Conservation laws for collisions of branes (or shells) in general relativity

TL;DR

This paper derives a geometric constraint for collisions of self-gravitating branes in higher-dimensional spacetime, which can be interpreted as energy or momentum conservation laws.

Contribution

It introduces a simple sum rule for Lorentz boost angles that governs brane collisions, linking geometry with conservation laws in higher-dimensional gravity.

Findings

Derived a geometric sum rule for brane collision angles

Reinterpreted the sum rule as energy and momentum conservation

Applicable to self-gravitating branes in (n+2)-dimensional spacetime

Abstract

We consider the collision of self-gravitating n-branes in a (n+2)-dimensional spacetime. We show that there is a geometrical constraint which can be expressed as a simple sum rule for angles characterizing Lorentz boosts between branes and the intervening spacetime regions. This constraint can then be re-interpreted as either energy or momentum conservation at the collision.