New Classes of Exact Multi-String Solutions in Curved Spacetimes

TL;DR

This paper discovers new exact multi-string solutions in various curved spacetimes, analyzing their physical properties and behaviors, including stationary, dynamical, and multi-string configurations in anti de Sitter, de Sitter, and black hole backgrounds.

Contribution

It introduces novel classes of exact multi-string solutions in curved spacetimes using elliptic functions, expanding understanding of string dynamics in these backgrounds.

Findings

Infinite stationary strings in anti de Sitter with equal energy but different pressures.

Dynamical strings in de Sitter spacetime infalling and scattering at the horizon.

No multi-string solutions in black hole spacetimes without cosmological constant.

Abstract

We find new classes of {\it exact} string solutions in a variety of curved backgrounds. They include stationary and dynamical (open, closed, straight, finitely and infinitely long) strings as well as {\it multi-string} solutions, in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. In anti de Sitter spacetime, the solutions describe an {\it infinite} number of infinitely long stationary strings of equal energy but different pressures. In de Sitter spacetime, outside the horizon, they describe infinitely many {\it dynamical} strings infalling non-radially, scattering at the horizon and going back to spatial infinity in different directions. For special values of the constants of motion, there are families of solutions with {\it selected finite} numbers of different and independent strings. In black hole spacetimes (without cosmological constant), {\it no} multi-string solutions are found. In the Schwarzschild black hole, inside the horizon, we find one straight string infalling non-radially, with {\it indefinetely} growing size, into the $r=0$ singularity. In the $2+1$ black hole anti de Sitter background, the string stops at $r=0$ with {\it finite} length.