## Abstract

The postulate is made that across a given hypersurface*N* the metric and its first derivatives are continuous. This postulate is used to derive conditions which must be satisfied by discontinuities in the Riemann tensor across*N*. These conditions imply that the conformal tensor jump is uniquely determined by the stress-energy tensor discontinuity if*N* is non-null (and to within an additive term of type Null if*N* is lightlike). Alternatively,\([C^{\alpha \beta } _{\gamma \delta } ]\) and [*R*] determine\(\left[ {R_{\mu v} - \frac{1}{4}Rg_{\mu v} } \right]\) if*N* is non-null. These relationships between the conformal tensor and stress-energy tensor jumps are given explicitly in terms of a three-dimensional complex representation of the antisymmetric tensors. Application of these results to perfect-fluid discontinuities is made:\([C^{\alpha \beta } _{\gamma \delta } ]\) is of type D across a fluid-vacuum boundary and across an internal, non-null shock front.\([C^{\alpha \beta } _{\gamma \delta } ]\) is of type I (non-degenerate) in general across fluid interfaces across which no matter flows, except for special cases.

## Keywords

Neural Network Statistical Physic General Relativity Complex System Nonlinear Dynamics## Preview

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## References

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