitomagnetic clock effect involves a coupling between the orbital motion of a test particle and the rotation of the central mass and results in a difference in the proper periods of two counter-revolving…
The passage of time is tracked by counting oscillations of a frequency reference, such as Earth's revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any…
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…