Publikace ÚTF

All solutions of Einstein’s equations in 2+1 dimensions: Λ-vacuum, pure radiation, or gyratons

Podolský, J., Švarc, R. and Maeda, H.

Under a weak assumption of the existence of a geodesic null congruence,
we present the general solution of the Einstein feld equations in three
dimensions with any value of the cosmological constant, admitting an aligned
null matter feld, and also gyratons (a matter feld in the form of a null dust
with an additional internal spin). The general local solution consists of the
expanding Robinson–Trautman class and the non-expanding Kundt class.
The gyratonic solutions reduce to spacetimes with a pure radiation matter
feld when the spin is set to zero. Without matter felds, we obtain new forms
of the maximally symmetric vacuum solutions. We discuss these complete
classes of solutions and their various subclasses. In particular, we identify the
gravitational feld of an arbitrarily accelerating source (the Kinnersley photon
rocket, which reduces to a Vaidya-type non-moving object) in the Robinson–
Trautman class, and pp-waves, vanishing scalar invariants (VSI) spacetimes,
and constant scalar invariants (CSI) spacetimes in the Kundt class.
typ:article
journal:Class. Quantum Grav.
volume:36
pages:015009
year:2019

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