Related papers: Newtonian gravity in d dimensions

The holographic principle is often (and hastily) attributed to quantum gravity and domains of the Planck size. Meanwhile it can be usefully applied to problems where gravitation effects are negligible and domains of less exotic size. The…

We consider a Weyl-invariant formulation of gravity with a cosmological constant in d-dimensional spacetime and show that near two dimensions the classical action reduces to the timelike Liouville action. We show that the renormalized…

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…

We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…

We derive the effect of the Schr\"odinger--Newton equation, which can be considered as a non-relativistic limit of classical gravity, for a composite quantum system in the regime of high energies. Such meson-antimeson systems exhibit very…

The quest for a microscopic foundation of Thermodynamics is addressed within the Nonunitary Newtonian Gravity model through the study of a specific closed system, namely a three-dimensional harmonic nanocrystal. A numerical calculation of…

We derive the Virial theorem appropriate to the generalized Smoluchowski-Poisson system describing self-gravitating Brownian particles and bacterial populations (chemotaxis). We extend previous works by considering the case of an unbounded…

We study (3+1)+D dimensional spacetime, where D extra dimensions are timelike. Compactification of the D timelike dimensions leads to tachyonic Kaluza-Klein gravitons. We calculate the gravitational self-energies of massive spherical bodies…

Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…

Gravity in d dimensions is formulated as the gauge theory of local SO(2,d-1) gauge group. The Chern-Pontryagin index ${\cal P}_{2n}$ plays a crucial role in both gravity and gauge theories. ${\cal P}_{2n}(gravity)$ gives the gravitational…

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…

We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…

A D-dimensional gravitational model with Gauss-Bonnet and cosmological term is considered. When ansatz with diagonal cosmological metrics is adopted, we overview recent solutions for zero cosmological term and find new examples of solutions…

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this…

I review some ways in which spacetime dimensionality enters explicitly in gravitation. In particular, I recall some unusual geometrical gravity models that are constructible in dimensions different from four, especially in D=3 where even…

We review the out-of-equilibrium properties of a self-gravitating gas of particles in the presence of a strong friction and a random force (canonical gas). We assume a bare diffusion coefficient of the form $D(\rho)=T\rho^{1/n}$, where…

We discuss the nature of phase transitions in the self-gravitating Fermi gas at non-zero temperature. This study can be relevant for massive neutrinos in Dark Matter models and for collisionless self-gravitating systems experiencing a…

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…