相关论文: Vacuum space-times with controlled singularities a…
In this paper we investigate four dimensional Lorentzian spacetimes with constant curvature invariants ($CSI$ spacetimes). We prove that if a four dimensional spacetime is $CSI$, then either the spacetime is locally homogeneous or the…
A d-dimensional spacetime is "axisymmetric" if it possesses an SO(d-2) isometry group whose orbits are (d-3)-spheres. In this paper, algebraically special, axisymmetric solutions of the higher dimensional vacuum Einstein equation (with…
Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant…
We develop a local theory for the construction of singular spacetimes in all spacetime dimensions which become asymptotically self-similar as the singularity is approached. The techniques developed also allow us to construct and classify…
We classify simply-connected homogeneous ($D+1$)-dimensional spacetimes for kinematical and aristotelian Lie groups with $D$-dimensional space isotropy for all $D\geq 0$. Besides well-known spacetimes like Minkowski and (anti) de Sitter we…
In this paper, we construct a class of collapsing spacetimes in vacuum without any symmetries. The spacetime contains a black hole region which is bounded from the past by the future event horizon. It possesses a Cauchy hypersurface with…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
We present a singularity free class of inhomogeneous cylindrical universes filled with stiff perfect fluid $(\rho = p)$. Its matter free $ (\rho = 0)$ limit yield two distinct vacuum spacetimes which can be considered as analogues of Kasner…
Space-time symmetries and internal quantum symmetries can be placed on equal footing in a hyperspin geometry. Four-dimensional classical space-time emerges as a result of a decoherence that disentangles the quantum and the space-time…
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropic, ideal fluid flows. The initial velocity is assumed to be…
We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of…
The concept of Euclidean time is proposed which is dual to the usual Minkowski time. The De Sitter solution is shown to be dual to the anti-De Sitter solution under the dual transformation in which Euclidean time and Minkowski time are…
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding…
We discuss the question of whether the existence of singularities is an intrinsic property of 4D spacetime. Our hypothesis is that singularities in 4D are induced by the separation of spacetime from the other dimensions. We examine this…
We provide a new class of exact solutions for the interior in (2 + 1) dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant ($\Lambda$) are found to be regular and singularity…
We present a physics model for a time-symmetric Milne-like universe. The model is based on the $q$-theory approach to the cosmological constant problem, supplemented by an assumed vacuum-matter energy exchange possibly due to…
Electrovacuum solutions devoid of usual mass sources are classified in the case of one, two and three commuting Killing vectors. Three branches of solutions exist. Electromagnetically induced mass terms appear in some of them.
We review recent results by the author, in collaboration with Erwann Delay, Olivier Lengard, and Rafe Mazzeo, on existence and properties of space-times with controlled asymptotic behavior at null infinity.
We show that the static and asymptotically flat black hole spacetime is unique to be Schwarzschild spacetime in the dynamical Chern-Simons gravity. In addition, we show that the strictly static spacetimes should be the Minkowski spacetime.
It is argued that the problems of the cosmological constant, stability and renormalizability of quantum gravity can be solved if the space-time manifold arises through spontaneous symmetry breaking. A ``pre-manifold" model is presented in…