Related papers: Spherical spaces for cosmic topology and multipole…
We extend the treatment of quantum cosmology to a manifold with torsion. We adopt a model of Einstein-Cartan-Sciama-Kibble compatible with the cosmological principle. The universe wavefunction will be subject to a $\mathcal{PT}$-symmetric…
We derive, in order of magnitude, the observed astrophysical and cosmological scales in the Universe, from neutron stars to superclusters of galaxies, up to, asymptotically, the observed radius of the Universe. This result is obtained by…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
Combining intervals of ekpyrotic (ultra-slow) contraction with a (non-singular) classical bounce naturally leads to a novel cyclic theory of the universe in which the Hubble parameter, energy density and temperature oscillate periodically,…
On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was…
We prove the existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on the sphere $S^{10}.$ Previously, the only even-dimensional spheres known to admit non-round Einstein metrics were $S^6$ and $S^8.$
In this work a class of interior solution for Einstein field equations corresponding to a spherically symmetric anisotropic fluid sphere has been obtained under the assumption that the cosmological constant is spatially variable. The…
Astrophysical observations indicate the expansion of the universe is accelerating. Applying the holographic entropy conjecture to the cosmological horizon in an accelerating universe suggests the universe has only a finite number of degrees…
In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This…
We study a class of spherically symmetric Stephani cosmological models in the presence of a self-interacting scalar field in both classical and quantum domains. We discuss the construction of `canonical' wave packets resulting from the…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
The Vlasov-Einstein system describes a self-gravitating, collisionless gas within the framework of general relativity. We investigate the initial value problem in a cosmological setting with spherical, plane, or hyperbolic symmetry and…
Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we intend to show that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.
Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…
We consider a spatially homogeneous and isotropic cosmological model where Dirac spinors are coupled to classical gravity. For the Dirac spinors we choose a Hartree-Fock ansatz where all one-particle wave functions are coherent and have the…
We study Einstein warped space with a quarter symmetric connection. As a result, first, we find basic results on curvature, Ricci and scalar tensors with respect to the quarter symmetric connection. Moreover, we prove some results…
It has long been considered that conformal superspace is the natural configuration space for canonical general relativity. However, this was never definitively demonstrated. We have found that the standard conformal method of solving the…
This note concerns the area growth and bottom spectrum of complete stable minimal surfaces in a three-dimensional manifold with scalar curvature bounded from below. When the ambient manifold is the Euclidean space, by an elementary…
Within the scope of a spherically symmetric space-time we study the role of different types of matter in the formation of different configurations with spherical symmetries. Here we have considered matter with barotropic equation of state,…
In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory…