Strings propagating in the (2+1)-dimensional black hole anti-de Sitter spacetime.
We study the string propagation in the 2+1 black hole anti de Sitter background (2+1 BH-ADS). We find the first and second order fluctuations around the string center of mass and obtain the expression for the string mass. The string motion is stable, all fluctuations oscillate with real frequencies and are bounded, even at $r=0.$ We compare with the string motion in the ordinary black hole anti de Sitter spacetime, and in the black string background, where string instabilities develop and the fluctuations blow up at $r=0.$ We find the exact general solution for the circular string motion in all these backgrounds, it is given closely and completely in terms of elliptic functions. For the non-rotating black hole backgrounds the circular strings have a maximal bounded size $r_m,$ they contract and collapse into $r=0.$ No indefinitely growing strings, neither multi-string solutions are present in these backgrounds. In rotating spacetimes, both the 2+1 BH-ADS and the ordinary Kerr-ADS, the presence of angular momentum prevents the string from collapsing into $r=0.$ The circular string motion is also completely solved in the black hole de Sitter spacetime and in the black string background (dual of the 2+1 BH-ADS spacetime), in which expanding unbounded strings and multi-string solutions appear.
Geodesic structure of the (2 + 1)-dimensional BTZ black hole
Null and time-like geodesics around a 2+1 black hole are determined. Complete geodesics of both types exist in the rotating black-hole background, but not in the spinless case. Upper and lower bounds for the radial size of the orbits are given in all cases and the possibility of passing from one black-hole exterior spacetime to another is discussed using Penrose diagrams. An analysis of particle motions by means of effective potentials and orbit graphs is also included.
Chapter 1 – Nanotechnology: A Toolkit for Cell Behavior
Tissue engineering seeks to effectively manipulate cellular populations to improve the function of damaged or diseased tissues and organs. Many techniques can affect cell behavior; however, in order to maintain desirable function, scientists and engineers design solutions that are as biomimetic as possible. True biomimeticity is very challenging without the incorporation of nanotechnology. Since cells in human tissues are surrounded by a 3D hierarchical tissue extracellular matrix containing numerous nano components, a revolutionary change in tissue engineering is to explore biomimetic nanobiomaterials and advanced 3D nano/microfabrication techniques for creating novel tissue constructs and regulating cell behavior. This chapter will provide an overview of recent nanotechnology in tissue engineering applications. We will put special emphasis on integrating cutting-edge 3D nano/microfabrication techniques with nanobiomaterials for complex tissue and organ regeneration.