An Online Interactive Geometric Database: Including Exact Solutions of Einstein's Field Equations

TL;DR

The paper introduces GRDB, an interactive online database of geometric objects including exact solutions to Einstein's field equations, designed for researchers and educators in physics and mathematics.

Contribution

It presents a modular, platform-independent web-based database with integrated computational tools for differential geometry and general relativity research.

Findings

Provides a flexible search environment for diverse research needs

Includes a virtual calculator for online tensor calculations

Enables systematic self-checking and minimal internal records

Abstract

We describe a new interactive database (GRDB) of geometric objects in the general area of differential geometry. Database objects include, but are not restricted to, exact solutions of Einstein's field equations. GRDB is designed for researchers (and teachers) in applied mathematics, physics and related fields. The flexible search environment allows the database to be useful over a wide spectrum of interests, for example, from practical considerations of neutron star models in astrophysics to abstract space-time classification schemes. The database is built using a modular and object-oriented design and uses several Java technologies (e.g. Applets, Servlets, JDBC). These are platform-independent and well adapted for applications developed to run over the World Wide Web. GRDB is accompanied by a virtual calculator (GRTensorJ), a graphical user interface to the computer algebra system GRTensorII used to perform online coordinate, tetrad or basis calculations. The highly interactive nature of GRDB allows for systematic internal self-checking and a minimization of the required internal records.