On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources

J Biák (1, 2) , M Scholtz (1, 2) , P Tod (1, 3)

1 Faculty of Mathematics and Physics [Praha/Prague]
2 AEI - Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
3 MI - Mathematical Institute [Oxford]

We extend the work in our earlier article [ 4 ] to show that timeperiodic , asymptotically-flat solutions of the Einstein equations analytic at I, whose source is one of a range of scalar-field models, are necessarily stationary. We also show that, for some of these scalar-field sources, in stationary, asymptoticallyflat solutions analytic at I, the scalar field necessarily inherits the symmetry. To prove these results we investigate miscellaneous properties of massless and conformal scalar fields coupled to gravity, in particular Bondi mass and its loss.

Mots clés: Physical Sciences

J Biák, M Scholtz, P Tod. On asymptotically flat solutions of Einstein's equations periodic in time: II. Spacetimes with scalar-field sources. Classical and Quantum Gravity, 2010, 27 (17), pp.175011. ⟨10.1088/0264-9381/27/17/175011⟩. ⟨hal-00619940⟩