We consider “kink” solutions of 1+1 dimensional scalar field models with a canonical kinetic term and a potential for the scalar. Classical, static, soliton solutions are found as solutions of the classical mechanics motion in an inverted (V = -U) potential. The cases of the $\phi^4$ and Higgs models are analyzed, and the Higgs “kink” solution is found and described. The sine–Gordon model is also analyzed and its soliton found. The topology of the solutions is characterized. Finally, embedding of the solution in higher dimensions as a “domain wall” is also considered.

We consider “dimensionally reduced” gravitational solutions. We write a domain wall ansatz and solve the Einstein equations for it, first for a perturbative nonrelativistic solution, and then for a nonperturbative relativistic one. We write a cosmic string ansatz and solve Einsein's equations by dimensional reduction to 2+1 dimensions, and alternatively in the weak field limit. We define the cosmological constant and write an ansatz for a 2+1 dimensional black hole in a space with cosmological constant, obtaining the BTZ black hole solution. Anti–de Sitter space is defined in general, starting from the BTZ black hole for M = –1.