Related papers: On the relation between the Einstein field equatio…
We prove that, contrary to the situation with time-like and space-like parallel vector fields, there are real gravitational fields satisfying Einsteins equations of gravity and admitting nontrivial light-like parallel vector fields; we…
We formulate extensions of Wilking's Jacobi field splitting theorem to uniformly positive sectional curvature and also to positive and nonnegative intermediate Ricci curvatures.
Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology…
The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally…
We will present a complete set of equations, in the form of an Einstein-Bianchi system, that describe the evolution of generic smooth lattices in spacetime. All 20 independent Riemann curvatures will be evolved in parallel with the…
Extending black-hole entropy to ordinary objects, we propose kinetic entropy tensor, based on which a quantum gravity tensor equation is established. Our investigation results indicate that if N=1, the quantum gravity tensor equation…
The Jackiw-Teitelboim gauge formulation of the 1+1 dimensional gravity allows us to relate different gauge fixing conditions with integrable hierarchies of evolution equations. We show that the equations for the Zweibein fields can be…
General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics.…
This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field. On a given…
Here, we have investigated the interaction of Bianchi type I anisotropic cloud string cosmological model universe with electromagnetic field in the context of general relativity. In this paper, the energy momentum tensor is assumed to be…
In many cases a scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject particularly on type I Bianchi space-time. In this paper, global existence to the coupled…
Recently, it has been shown that the effective field theory of the Ponzano-Regge model with which spinless massive particles are coupled is given by three dimensional Euclidean noncommutative scalar field theory in the Lie algebraic…
We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
In this series of papers, we investigate coupled systems arising in the study of two-component Bose--Einstein condensates, and we establish classification results for solutions of De Giorgi conjecture type. In the first paper of the series,…
The divergence of relativistic accelerations generates field masses and the corresponding Ricci scalar in the gravitational integral of the Hilbert action. The covariant description of the elastic hierarchy with a specific time flow and…
We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation. Using modular theory, we establish that the relative entropy between the vacuum…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de…