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We discuss theoretical formalisms concerning with experimental verification of General Relativity (GR). Non-metric generalizations of GR are considered and a system of postulates is formulated for metric-affine and Finsler gravitational…
By using simplified 2D gravitational, non-local Lorentz invariant actions constructed upon the torsion tensor, we discuss the physical meaning of the remnant symmetries associated with the near-horizon (Milne) geometry experienced by a…
Fundamental fields are a natural outcome in cosmology and particle physics and might therefore serve as a proxy for more complex interactions. The equivalence principle implies that all forms of matter gravitate, and one therefore expects…
The relative motion of material, point-like observers is analysed in terms of coordinate maps between the respective rest-frame of each observer. Under the assumption these maps are $C^{2}$-regular, conservation laws are deduced, which in…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass…
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
Gravitational wave astronomy has tremendous potential for studying extreme astrophysical phenomena and exploring fundamental physics. The waves produced by binary black hole mergers will provide a pristine environment in which to study…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
It is assumed that the radial propagation of light with respect to the naive coordinate system of the observer is uniform and isotropic and that the physical rate of propagation of light is the same for all observers. In accelerated frames…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
We present a method based on the so-called Quantum Energy Inequalities, which allows to compare, and bound, the expectation values of energy-densities of ground states of quantum fields in spacetimes possessing isometric regions. The method…
Quantum gravitational effects can become important at low energy if the wavefunction of the metric field fails to be peaked around a classical configuration. We try to understand such deviations from classicality within canonical quantum…
We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle, that comprises the effects of spacetime curvature at large distances.…
We present a quantum optics treatment of the near horizon behaviour of a quantum oscillator freely-falling into a pre-existing Schwarzschild black hole. We use Painleve-Gullstrand coordinates to define a global vacuum state. In contrast to…
The usual gravitational wave memory effect can be understood as a change in the separation of two initially comoving observers due to a burst of gravitational waves. Over the past few decades, a wide variety of other, "persistent"…
Einstein's famous equivalence principle is certainly one of the most striking features of the gravitational interaction. In a strict reading, it states that the effects of gravity can be made to disappear $locally$ by a convenient choice of…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…