Relativistic membrane solutions in AdS$_4$

TL;DR

This paper explores different classical membrane solutions in AdS$_4$ spacetime, including polynomial embeddings, non-linear wave solutions, and piecewise linear configurations, contributing to the understanding of membrane dynamics in curved backgrounds.

Contribution

It introduces new classes of membrane solutions in AdS$_4$, expanding the known solution space with polynomial, non-linear wave, and piecewise linear configurations.

Findings

Identified polynomial membrane embeddings in AdS$_4$

Constructed non-linear wave solutions for membranes

Developed piecewise linear membrane solutions

Abstract

In this note we discuss various classical membrane solutions in AdS$_4$ spacetime: simple embeddings given by polynomials in ambient space, solutions with non-linear waves, and piecewise linear solutions.