Related papers: On Breakdown Criteria for Nonvacuum Einstein Equat…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
We consider the Einstein-Boltzmann system for massless particles in the Bianchi I space-time with scattering cross-sections in a certain range of soft potentials. We assume that the space-time has an initial conformal gauge singularity and…
It is shown that Einstein's field equations for \emph{all} perfect-fluid $k=0$ FLRW cosmologies have the same form as the topological normal form of a fold bifurcation. In particular, we assume that the cosmological constant is a…
It is shown by several authors going back to Huisken-Yau that asymptotically Schwarzschildean time-slices possess a unique foliation by stable constant mean curvature (CMC) spheres defining the so-called CMC center of mass. We analyze how…
In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes…
We prove global completeness in the expanding direction of spacetimes satisfying the vacuum Einstein equations on a manifold of the form $\Sigma \times S^{1}\times R$ where $\Sigma $ is a compact surface of genus $G>1.$ The Cauchy data are…
We derive evolution and constraint equations for second order perturbations of flat dust homogeneous and isotropic solutions to the Einstein field equations using all scalar, vector and tensor perturbation modes. We show that the…
We establish purely geometric or metric-based criteria for the validity of the separate universe ansatz, under which the evolution of small-scale observables in a long-wavelength perturbation is indistinguishable from a separate…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
We study the effects of trans-planckian censorship conjecture (TCC) bounds on geodesic completeness of spacetime and the associated existence for an infinite proper time. Using Gronwall's lemma, TCC bounds can be derived directly, leading…
The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills'…
We investigate the problem of metric fluctuations in the presence of the vacuum fluctuations of matter fields and critically assess the usual assertion that vacuum energy implies a Planckian cosmological constant. A new stochastic classical…
We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic…
In previous papers I expounded non-linear Schrodingerist quantum mechanics as a solution of the Measurement Problem. Here I show that NLQM is compatible with Einstein's theory of General Relativity. The extension to curved space-times…
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The constraints translate into a parabolic equation, with radius…
The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and…
Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite…
We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr-Schild ansatz that includes a spacelike vector field as well as the usual Kerr-Schild null vector. We show that many, although not all, of…
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…
Starting from the classic Friedmann-Robertson-Walker theory with big bang it is shown that the solutions of the field equations can be extended to negative times. Choosing a new cosmic time scale instead of proper time one achieves complete…