Black Hole Horizon in a Causal Web ⚡ экспресс
Since in general relativity the causal structure is dynamic and can split spacetime into regions with horizons, and in causal set theory the basic element is the causal relations between discrete events, the task of horizon identification in this framework is relevant. In this work, first a local diagnostic criterion is constructed to approximate the global event horizon based on discrete timelike curves. Then the apparent horizon is considered, defined by local properties of geodesics; 'ladders' are used as indicators of null geodesics to detect it. It is shown that the discrete analogue of expansion changes sign when crossing the black hole horizon. The concept of 'blurred ladder' is introduced, allowing null geodesics to be tracked over large intervals of affine parameter, and on this basis, part of the discrete horizon is constructed in a 1+1-dimensional toy model of black hole spacetime.
In causal set theory, spacetime is not a smooth sheet but a web of tiny points connected by arrows of cause and effect. A point is linked to another only if the first can influence the latter. In such a web, a black hole is described differently: its horizon—the boundary from which signals cannot return—must be redefined.
To find the horizon, researchers weave chains of causally related points through the web—they resemble light rays, only spun from causality. Near the horizon, something unexpected happens: an indicator that measures the divergence of these chains switches sign. It’s as if a thread in the web suddenly changes its tension, exposing an invisible edge.
For large horizons, the method was improved with “blurred” chains that span multiple paths at once. Thus, for the first time in this discrete world of causes, a sign of the horizon has been detected—a step continuing the path of Stephen Hawking.
🎯 In the causal web, the horizon isn’t set in advance—it only reveals itself in the shifting behavior of the chains, like an invisible crack in the web’s pattern.
🎬 In Interstellar, the tesseract built from threads of causality—perhaps that’s exactly how spacetime appears if you peer inside the web.