Related papers: Wheeler-DeWitt equation in Null-foliated spacetime…
The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain…
The Wightman function i.e. vacuum two-point function, for a massless free scalar field in Fock quantization is inversely proportional to the invariant distance squared between the corresponding spacetime points. Naturally it diverges when…
The scope of this paper is to compare two different approaches for solving the Wheeler-DeWitt (WDW) equation in the presence of homogeneous matter (inflaton) and perturbations around it. The standard Born-Oppenheimer (BO) decomposition,…
We consider the induced $2$d-gravity in the minisuperspace approach. The general solution to the Wheeler-DeWitt equation is given in terms of different kind of Bessel functions of purely real or imaginary orders. We study the properties of…
The Wheeler -- DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature the opinion that the Wheeler -- DeWitt equation is even more…
We study the problem of quantization of thin shells in a Weyl-Dirac theory by deriving a Wheeler-DeWitt equation from the dynamics. Solutions are found which have interpretations in both cosmology and particle physics.
In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended…
We present the "classical" Nielsen-Olesen vortex solution on a warped five dimensional space time, where we solved the effective four-dimensional equations from the five-dimensional equations together with the junction and boundary…
The (4,4) null superstring equations of motions and constraints on de Sitter space are given by using the harmonic superspace. These are solved explicitly by performing a perturbative expansion of the (4,4) superstring coordinates in powers…
In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface {\it orthogonal} to the extra dimension in a five-dimensional bulk. We show that the FRW line element can…
We study ambiguities in the precise formulation of the Wheeler-DeWitt equation for the wavefunction of the Universe that arise due to different operator orderings in the quantum Hamiltonian. We first examine the simpler case of the…
We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…
We solve the Wheeler-DeWitt equation for {\it four}-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or…
The purpose of this work is to analyze the wellposedness and the blow-up of solutions of the higher-order parabolic semilinear equation \[ u_t+(-\Delta)^{d}u=|x|^{\alpha}|u|^{p}+\zeta(t){\mathbf w}(x) \ \quad\mbox{for }…
In this paper, we investigate the null (light-like) sectional curvatures of Lorentzian warped product manifolds. We derive the formulas for the null sectional curvature of many well-known warped product space-time models such as multiply…
One of the central difficulties in the quantization of the gravitational interactions is that they are described by a set of constraints. The standard strategy for dealing with the problem is the Dirac quantization procedure, which leads to…
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are…
We present perfect fluid Friedmann-Robertson-Walker quantum cosmological models in the presence of negative cosmological constant. In this work the Schutz's variational formalism is applied for radiation, dust, cosmic string, and domain…
Quasiclassical generalized Weierstrass representation (GWR) for highly corrugated surfaces with slow modulation in the four-dimensional Euclidean space is proposed. Integrable deformations of such surfaces are described by the…
In general relativity, the double null foliation is one for which $d$-dimensional spacetime is foliated by two families of intersecting null hyper surfaces (i.e. surfaces whose normal vectors are null) of $(d-1)$ dimensions. Their…