Related papers: Quantization of static inhomogeneous spacetime
We present some results concerning the large volume limit of loop quantum cosmology in the flat homogeneous and isotropic case. We derive the Wheeler-De Witt equation in this limit. Looking for the action from which this equation can also…
We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For…
We study homogenization problem for non-autonomous parabolic equations of the form $\partial_t u=L(t)u$ with an integral convolution type operator $L(t)$ that has a non-symmetric jump kernel which is periodic in spatial variables and in…
We briefly show how we can obtain Hamiltonians for spatially compact locally homogeneous vacuum spacetimes. The dynamical variables are categorized into the curvature parameters and the Teichm\"{u}ller parameters. While the Teichm\"{u}ller…
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension…
We consider the quantization of a general spatially homogeneous space-time belonging to an arbitrary but fixed Class A Bianchi type. Exploiting the information furnished by the quantum version of the momentum constraints, we use as…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such ``spontaneous dimensional reduction,'' and suggest an additional argument coming from the…
In this work we present a supersymmetric extension of the Reissner-Nordstr\"om spacetime in the framework of quantum cosmology. We achieve this by supersymmetrizing the Wheeler-DeWitt equation for a Kantowski-Sachs cosmological model…
The Wheeler-DeWitt equation is obtained for Kasner-like cosmologies. Some solutions to this equation are presented for empty space, space filled with a cosmological constant and in the presence of a scalar field. We also briefly discuss a…
The Wheeler-DeWitt equation is solved for some scalar-tensor theories of gravitation in the case of homogeneous and isotropic cosmological models.We present general solutions corresponding to cosmological term: (i)\lambda(\phi)=0$ and $(ii)…
This paper studies intermediate homogenization of inhomogeneous cosmological models. It shows that spherically symmetric models, regardless of the equation of state, can undergo intermediate homogenization, i.e. a model can approach a…
In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some…
For any configuration of a static plane-symmetric distribution of matter along space-time, there are coordinates where the metric can be put explicitly as a functional of the energy density and pressures. It satisfies Einstein equations as…
We obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the…
We consider minisuperspace models with two-derivative kinetic terms, assuming a flat target space and a closed Universe. We show that, upon canonical quantization of the Hamiltonian, only a restricted class of operator orderings is…
For a large class of time-dependent non-Hermitain Hamiltonians expressed in terms linear and bilinear combinations of the generators for an Euclidean Lie-algebra respecting different types of PT-symmetries, we find explicit solutions to the…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
We discuss the problem of time in spherically symmetric pure Einstein gravity with the cosmological term by using an exact solution to the Wheeler-DeWitt equation. A positive definite inner product is defined, based on the momentum…
This paper discusses the problem of inflation in the context of Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of variables, one can quantize the problem in a way which parallels the classical discussion. The…