geo_timelike_length_h.ipynb

Kernel: SageMath 9.1.beta8

Length of timelike curve

This Jupyter/SageMath notebook is relative to the lectures Geometry and physics of black holes.

%display latex

integrate(sqrt(1-x^2), x)

f(x) = (sqrt(1-x^2) + asin(x)/x)/2
f(x)

taylor(f(x), x, 0, 5)

g = plot(f(x), (x, -1, 1), thickness=2, gridlines='major',
         axes_labels=[r'$h$', r'$L_{(p,q)}(\mathscr{L}_h)/T$'],
         fontsize=14)
g

g.save('geo_timelike_length_h.pdf')