Stellar structure equations in extended Palatini gravity

Abstract

We consider static spherically symmetric stellar configurations in Palatini theories of gravity in which the Lagrangian is an unspecified function of the form f (R, R µν R µν ). We obtain the Tolman-Oppenheimer-Volkov equations corresponding to this class of theories and show that they recover those of f (R) theories and General Relativity in the appropriate limits. We show that the exterior vacuum solutions are of Schwarzschild-de Sitter type and comment on the possible expected modifications, as compared to GR, of the interior solutions.

Nonlinear σ -models in the Eddington-inspired Born-Infeld gravity

“…The regular case somehow generalizes the solution found in [37] to cases with nonzero topological charge. We have shown that the parameter δ 1 , which is related to the constant C, is bounded below by the purely electric case.…”

“…This parameter controls the traversability of the wormhole, in the sense that depending on the charge-to-mass ratio of the monopole charge an event horizon may be present or not. In [37] the wormhole is always traversable even for massive particles, without the pathologies found here regarding geodesic motion.…”

“…means that the canonical model only supports regular solutions when the mass is zero, as seen in the previous subsection. Now, if we take η = 0, the solution boils down to that of an electric charge, where δ 1 ≡ κ 2 Q 2 2M 0 r min 0.572 [37,39]. When one allows for the simultaneous coexistence of both charges (η = 0, Q = 0), the effect of the GM charge translates into a "regularization" constant δ 1 bigger than that predicted in the pure electric case, as illustrated in Fig.1.…”

“…If we define Q 2 ≡ βη 4 we will have ρ = η 2 r 2 + Q 2 r 4 , which represents the sum of the energy densities produced by a GM (outside of its core) plus an electric charge Q [37]. In this way we can interpret the NLSM (38) as engendering an electric charge Q plus a GM charge η.…”

“…Taking the proper limits (Q = 0 or η = 0) we directly retrieve the cases already studied [23,37,39].…”