Topology Change of Spacetime and Resolution of Spacetime Singularity in Emergent Gravity

Emergent gravity is based on the Darboux theorem or the Moser lemma in symplectic geometry stating that the electromagnetic force can always be eliminated by a local coordinate transformation as far as U(1) gauge theory is defined on a spacetime with symplectic structure. In this approach, the spacetime geometry is defined by U(1) gauge fields on noncommutative (NC) spacetime. Accordingly the topology of spacetime is determined by the topology of NC U(1) gauge fields. We show that the topology change of spacetime is ample in emergent gravity and the subsequent resolution of spacetime singularity is possible in NC spacetime. Therefore the emergent gravity approach provides a well-defined mechanism for the topology change of spacetime which does not suffer any spacetime singularity in sharp contrast to general relativity.Comment: 6 pages with two columns; expanded version to appear in Phys. Rev.

Is classical flat Kasner spacetime flat in quantum gravity?

Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology. We find that even though the spacetime curvature vanishes at the classical level, non-trivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces non-vanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The non-curvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with non-trivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.Comment: 14 pages, 2 figures. Prepared for IJMPD special issue on Loop Quantum Cosmolog

Uniform-Velocity Spacetime Crystals

We perform a comprehensive analysis of uniform-velocity bilayer spacetime crystals, combining concepts of conventional photonic crystallography and special relativity. Given that a spacetime crystal consists of a sequence of spacetime discontinuities, we do this by solving the following sequence of problems: 1) the spacetime interface, 2) the double spacetime interface, or spacetime slab, 3) the unbounded crystal, and 4) the truncated crystal. For these problems, we present the following respective new results: 1) an extension of the Stokes principle to spacetime interfaces, 2) an interference-based analysis of the interference phenomenology, 3) a quick linear approximation of the dispersion diagrams, a description of simultaneous wavenumber and frequency bandgaps, and 4) the explanation of the effects of different types of spacetime crystal truncations, and the corresponding scattering coefficients. This work may constitute the foundation for a virtually unlimited number of novel canonical spacetime media and metamaterial problems

Constant scalar curvature hypersurfaces in (3+1)(3+1)-dimensional GHMC Minkowski spacetimes

We prove that every $(3+1)$-dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In otherwords, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is a smooth submersion

Geometric Analysis of Particular Compactly Constructed Time Machine Spacetimes

We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we present an analysis of its geodesics analogous to the one conducted in the case of the Schwarzschild spacetime. We conclude that the pseudo Schwarzschild spacetime is geodesically incomplete and not extendible to a complete spacetime. We then introduce a rotating generalization of the pseudo Schwarzschild metric, which we call the the pseudo Kerr spacetime. We establish its time machine structure and analyze its global properties.Comment: 14 pages, 3 figure