Authors: Faisal Amin Yassein Abdelmohssin
I applied the method of the second variations of the Calculus of Variations to the Einstein-Hilbert action. Since the Einstein-Hilbert’s Lagrangian for a gravitational field is proportional to the Ricci curvature scalar construction of the Euler-Lagrange equations requires dealing with the tensor quantities from which the Ricci curvature scalar is composed rather than the Ricci curvature scalar itself. As the result of applying this method two Euler-Lagrange equations emerged; both equations yielded the same Einstein’s field equations in absence of energy-momentum fields.
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