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We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
Starting from the assumption that general relativity might be an emergent phenomenon showing up at low-energies from an underlying microscopic structure, we re-analyze the stability of a static closed Universe filled with radiation. In this…
We develop a systematic framework for formulating and solving the conditions that lead to separability in stationary, axisymmetric spacetimes in the presence of matter fields. Guided by Carter's metric form, we introduce a general…
I give a summary review of the research program using noncommutative geometry as a framework to determine the structure of space-time. Classification of finite noncommutative spaces under few assumptions reveals why nature chose the…
The general metric for conformally flat stationary cyclic symmetric noncircular spacetimes is explicitly given. In spite of the complexity introduced by the inclusion of noncircular contributions, the related metric is derived via the full…
Vacuum static, axially symmetric space-times in $D$-dimensional general relativity with a Ricci-flat internal space are discussed. It is shown, in particular, that some of the monopole-type solutions are free of curvature singularities and…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
Despite the many applications of rate-independent systems, their regularity theory is still largely unexplored. Usually, only weak solution with potentially very low regularity are considered, which requires non-smooth techniques. In this…
Global structure of the (anti-)de~Sitter ((A)dS) generalization of the Roberts solution in general relativity with a massless scalar field and its topological generalization is clarified. In the case with a negative cosmological constant,…
We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
We present a class of conformally flat solutions of the Einstein's field equations for spherical systems undergoing gravitational collapse accompanied with radial heat flux. The interior space-time of the collapsing matter is chosen to be…
Linearized gravitational waves in de Sitter space-time are analyzed in detail to obtain guidance for constructing the theory of gravitational radiation in presence of a positive cosmological constant in full, nonlinear general relativity.…
We prove non-existence of static, vacuum, appropriately regular, asymptotically flat black hole space-times with degenerate (not necessarily connected) components of the event horizon. This finishes the classification of static, vacuum,…
This paper presents a new line element based on the assumption of the variable rest mass in gravitational field, and explores some its implications. This line element is not a vacuum solution of Einstein's equations, yet it is sufficiently…
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary…
A theory of gravitation is presented. This theory does not relate gravitation to curvature of space-time. It explains the three standard results of general relativity in agreement with observations and suggests new experiments.
A time-flat condition on spacelike 2-surfaces in spacetime is considered here. This condition is analogous to constant torsion condition for curves in three dimensional space and has been studied in [2, 4, 5, 12, 13]. In particular, any…
A theory of gravity with a generic action functional and minimally coupled to N matter fields has a nontrivial fixed point in the leading large N approximation. At this fixed point, the cosmological constant and Newton's constant are…
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…