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sparse-tensor-0.2.1.1: typesafe tensor algebra library

Copyright(c) 2019 Tobias Reinhart and Nils Alex
LicenseMIT
Maintainertobi.reinhart@fau.de, nils.alex@fau.de
Safe HaskellNone
LanguageHaskell2010

Math.Tensor.Examples.Gravity.SchwarzschildSymbolic

Description

This module provides the Schwarzschild metric as an example for a tensor with symbolic values as well as functions to calculate Christoffel symbols, Ricci tensors and Einstein tensors from metric tensors with symbolic values.

Synopsis

Documentation

schwarzschildS :: STTens 0 2 SSymbolic Source #

Schwarzschild metric g=(1rsr)dtdt11rsrdrdrr2dθdθr2sin2θdϕdϕ.

schwarzschildS' :: STTens 2 0 SSymbolic Source #

Inverse Schwarzschild metric g=11rsrtt(1rsr)rr1r2θθ1r2sin2θϕϕ.

christoffelS :: STTens 0 2 SSymbolic -> STTens 2 0 SSymbolic -> STTens 1 2 SSymbolic Source #

Christoffel symbols of any symbolic metric.

ricciS :: STTens 0 2 SSymbolic -> STTens 2 0 SSymbolic -> STTens 0 2 SSymbolic Source #

Ricci tensor of any symbolic metric.

einsteinS :: STTens 0 2 SSymbolic -> STTens 2 0 SSymbolic -> STTens 0 2 SSymbolic Source #

Einstein tensor of any symbolic metric. The components evaluate to zero:

>>> let g  = schwarzschildS
>>> let g' = schwarzschildS'
>>> let e  = einsteinS g g'
>>> print e
ZeroTensor -- modulo symbolic simplification, which is not implemented yet.