Related papers: A cosmologically motivated reference formulation o…
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order…
We argue that our recent success in using our resummed quantum gravity approach to Einstein's general theory of relativity, in the context of the Planck scale cosmology formulation of Bonanno and Reuter, to estimate the value of the…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
The astrophysics of compact objects, which requires Einstein's theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by…
A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological…
We discuss how the modifications of the standard Einstein's equations needed to support the cosmological bounce can at the same time lead to vanishing of the well known cosmological constant problem, while also studying the effects of…
We develop a simple model to study classical fields on the background of a fluctuating spacetime volume. It is applied to formulate the stochastic Einstein equations with a perfect-fluid source. We investigate the particular case of a…
We develop a new approach to building cosmological models, in which small pieces of perturbed Minkowski space are joined together at reflection-symmetric boundaries in order to form a global, dynamical space-time. Each piece of this…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is assumed in order to derive exact analytic cosmological solutions to Einstein's gravity with two fluids: a barotropic perfect fluid…
We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
It is argued that when the dimension of space is a constant integer the full set of Einstein's field equations has more information than the spatial components of Einstein's equation plus the energy conservation law. Applying the former…
It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…