In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms holonomy-flux variables, and show how it related to continuous general relativity. particular, prove an isomorphism between gravity symplectic reduction with respect a flatness constraint. This gives for first time precise relationship continuum variables. our construction, fluxes not only depend on three-geometry, but also explicitly connection, providing natural explanation their...

We present a polymer quantization of the $\ensuremath{-}\ensuremath{\lambda}∕{r}^{2}$ potential on positive real line and compute numerically bound state eigenenergies in terms dimensionless coupling constant $\ensuremath{\lambda}$. The singularity at origin is handled two ways: first, by regularizing adopting either symmetric or antisymmetric boundary conditions; second, keeping unregularized but allowing to be balanced an condition. results are compared semiclassical limit theory...

We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painlev\'e-Gullstrand coordinates. Near criticality system exhibits Choptuik scaling with a mass gap and new relationship dependant upon length scale. Classical singularities are resolved by radiationlike phase collapse: black hole consists compact region spacetime bounded single, smooth trapping horizon. The ``evaporation'' is not complete but leaves behind small expanding...

It is well known that the SU(2)-gauge invariant phase space of loop gravity can be represented in terms twisted geometries.These are piecewise-linear-flat geometries obtained by gluing together polyhedra, but resulting not continuous across faces.Here we show this also continuous, piecewise-flat three-geometries called spinning composed metric-flat three-cells glued consistently.The geometry each cell and manner which they compatible with choice fluxes holonomies.We first remark provide edge...

We study the quantum mechanics of self-gravitating thin shell collapse by solving polymerized Wheeler-DeWitt equation. obtain energy spectrum and solve time-dependent equation using numerics. In contradistinction to continuum theory, we are able consistently quantize theory for super-Planckian black holes, find two choices boundary conditions which conserve probability, as opposed one in theory. Another feature unique polymer is existence negative stationary states that disappear from scale...

We study numerically black-hole formation from a collapsing massless scalar field. The use of Painlev\'e-Gullstrand coordinates allows the evolution to proceed until singularity formation. generate spacetime maps collapse, illustrating apparent horizons for various initial data. A Choptuik scaling reveals expected universal values critical exponent and echoing period. periodic oscillations in supercritical horizon relation, while with respect data, show unexpected structure large amplitude cusps.

A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and existence Birkhoff theorem. gravitational potential can be chosen as function areal radius to yield specific non-singular static solutions generically have two horizons. For choice stress tensor violates only dominant condition. violations...

We study general relativity with pressureless dust in the canonical formulation, field chosen as a matter time gauge. The resulting theory has three physical degrees of freedom metric field. linearized reveals two graviton modes and scalar mode. find that remain Lorentz covariant despite gauge, mode is ultralocal. also discuss modification to include parameter Hamiltonian analogous Horava–Lifshitz models. In this case no longer ultralocal it acquires propagation speed dependent on...

We analyze the quasinormal modes of $D$-dimensional Schwarzschild black holes with Gauss-Bonnet correction in large damping limit and show that standard analytic techniques cannot be applied a straightforward manner to case infinite damping. However, by using combination numeric we are able calculate mode frequencies range where is but finite. for this region famous $\ln(3)$ appears real part frequency. In our calculations, coupling, $α$, taken much smaller than parameter $μ$, which related...

We study the Einstein gravity and dust system in three spacetime dimensions as an example of a nonperturbative quantum model with local degrees freedom. derive Hamiltonian theory time gauge show that it has rich class exact solutions. These include Ba\~nados--Teitelboim--Zanelli black hole, static solutions naked singularities, traveling wave dynamical horizons. give complete quantization sector theory, including definition self-adjoint metric operator. This operator is used to demonstrate...

We develop a Hamiltonian description of point particles in (2+1)-dimensions using connection and frame-field variables for general relativity. The topology each spatial hypersurface is that punctured two-sphere with residing at the punctures. describe this CW complex (a collection two-cells glued together along edges), use to fix gauge reduce Hamiltonian. equations motion fields dynamical triangulation where vertex moves according equation free relativistic particle. evolution continuous...

Three-dimensional gravity coupled to pressureless dust is a field theory with one local degree of freedom. In the canonical framework, dust-time gauge encodes this physical freedom as metric function. We find that dynamics field, up spatial diffeomorphism flow, independent derivatives and therefore ultralocal. also derive linearized equations about flat spacetime, show may be viewed either traceless or transverse mode.

Beginning from the Ashtekar formulation of general relativity, we derive a physical Hamiltonian written in terms (classical) loop gravity variables. This is done by defining gravitational fields within complex three-dimensional cells and imposing that curvature torsion vanish each cell. The resulting theory holographic, with bulk dynamics being captured completely degrees freedom living on cell boundaries. Quantization readily obtainable existing methods.

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to Coulomb-Dirac equation on half line. The Hamiltonian has one-parameter family self-adjoint extensions with discrete energy spectrum $|E|<m$, and continuum scattering states for $|E|>m$, where $m$ rest mass $E$ Arnowitt-Deser-Misner mass. For sufficiently large $m$, ground state level negative. This suggests classical positivity does not survive quantization. provide realization singularity...

In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms holonomy-flux variables, and show how it related to continuous general relativity. particular, prove an isomorphism between gravity symplectic reduction with respect a flatness constraint. This gives for first time precise relationship continuum variables. Our construction shows that fluxes depend on three-geometry, but also explicitly connection, explaining their non commutativity. It...