def test_flrw(self):
"""Test Predefined FLRW metric"""
assert repr(metric.flrw(cartesian=True)) == ('-c**2*TensorProduct(dt, dt) + a(t)**2*(TensorProduct(dx, dx) + '
'TensorProduct(dy, dy) + TensorProduct(dz, dz))')
assert repr(metric.flrw()) == ('-c**2*TensorProduct(dt, dt) + '
'a(t)**2*(r**2*(sin(\\theta)**2*TensorProduct(d\\varphi, d\\varphi) + '
'TensorProduct(d\\theta, d\\theta)) + TensorProduct(dr, dr)/(-k*r**2 + 1))')
assert repr(metric.flrw(curvature_constant=1)) == ('-c**2*TensorProduct(dt, dt) + '
'a(t)**2*(r**2*(sin(\\theta)**2*TensorProduct(d\\varphi, d\\varphi) + '
'TensorProduct(d\\theta, d\\theta)) + TensorProduct(dr, dr)/(1 - r**2))')
def test_flrw_einstein_k(self):
"""FLRW Einstein"""
g = metric.flrw()
G_tt = curvature.einstein_tensor_component(0, 0, g)
assert str(
clean_expr(G_tt)) == '3*(k + Derivative(a(t), t)**2)/a(t)**2'
def test_flrw_ricci_scalar_cartesian(self):
"""FLRW Ricci Cartesian"""
g = metric.flrw(cartesian=True)
R = curvature.ricci_scalar(g)
assert str(
clean_expr(R)
) == '6*(a(t)*Derivative(a(t), (t, 2)) + Derivative(a(t), t)**2)/a(t)**2'
def test_flrw_ricci_cartesian(self):
"""FLRW Ricci Cartesian"""
g = metric.flrw(cartesian=True)
R_tt = curvature.ricci_tensor_component(0, 0, g)
R_xx = curvature.ricci_tensor_component(1, 1, g)
R_yy = curvature.ricci_tensor_component(2, 2, g)
R_zz = curvature.ricci_tensor_component(3, 3, g)
assert str(clean_expr(R_tt)) == '-3*Derivative(a(t), (t, 2))/a(t)'
assert str(
clean_expr(R_xx)
) == 'a(t)*Derivative(a(t), (t, 2)) + 2*Derivative(a(t), t)**2'
assert str(
clean_expr(R_yy)
) == 'a(t)*Derivative(a(t), (t, 2)) + 2*Derivative(a(t), t)**2'
assert str(
clean_expr(R_zz)
) == 'a(t)*Derivative(a(t), (t, 2)) + 2*Derivative(a(t), t)**2'
def met(self):
"""Make metric for other tests"""
return metric.flrw(cartesian=True)
def test_flrw_einstein_cartesian(self):
"""FLRW Einstein"""
g = metric.flrw(cartesian=True)
G_tt = curvature.einstein_tensor_component(0, 0, g)
assert str(clean_expr(G_tt)) == '3*Derivative(a(t), t)**2/a(t)**2'
def test_flrw_christoffel_symbols(self):
"""Test FLRW Christoffel Symbols"""
g = metric.flrw(cartesian=True)
G_t_xx = curvature.christoffel_symbol_component(0, 1, 1, g)
assert str(clean_expr(G_t_xx)) == 'a(t)*Derivative(a(t), t)'
def met(self):
"""Make metric for other tests"""
return metric.flrw()