Related papers: A Comment on Bonnor-Steadman Closed Timelike Curve…
We review the properties of naked time-like singularities in the General Relativity and quantum effects in their vicinity. We demonstrate that only line-like singularities can be formed by a collapse and are the only candidates to break the…
The conceptual definition and understanding of time, both quantitatively and qualitatively is of the utmost difficulty and importance. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note…
The classical world structures borne by spacetimes endowed with torsionful affinities are reviewed. Subsequently, the definition and symmetry properties of a typical pair of Witten curvature spinors for such spacetimes are exhibited along…
In the present work, inhomogeneous Tolman-Bondi type dust space-time is studied on the brane. There are two sets of solutions of the above model. The first solution represents either a collapsing model starting from an infinite volume at…
The properties of a stationary massless string endowed with intrinsic spin are discussed. The spacetime is Minkowskian geometrically but the topology is nontrivial due to the horizon located on the surface $r=0$, similar with Rindler's…
We consider a class of higher order corrections with arbitrary power $n$ of the curvature tensor to the standard gravity action in arbitrary space-time dimension $D$. The corrections are in the form of Euler densities and are unique at each…
Assuming that at small distances space-time is equivalent to an elastic medium which is isotropic in space and time directions, we demonstrate that the quantum nematic liquid arising from this crystal by spontaneous proliferation of…
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.
By variational methods, we prove existence of planar closed curves with prescribed curvature for some classes of curvature functions. The main difficulty is to obtain bounded Palais-Smale sequences. This is achieved by adding a parameter in…
We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric,…
We generalize our previous thick shell formalism to incorporate any codimension-1 thick wall with a peculiar velocity and proper thickness bounded by arbitrary spacetimes. Within this new formulation we obtain the equation of motion of a…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
A theorem about local in time existence of spacelike foliations with prescribed mean curvature in cosmological spacetimes will be proved. The time function of the foliation is geometrically defined and fixes the diffeomorphism invariance…
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the…
The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their…
We prove the stability of a spacetime with a naked singularity under scalar field perturbations, where the perturbations are regular at the singularity. This spacetime, found by Janis, Newman and Winicour, and independently by Wyman, is…
We study graphical mean curvature flow of complete solutions defined on subsets of Euclidean space. We obtain smooth long time existence. The projections of the evolving graphs also solve mean curvature flow. Hence this approach allows to…
General relativity allows solutions exhibiting closed timelike curves. Time travel generates paradoxes and quantum mechanics generalizations were proposed to solve those paradoxes. The implications of self-consistent interactions on acausal…
We consider an exotic `compactification' of spacetime in which there are two infinite extra dimensions, using a global string instead of a domain wall. By having a negative cosmological constant we prove the existence of a nonsingular…
We consider complete spacelike hypersurfaces with constant mean curvature in the open region of de Sitter space known as the steady state space. We prove that if the hypersurface is bounded away from the infinity of the ambient space, then…