Post-Newtonian Theories

Antonio Romano () and Mario Mango Furnari ()
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Antonio Romano: Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Mario Mango Furnari: Consiglio Nazionale delle Ricerche, Istituto di Cibernetica

Chapter 21 in The Physical and Mathematical Foundations of the Theory of Relativity, 2026, pp 603-619 from Springer

Abstract: Abstract In the preceding chapters, the motivations that led Einstein to replace Newtonian gravitation with the theory of general relativity have been outlined. This theory replaces the action-at-a-distance of Newtonian gravitational force with the curvature of space-time induced by the energy–momentum tensor. This new formulation of the gravitational field has explained phenomena such as the precession of Mercury’s perihelion, the deflection of light near the solar boundary, and the gravitational time dilation experienced by clocks in a gravitational field. However, Einstein’s field equations are highly nonlinear, making them extremely difficult to solve except in highly symmetric or idealized cases. For instance, known solutions include the Schwarzschild solution for a spherically symmetric mass, the Kerr solution for a rotating body, and the Robertson–Walker solution for cosmological models. All these results are derived under the assumption of strong symmetries imposed a priori but physically justified.

Date: 2026
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DOI: 10.1007/978-3-032-23179-6_21

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