The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse...

The separate contributions to cosmology of the above researchers are revisited and a cosmology encompassing their basic ideas is proposed. We study Dirac’s article on the large number hypothesis (Proc.Roy.Soc. Lon. A 165,199; 1938), Sciama’s proposal of realizing Mach’s principle (MNRAS 113, 34; 1953), and Robert Dicke’s considerations on an ‘electromagnetic’ theory of gravitation with a variab...

A hypothetical time variation of the gravitational constant G would cause neutron star matter to depart from beta equilibrium, due to the changing hydrostatic equilibrium. This induces nonequilibrium beta processes, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains...

Proposals that quantum gravity gives rise to non-commutative spacetime geometry and deformations of Poincaré symmetry are examined in the context of (2+1)dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck’s constant and the cosmological constant enter the non-commutative and non-cocommutative structures arising in (2+1)...

We present the spherical harmonic equation for the gravitational potential inside the Earth. The equation satisfies Poisson's equation and converges uniformly. It obviates the need for downward continuation of the exterior potential with its attendant convergence difficulties but of course requires some knowledge of the Earth's density distribution. Equipped with the equation, we derive the gen...

The gravity water wave black (GWBH) hole analog discovered by Schutzhold and Unruh (SU) is extended to allow for the presence of turbulent shear flow. The Riemannian geometry of turbulent black holes (BH) analogs in water waves is computed in the case of lami-nar tirbulent shear flow. The Riemann curvature is constant and the geodesic deviation equation shows that the curvature acts locally as ...

A multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor-spaces Mi in the presence of a one-component anisotropic fluid is considered. The pressures in all spaces are proportional to the density: pi = wiρ , i = 0, ..., n . Solutions with accelerated expansion of our 3-space M0 and small enough variation of the gravitational constant G are found. These solutions exi...

The amount of dark matter in the Milky Way and beyond is examined by taking into account the possible running of the gravitational constant G as a function of distance scale. If the running of G, as suggested by the Asymptotically-Free Higher-Derivative quantum gravity, is incorporated into the calculation of the total dark matter in the galactic halo, the amount of dark matter that is necessar...