Zusammenfassung
In this work, we present black hole solutions with a cosmological
constant in bumblebee gravity, which provides a mechanism for the
Lorentz symmetry violation by assuming a nonzero vacuum expectation
value for the bumblebee field. From the gravitational point of view,
such solutions are spherically symmetric black holes with an effective
cosmological constant and are supported by an anisotropic
energy-momentum tensor, conceived of as the manifestation of the
bumblebee field in the spacetime geometry. Then we calculate the shadow
angular radius for the proposed black hole solution with a positive
effective cosmological constant. In particular, our results are the very
first relation between the bumblebee field and the shadow angular size.
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