Computer algebra in spacetime embedding

TL;DR

This paper presents an algorithm for finding normal vectors to a spacetime embedded in a higher-dimensional pseudo-Euclidean space, demonstrated on Schwarzschild spacetime using REDUCE.

Contribution

It introduces a novel algorithm for computing normal vectors in spacetime embeddings and applies it to Schwarzschild geometry with algebraic software.

Findings

Algorithm successfully computes normal vectors for embedded spacetimes

Application to Schwarzschild spacetime demonstrates practical utility

Uses REDUCE for algebraic computations in differential geometry

Abstract

In this paper we describe an algorithm to determine the vectors normal to a space-time V4 embedded in a pseudo-Euclidean manifold M4+n. An application of this algorithm is given considering the Schwarzchild space-time geometry embedded in a 6 dimensional pseudo-Euclidean manifold, using the algebraic computing system REDUCE.