No abstract

For asymptotically flat spacetimes, using the inverse mean curvature flow, we show that any compact 2-surface, S0, whose mean curvature and its derivative for outward direction are positive in spacelike hypersurface with non-negative Ricci scalar satisfies the inequality A0 ≤ 4π(3Gm) 2 , where A0 is the area of S0 and m is the total mass. The upper bound is realized when S0 is the photon sphere in a hypersurface isometric to t =const. slice of the Schwarzschild spacetime.

We present a new definition of the wormhole throat including the flare-out condition and the traversability for general dynamical spacetimes in terms of null geodesic congruences. We will examine our definition for some examples and see advantages compared to the others.

We discuss the uniqueness of the static spacetimes with non-trivial conformal scalar field. Then, we can show that the spacetime is unique to be the Bocharova-Bronnikov-Melnikov-Bekenstein solution outside the surface composed of the unstable circular orbit of photon(photon surface). In addition, we see that multi-photon surfaces having the same scalar field values do not exist.