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Einstein's static model is the first relativistic cosmological model. The model is static, finite and of spherical spatial symmetry. I use the solution of Einstein's field equations in a homogeneous and isotropic universe -- Friedmann's…
Gauge-invariant treatments of the second-order cosmological perturbation in a four dimensional homogeneous isotropic universe are formulated without any gauge fixing. We have derived the Einstein equations in the case of the single perfect…
A stability analysis is made for a non-singular pre-big-bang like cosmological model based on 1-loop corrected string effective action. Its homogeneous and isotropic solution realizes non-singular transition from de Sitter universe to…
Keeping Einstein's equations in second order form can be appealing for computational efficiency, because of the reduced number of variables and constraints. Stability issues emerge, however, which are not present in first order…
This paper is concerned with the behavior of the ergodic constant associated with convex and superlinear Hamilton-Jacobi equation in a periodic environment which is perturbed either by medium with increasing period or by a random Bernoulli…
One of the possible extensions of Einstein's General Theory of Relativity consists in allowing for the presence of spacetime torsion. The form of the underlying torsion tensor can be chosen such that the homogeneity and isotropy of…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
It has been shown that a contracting universe with a dust-like ($w \approx 0$) fluid may provide an almost scale invariant spectrum for the gravitational scalar perturbations. As the universe contracts, the amplitude of such perturbations…
This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational…
For axially symmetric solutions of Einstein equations there exists a gauge which has the remarkable property that the total mass can be written as a conserved, positive definite, integral on the spacelike slices. The mass integral provides…
Using numerical methods, we examine, under a Gowdy symmetry assumption, the dynamics of nonlinearly perturbed FLRW fluid solutions of the Einstein-Euler-scalar field equations in the contracting direction for linear equations of state $p =…
Based on the gauge invariant variables proposed in our previous paper [K. Nakamura, Prog. Theor. Phys. vol.110 (2003), 723.], some formulae of the perturbative curvatures of each order are derived. We follow the general framework of the…
The Lemaitre-Tolman-Bondi solution has received much attention as a possible alternative to Dark Energy, as it is able to account for the apparent acceleration of the Universe without any exotic matter content. However, in order to make…
Recently a new approach in constructing the conserved charges in cosmological Einstein's gravity was given. In this new formulation, instead of using the explicit form of the field equations a covariantly conserved rank four tensor was…
We study the question whether a possible metastable vacuum state is actually populated in a phase transition in the early universe, as is usually assumed in the discussion of vacuum stability bounds e.g. for Standard Model parameters. A…
Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have…
We give necessary and/or sufficient conditions for stochastic stability of second-order linear autonomous systems with parameters, which are perturbed by a random process of the "white noise" type. The Ito's and Stratonovich's forms of…
A gauge-invariant treatment of the monopole- ($l=0$) and dipole ($l=1$) modes in linear perturbations of the Schwarzschild background spacetime is proposed. Through this gauge-invariant treatment, we derived the solutions to the linearized…
The Cauchy problem of the vacuum Einstein's equations aims to find a semi-metric $g_{\alpha\beta}$ of a spacetime with vanishing Ricci curvature $R_{\alpha,\beta}$ and prescribed initial data. Under the harmonic gauge condition, the…