# 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 $O(\epsilon )$.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00849249
Contributor : Marc Soret <>
Submitted on : Tuesday, July 30, 2013 - 3:00:24 PM
Last modification on : Friday, February 19, 2021 - 4:10:02 PM

### Identifiers

• 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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