Related papers: A Minkowski inequality for the static Einstein-Max…
Quantization of the time symmetric system of interacting strings requires that gravity, just as electromagnetism in Wheeler-Feynman's time symmetric electro- dynamics, also be an "adjunct field" instead of an independent entity. The…
Let $\Omega$ be a compact and mean-convex domain with smooth boundary $\Sigma:=\partial\Omega$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior. If $\Sigma$ is spacelike in a spacetime $(\E^4,g\_\E)$ with…
In this essay I point out that, in the context of semi-classical gravity, the equivalence principle can mitigate the cosmological constant problem. On a Minkowski space-time background with the usual $\mathbb{R}^4$ topology, the vacuum…
It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the…
We show that a nontrivial topologies of the spatial section of Minkowski space-time allow for motion of a charged particle under quantum vacuum fluctuations of the electromagnetic field. This is a potentially observable effect of these…
We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it…
Spacelike intrinsic rotational surfaces with constant mean curvature in the Lorentz-Minkowski space $\E_1^3$ have been recently investigated by Brander et al., extending the known Smyth's surfaces in Euclidean space. Assuming that the…
A general integral inequality is established for compact spacelike submanifolds of codimension two in the Lorentz-Minkowski spacetime under the assumption that the mean curvature vector field is parallel. This inequality is then used to…
The famous Minkowski inequality provides a sharp lower bound for the mixed volume $V(K,M[n-1])$ of two convex bodies $K,M\subset\mathbb{R}^n$ in terms of powers of the volumes of the individual bodies $K$ and $M$. The special case where $K$…
We prove the timelike Brunn-Minkowski inequality $\mathsf{TBM}(K,N)$ implies a timelike lower bound on the Bakry-\'Emery-Ricci curvature on weighted globally hyperbolic spacetimes. This result, together with the well-known equivalence…
In this paper we derive some new invariant solutions of Einstein-Maxwell's field equations for string fluid as source of matter in cylindrically symmetric space-time with Variable Magnetic Permeability. We also discuss the physical and…
Trace-free Einstein gravity, in the absence of matter fields and using the Friedmann-Robertson-Walker (FRW) metric, is solvable both classically and quantum mechanically. This is achieved by using the conformal time as the time variable and…
In this paper, we first show that the Einstein field equations for all perfect-fluid FLRW cosmologies can be written as a planar dynamical system with the equation of state parameter $w$ and cosmological constant $\Lambda$ as parameters. An…
This paper studies the self-similar singularity phenomenon of zero mean curvature equation including Born-Infeld equation, space-like surfaces with vanishing mean curvature equation and membrane equation which arises in string theory and…
We prove the stability of de Sitter space-time as a solution to the Einstein-Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lema\^itre--Robertson--Walker,…
We develop a framework for understanding the existence of asymptotically flat solutions to the static vacuum Einstein equations with prescribed boundary data consisting of the induced metric and mean curvature on a 2-sphere. A partial…
In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature…
In this paper, we consider the evolution of spacelike graphic curves defined over a piece of hyperbola $\mathscr{H}^{1}(1)$, of center at origin and radius $1$, in the $2$ dimensional Lorentz-Minkowski plane $\mathbb{R}^{2}_{1}$ along an…