# Mixed gravitational field equations on globally hyperbolic spacetimes

Abstract : For every globally hyperbolic spacetime $M$ we derive new gravitational field equations embodying the smooth Geroch infinitesimal splitting $T(M) = {\mathcal D} \oplus \nabla {\mathcal T}$ of $M$, as exhibited by A.N. Bernal \& M. Sánchez, \cite{BeSa2}. We solve the linearized field equations ${\rm Ric}_{\mathcal D} (g)_{\mu\nu} - \rho_{\mathcal D}(g) \, g_{\mu\nu} = 0$ for the empty space. If $g_\epsilon = g_0 + \epsilon \gamma$ is a solution to the linearized ($\epsilon << 1$) field equations then each leaf of $\mathcal D$ is totally geodesic in $({\mathbb R}^4 \setminus {\mathbb R}, g_\epsilon )$ to order $O(\epsilon )$.
Type de document :
Article dans une revue
Classical and Quantum Gravity, IOP Publishing, 2013, 30 (8), pp.085015

https://hal.archives-ouvertes.fr/hal-00849249
Contributeur : Marc Soret <>
Soumis le : mardi 30 juillet 2013 - 15:00:24
Dernière modification le : samedi 9 juin 2018 - 01:17:17

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• HAL Id : hal-00849249, version 1

### Citation

Marc Soret, Sorin Dragomir, Elisabetta Barletta, Vladimir Rovenski, Marc Soret, et al.. Mixed gravitational field equations on globally hyperbolic spacetimes. Classical and Quantum Gravity, IOP Publishing, 2013, 30 (8), pp.085015. 〈hal-00849249〉

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