Black hole shadow and Maximal Black room

Abstract: To comprehend the shadow of a black hole in a general spacetime, we have investigated the concept of the maximal black room (MBR). The boundary of the MBR is a non-spacelike hypersurface that contains at least one null geodesic tangent to its boundary, which we refer to as the rays' surface. Our aim is to explore the geometry of this surface. From our current study, we have observed that the boundary of the MBR is globally unstable. Leveraging this instability, we can determine the boundary based on the physical choice of the initial spacelike hypersurface and the orthogonal condition at that point. Upon examining the existence of the MBR, we can observe that it encompasses any arbitrary black hole. Additionally, we can investigate the possibility of using the MBR to differentiate a black hole from an exotic star with a photon sphere. In spherically symmetric spacetime, subject to energy conditions, the rays' surface encloses a black hole, a naked singularity, or exotic matter that has an inner universe.