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A method of general applicability has been developed, whereby the null geodesic equations of the Einstein-Straus-de Sitter metric can be integrated simultaneously in terms of the curvature constant $k$. The purpose is to generalize the…

A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean…

We present a simple derivation of the Lorentz transformations for the space-time coordinates of the same event. It is based on the relative character of length and time interval as measured by observes in relative motion. We begin by…

We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experiment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the…

Globular clusters are among the first objects used to establish the distance scale of the Universe. In the 1970-ies it has been recognized that the differential magnitude distribution of old globular clusters is very similar in different…

We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a…

We derive the deflection angle up to $O(m^2a)$ due to a Kerr gravitational lens with mass $m$ and specific angular momentum $a$. It is known that at the linear order in $m$ and $a$ the Kerr lens is observationally equivalent to the…

The Optical Gravitational Lensing Experiment (OGLE) is one of the most productive and influential photometric sky surveys in the history of observational astronomy. Originally designed to detect dark matter through gravitational…

Comparing probability distributions is an indispensable and ubiquitous task in machine learning and statistics. The most common way to compare a pair of Borel probability measures is to compute a metric between them, and by far the most…

Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest…

At the end of the 17th century, the collection was established through the acquisition of Leiden instrumentmaker Musschenbroek's collection. Its aim was to demonstrate physical phenomena. Until the end of the 18th century, the collection…

The letter reminds the historical fact that the known "Lorenz gauge" (or "Lorenz condition/relation") is first mentioned in a written form and named after Ludwig Valentin Lorenz and not by/after Hendrik Antoon Lorentz.

To test the theory of gravity one needs to test, on one hand, how space and time are distorted by matter and, on the other hand, how matter moves in a distorted space-time. Current observations provide tight constraints on the motion of…

Students at Colorado College and cadets at the US Air Force Academy have conducted an experimental test of gravitational time dilation. This relativistic effect, highlighted in the movie Interstellar, causes clocks to tick more slowly near…

There are now 10 firm time delay measurements in gravitational lenses. The physics of time delays is well understood, and the only important variable for interpreting the time delays to determine H_0 is the mean surface mass density <k> (in…

Current sky surveys have been conducted very accurately in order to understand our universe. One of the phenomena survey maps provide is gravitational effect. Albert Einstein (1936) first discussed the possibilities of gravitational lensing…

Context. Astrometric gravitational microlensing can be used to determine the mass of a single star (the lens) with an accuracy of a few percent. To do so, precise measurements of the angular separations between lens and background star with…

We estimate the changes in solar system tests of general relativity when "dark energy" arises from a Weyl scaling invariant action, using the modified Schwarzschild-like spherically symmetric solution obtained in this case by Adler and…

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…

In this paper we develop a differential astrometric framework that is appropriate for a scanning space satellite such as Gaia. We apply it to the first of the GAREQ fields, which is the fruit of dedicated efforts within the Gaia project…