BSSNextrinTensor.hpp

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#pragma once
 
#include "../../Core/Derivate.hpp"
#include "../../Core/Matrix.hpp"
#include "../../Core/Tensor.hpp"
#include "../../Core/Vector.hpp"
#include "../Metric.hpp"
#include "BSSNSetup.hpp"
 
namespace tensorium_RG {
template <typename K> class ExtrinsicCurvature {
  public:
    using Vec = tensorium::Vector<K>;
    using Mat = tensorium::Tensor<K, 2>;
 
    template <typename T>
    tensorium::Tensor<T, 2>
    compute_Kij(const tensorium::Tensor<T, 2> &dgt, const tensorium::Tensor<T, 2> &gamma,
                const tensorium::Vector<T> &beta, const tensorium::Tensor<T, 2> &partial_beta,
                const tensorium::Tensor<T, 3> &christoffel, const T alpha) {
        tensorium::Tensor<T, 2> Kij({3, 3});
 
        for (size_t i = 0; i < 3; ++i) {
            for (size_t j = 0; j < 3; ++j) {
                T sym_grad_beta = partial_beta(i, j) + partial_beta(j, i);
                T gamma_beta = T(0.0);
 
                for (size_t k = 0; k < 3; ++k)
                    gamma_beta += 2.0 * christoffel(k, i, j) * beta(k);
 
                Kij(i, j) = -0.5 / alpha * (dgt(i, j) - (sym_grad_beta - gamma_beta));
            }
        }
        for (size_t i = 0; i < 3; ++i)
            for (size_t j = i + 1; j < 3; ++j) {
                T sym_val = 0.5 * (Kij(i, j) + Kij(j, i));
                Kij(i, j) = Kij(j, i) = sym_val;
            }
 
        return Kij;
    }
};
 
} // namespace tensorium_RG