Complexity in de Sitter space

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Super algebra and Harmonic Oscillator in Anti de Sitter space

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

Rotating De Sitter Space

An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus, which may shed light on the origin of highly collimated jets from compact objects.

Cohomogeneity One Anti De Sitter Space H_1^3

Adventures in de Sitter space

This is my contribution to the Festschrift honoring Stephen Hawking on his 60th birthday. Twentyfive years ago, Gibbons and Hawking laid out the semi-classical properties of de Sitter space. After a summary of their main results, I discuss some further quantum aspects that have since been understood. The largest de Sitter black hole displays an intriguing pattern of instabilities, which can ren...