We present the GRjunction package which allows boundary surfaces and thin-shells in general relativity to be studied with a computer algebra system. Implementing the Darmois-Israel thin shell formalism requires a careful selection of definitions and algorithms to ensure that results are generated in a straight-forward way. We have used the package to correctly reproduce a wide variety of examples from the literature. We present several of these verifications as a means of demonstrating the packages capabilities. We then use GRjunction to perform a new calculation -joining two Kerr solutions with differing masses and angular momenta along a thin shell in the slow rotation limit.

We use the computer algebra system GRTensorII to examine invariants polynomial in the Riemann tensor for class B warped product spacetimes -those which can be decomposed into the coupled product of two 2-dimensional spaces, one Lorentzian and one Riemannian, subject to the separability of the coupling:with C(x γ ) 2 = r(u, v) 2 w(θ, φ) 2 and sig(Σ1) = 0, sig(Σ2) = 2ǫ ( ǫ = ±1) for class B1 spacetimes and sig(Σ1) = 2ǫ, sig(Σ2) = 0 for class B2. Although very special, these spaces include many of interest, for example, all spherical, plane, and hyperbolic spacetimes. The first two Ricci invariants along with the Ricci scalar and the real component of the second Weyl invariant J alone are shown to constitute the largest independent set of invariants to degree five for this class. Explicit syzygies are given for other invariants up to this degree. It is argued that this set constitutes the largest functionally independent set to any degree for this class, and some physical consequences of the syzygies are explored.

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GRTensor is an interactive PC-based program for tensor analysis primarily of interest for teaching and research in general relativity. It uses either maplev or mathematica as its algebraic engine. In this paper we use GRTensor to evaluate the Ricci and Weyl invariants for the radiating Kerr–Newman metric. This includes, as a special case, all nonvanishing invariants of the Kerr metric—the archetypical black hole solution in general relativity.