# Piecewise Conserved Quantities

## TL;DR

This paper reviews how conservation laws are adapted in spacetimes joined together with boundaries, exploring examples like Schwarzschild joins and signature changes, and examining properties of Lorentzian vector calculus.

## Contribution

It provides a comprehensive review of conservation laws in piecewise spacetimes and explores less obvious properties of Lorentzian vector calculus.

## Key findings

- Conservation laws require boundary terms in joined spacetimes
- Examples include joining Schwarzschild solutions of different masses
- Analysis of Lorentzian vector calculus properties

## Abstract

We review the treatment of conservation laws in spacetimes that are glued together in various ways, thus adding a boundary term to the usual conservation laws. Several examples of such spacetimes will be described, including the joining of Schwarzschild spacetimes of different masses, and the possibility of joining regions of different signatures. The opportunity will also be taken to explore some of the less obvious properties of Lorentzian vector calculus.