Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of f (R)-gravity is equivalent to the one of Brans-Dicke gravity with ωBD = 0, so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ωBD = 0 in order to characterize the homologous quantities of f (R)-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f (R)-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame. © 2010 Elsevier B.V. All rights reserved.

Comparing scalar-tensor gravity and f (R)-gravity in the Newtonian limit

CAPOZZIELLO, Salvatore;STABILE, ARTURO;TROISI, ANTONIO
2010-01-01

Abstract

Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of f (R)-gravity is equivalent to the one of Brans-Dicke gravity with ωBD = 0, so that the PPN parameters of these models turn out to be ill-defined. In this Letter, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with ωBD = 0 in order to characterize the homologous quantities of f (R)-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for an f (R)-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame. © 2010 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4687559
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