Are signatures of anti-de-Sitter black hole at the Galactic Center?

Abstract

Using Schwarzschild -- de-Sitter (Kottler) metric we derive a simple analytical relation between a shadow size and $\Lambda$-term. Current observations of the smallest spot to evaluate shadow size at the Galactic Center do not reach an accuracy comparable with cosmological $\Lambda$-term $\sim 10^{-52}{\rm m}^{-2}$, however, if in reality we have dark energy instead of a constant $\Lambda$-term then dark energy may be a function depending on time and space and it could be approximated with a local constant $\Lambda$-term near the Galactic Center and it is important to introduce a procedure to evaluate the $\Lambda$-term. We suggest such a procedure based on a black hole shadow evaluation. Surprisingly, current observational estimates of shadows are in agreement with anti-de-Sitter spacetimes corresponding to a negative $\Lambda$-term which is about $-0.4\times 10^{-20}{\rm m}^{-2}$. A negative $\Lambda$-term has been predicted in the framework of a some class of multidimensional string models.