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The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
This work is divided into two parts. The first examines recent proposals for "witnessing" quantum gravity via entanglement from the point of view of Bronstein's original objection to a quantization of gravity. Using techniques from open…
Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
Higher-dimensional theories of the kind which may unify gravitation with particle physics can lead to significant modifications of general relativity. In five dimensions, the vacuum becomes non-standard, and the Weak Equivalence Principle…
We show by direct calculation that the common Equivalence Principle explanation for why gravity must deflect light is quantitatively incorrect by a factor of three in Schwarzschild geometry. It is therefore possible, at least as a matter of…
The equivalence principle suggests to consider gravity as an infra-red phenomenon, whose effects are visible only outside Einstein's free-falling elevator. By curving spacetime, General Relativity leaves the smallest systems free of…
We investigate leading order deviations from general relativity that violate the Einstein equivalence principle in the gravitational standard model extension. We show that redshift experiments based on matter waves and clock comparisons are…
In this Chapter we illustrate the close connection between the violation of the weak equivalence principle typical of gravitational interactions at finite temperature, and similar violations induced by a breaking of the local Lorentz…
The issue of implementing the principle of general relativity in Einstein equations has been widely discussed, since Kretschmann's well-known criticism stated that general covariance of the Einstein equations is not suffice to express the…
General Relativity (GR) remains the cornerstone of gravitational physics, providing remarkable success in describing a wide range of astrophysical and cosmological phenomena. However, several challenges underscore the urgent need to explore…
The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR),…
The Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the…
We explore the notion of approximate global symmetries in quantum field theory and quantum gravity. We show that a variety of conjectures about quantum gravity, including the weak gravity conjecture, the distance conjecture, and the…
The Weak Gravity Conjecture holds that in a theory of quantum gravity, any gauge force must mediate interactions stronger than gravity for some particles. This statement has surprisingly deep and extensive connections to many different…
We review the underpinnings of the standard Newton-Einstein theory of gravity, and identify where it could possibly go wrong. In particular, we discuss the logical independence from each other of the general covariance principle, the…
Clusters of galaxies have been used to measure a subtle effect predicted by Einstein: gravitational redshift. This signal encodes pristine information about our Universe, since it is sensitive to the depth of the clusters' gravitational…
Some of the assumptions of cosmology, as based on the simplest version of General Relativity, are discussed. It is argued that by slight modifications of standard gravitation theory, our notion of the sources of gravity {the right hand side…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
Spacetime curvature plays the primary role in general relativity but Einstein later considered a theory where torsion was the central quantity. Just as the Einstein-Hilbert action in the Ricci curvature scalar R can be generalized to f(R)…