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Newton's inverse-square law of universal gravitation assumes constant mass. But mass increases with speed and perhaps with gravity. By SR, mass is increased over the rest mass by gamma. Rest mass is here postulated to increase under…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…
General relativity differs from other forces in nature in that it can be made to disappear locally. This is the essence of the equivalence principle. In general relativity the equivalence principle is implemented using differential…
Variational Monte Carlo is a many-body numerical method that scales well with system size. It has been extended to study the Green function only recently by Charlebois and Imada (2020). Here we generalize the approach to systems with open…
General Relativity (GR) exists in different formulations. They are equivalent in pure gravity but generically lead to distinct predictions once matter is included. After a brief overview of various versions of GR, we focus on metric-affine…
We present a new analytical framework for describing the dynamics of a gravitational binary system with unequal masses moving with arbitrary relative velocity, taking into account the backreaction from both compact objects in the form of…
We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
We consider the construction of gauge theories of gravity, focussing in particular on the extension of local Poincar\'e invariance to include invariance under local changes of scale. We work exclusively in terms of finite transformations,…
For slowly spinning matter the rate of energy loss via radiation of gravitational waves is estimated in General Relativity (GR) within a generally covariant superenergy approach. This estimation differs from Einstein's Quadrupole Formula…
Using the Post-Minkowskian formalism and considering rotation as a perturbation, we compute an approximate interior solution for a stationary perfect fluid with constant density and axial symmetry. A suitable change of coordinates allows…
The population analysis and estimation of merger rates of compact binaries is one of the important topics in gravitational wave (GW) astronomy. The primary ingredient in these analyses is the population-averaged sensitive volume. Typically,…
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…
In self-consistent N-body simulations of collisionless systems, gravitational interactions are modified on small scales to remove singularities and simplify the task of numerically integrating the equations of motion. This `gravitational…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
In the last few decades, extensions of General Relativity have reached always more attention especially in view of possible breakdowns of the standard $\Lambda$CDM paradigm at intermediate and high redshift regimes. If General Relativity…
A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply $S$-matrix techniques, based on unitarity and analyticity, we first derive an $S$-matrix free of…
The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the…
We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…