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Our concept of mass has evolved considerably over the centuries, most notably from Newton to Einstein, and then even more vigorously with the establishment of the standard model and the subsequent discovery of the Higgs boson. Mass is now…
The characterization of the gravitational field of isolated objects is still an open question in quadratic theories of gravity. We study static equilibrium solutions for a self-gravitating fluid in extensions of General Relativity including…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local…
The relative equilibria of planar Newtonian $N$-body problem become coorbital around a central mass in the limit when all but one of the masses becomes zero. We prove a variety of results about the coorbital relative equilibria, with an…
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…
If the information transfer between test particle and holographic screen in entropic gravity respects both the uncertainty principle and causality, a lower limit on the number of bits in the universe relative to its mass may be derived.…
Both particle physics and the 1890s Seeliger-Neumann modification of Newtonian gravity suggest considering a "mass term" for gravity, yielding a finite range due to an exponentially decaying Yukawa potential. Unlike Nordstr\"{o}m's…
Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise,…
A scalar theory of gravitation with a preferred reference frame (PRF) is considered, that accounts for special relativity and reduces to it if the gravitational field cancels. The gravitating system consists of a finite number of…
In Einstein's general relativity, gravity is mediated by a massless metric field. The extension of general relativity to consistently include a mass for the graviton has profound implications for gravitation and cosmology. Salient features…
It is argued that some approaches to non-perturbative quantum general relativity lack a sensible continuum limit that reproduces general relativity. The basic problem is that generic physical states lack long ranged correlations, because…
What is the right way to interpret a massive graviton? We generalize the kinematical framework of general relativity to multiple connections. The average of the connections is itself a connection and plays the role of the canonical…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
The primary constraints for general teleparallel quadratic gravity are presented. They provide a basic classification of teleparallel theories from the perspective of the full nonlinear theory and represent the first step towards a…
Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity,…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…
Many experiments have recently been proposed to test whether non-relativistic gravitational interactions can generate entanglement. In this note, I consider the extent to which these experiments can test if the graviton exists. Assuming…
In this chapter, we discuss recent work on precision Earth laboratory tests of different aspects of gravity. In particular the discussion is focused on those tests that can be used to probe hypothesis for physics beyond Newtonian gravity…
On large-scales, comparable to the horizon, the observable clustering properties of galaxies are affected by various general relativistic effects. To calculate these effects one needs to consistently solve for the metric, densities and…