Related papers: Quantum Gravitational Collapse in the Lemaitre-Tol…
In this paper, we consider a quantum model of gravitation interacting with a Born-Infeld(B-I) type scalar field $\phi$. The corresponding Wheeler-Dewitt equation can be solved analytically for both very large and small cosmological scale…
We analyze the Wheeler-DeWitt (WDW) equation in the context of a gravitational collapse. The physics of an expanding/collapsing universe and many details of a collapsing star can classically be described by the Roberston-Walker metric in…
The existence of gravitational radiation arriving at null infinity -- i.e. escaping from the physical system -- is addressed in the presence of a non-negative cosmological constant $\Lambda\geq 0$. The case with vanishing $\Lambda$ is well…
In the framework of a Varying Speed of Light theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. We find that the Wheeler-DeWitt…
We suggest a new formula, which allows the Schwarzschild's solution and the Einstein radius to be applied to the dynamic universe, when our universe is hypothetically regarded as a single dynamic black hole. In this study, a cosmological…
Lemaitre-Tolman-Bondi models as specific spherically symmetric solutions of general relativity simplify in their reduced form some of the mathematical ingredients of black hole or cosmological applications. The conditions imposed in…
In this contribution we sketch a branch-cut quantum formulation of the Wheeler-DeWitt equation analytically continued to the complex plane. As a starting point, we base our approach on the Ho\v{r}ava-Lifshitz formulation of gravity, which…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
In the framework of Horava-Lifshitz theory, we study the eigenvalues associated with the Wheeler-DeWitt equation representing the vacuum expectation values associated with the cosmological constant. The explicit calculation is performed…
Recent cosmological observations suggest the existence of a positive cosmological constant $\Lambda$ with the magnitude $\Lambda(G\hbar/c^3) \approx 10^{-123}$. This review discusses several aspects of the cosmological constant both from…
We study the Wheeler-DeWitt quantization of a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with pressureless dust (modeled via the Brown-Kucha\v{r} formalism) and a dynamical cosmological constant $\Lambda$ treated…
In the case of a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker universe in $f\left( R\right) $-gravity we write the Wheeler-DeWitt equation of quantum cosmology. The equation depends on the functional form of $f\left( R\right)…
In this paper we study the cosmological constant emerging from the Wheeler-DeWitt equation as an eigenvalue of the related Sturm-Liouville problem. We employ Gaussian trial functionals and we perform a mode decomposition to extract the…
Consider compact objects --such as neutron star or black hole binaries-- in \emph{full, non-linear} general relativity. In the case with zero cosmological constant $\Lambda$, the gravitational radiation emitted by such systems is described…
On the basis of qualitative analysis of the system of differential equations of the standard cosmological model it is shown that in the case of zero cosmological constant this system has a stable center corresponding to zero values of…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
In this paper, we consider the Wheeler-DeWitt equation modified by a deformation of the second quantized canonical commutation relations. Such modified commutation relations are induced by a Generalized Uncertainty Principle. Since the…
We consider the possibility of generalizing the Newtonian law of gravity and the transition to a general relativistic model for weak fields with the inclusion of a repulsive term identified as a cosmological constant. The analysis includes…
The Wheeler-DeWitt equation is considered in the context of generalized scalar-tensor theories of gravitation for Bianchi type I cosmology. Exact solutions are found for two selfinteracting potentials and arbitary coupling function. The WKB…
In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around…