Black holes with a cosmological constant in bumblebee gravity

TL;DR

This paper introduces new black hole solutions in bumblebee gravity with a cosmological constant, linking Lorentz symmetry violation to observable black hole shadow sizes.

Contribution

It presents the first black hole solutions in bumblebee gravity with a cosmological constant and relates the bumblebee field to black hole shadow measurements.

Findings

Derived spherically symmetric black hole solutions with effective cosmological constant.

Calculated the shadow angular radius for these black holes.

Established a novel connection between bumblebee field and black hole shadow size.

Abstract

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.