Related papers: Geometric Cone Surfaces and (2+1)- Gravity coupled…
(from the talk:) I shall here speak on gravity in (1+1)-dimensional space-time --- lineal gravity. The purpose of studying lower dimensional theories, and specifically lower dimensional gravity, is to gain insight into difficult…
Often it is possible to equip the space of all cone geodesics of a strongly convex cone structure with the structure of a smooth contact manifold. This generalizes the analogous notions for the space of light rays of a Lorentzian spacetime.…
Newtonian gravity arises as the nonrelativistic, static, weak-field limit of some Lorentzian spacetime geometry solving the generally covariant Einstein equations for a given matter field configuration. Spacetime geometry has a local…
We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved K\"ahler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex…
We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of…
We construct the Hermitian Schr\"{o}dinger Hamiltonian of spin-less as well as the gauge-covariant Pauli Hamiltonian of spin one-half particles in a magnetic field that are confined to cylindrical and spherical surfaces. The approach does…
Particles propagating in de Sitter spacetime can be described by the topological BF $\SO(4,1)$ theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which…
The quantization of Class A Bianchi Type VI and VII geometries -with all six scale factors, as well as the lapse function and the shift vector present- is considered. A first reduction of the initial 6-dimensional configuration space is…
We consider perturbations of a static and spherically symmetric background endowed with a metric tensor and a scalar field in the framework of the effective field theory of modified gravity. We employ the previously developed 2+1+1…
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…
We investigate the behaviour of classical and quantum fields in the conical space-time associated with a point mass in 2+1 dimensions. We show that the presence of conical boundary conditions alters the electrostatic field of a point charge…
We expand on our results in arXiv:2111.02429 to present a broad new class of gravitational observables in asymptotically Anti-de Sitter space living on general codimension-zero regions of the bulk spacetime. By taking distinct limits, these…
We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the…
We first prove that given a hyperbolic metric $h$ on a closed surface $S$, any flat metric on $S$ with negative singular curvatures isometrically embeds as a convex polyhedral Cauchy surface in a unique future-complete flat globally…
The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for…
A study of the lightcone of the G\"odel universe is extended to the so-called G\"odel-like spacetimes. This family of highly symmetric 4-D Lorentzian spaces is defined by metrics of the form $ds^2=-(dt+H(x)dy)^2+D^2(x)dy^2+dx^2+dz^2$,…
We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\R\times\Sigma^g$, where $\Sigma^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations…
We develop a Hamiltonian description of point particles in (2+1)-dimensions using connection and frame-field variables for general relativity. The topology of each spatial hypersurface is that of a punctured two-sphere with particles…
We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an $SU(3)\times Spin(6+n)$ structure within…
Isometric class of minimal surfaces in the Euclidean 3-space $\mathbb{R}^3$ has the rigidity: if two simply connected minimal surfaces are isometric, then one of them is congruent to a surface in the specific one-parameter family, called…