## General Relativity as Geometrical Approximation to a Field Theory of Gravity

**Authors:** Juan Ramón González Álvarez

It is broadly believed that general relativity --a geometric theory-- is fully equivalent to the field theory of a massless, self-interacting, spin-2 field. This belief is reinforced by statements in many textbooks. However, an increasing criticism to this belief has been published. To settle this old debate about the precise physical nature of gravitation, this author introduces a simple but exact argument --based in the equivalence principle-- that shows that general relativity is not equivalent to a field theory of gravity. Subsequently, both the general relativistic Lagrangian for a particle and the Hilbert & Einstein equations are obtained as an approximation from a field theory of gravity, somehow as geometric optics can be derived from physical optics. The approximations involved in the geometrization are two: (i) the neglect of $T_{grav}^{\mu\nu}$ and $T_{int}^{\mu\nu}$ in the field-theoretic tensor $\Theta^{\mu\nu}$ and (ii) the approximation of the effective metric by the curved spacetime metric $g_{\mu\nu} = \hat{g}_{\mu\nu} + O(h_{\mu\nu}^2)$. Further discussion of this derivation and of the approximations involved is given.
Several misunderstandings about the consistency and observability of the flat spacetime theories of gravity are corrected. A detailed analysis of the fundamental differences between geometric and field-theoretic expressions reveals that all the well-known deficiencies of general relativity --including the impossibility to obtain a consistent quantum general relativity-- are direct consequences of the geometrization of the gravitational interaction. Finally, remarks about the status of dark matter are given, from the perspective of a generalized theory of gravity.

**Comments:** 11 Pages.

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### Submission history

[v1] 2012-03-12 05:27:04

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