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angle Big Bang black hole boost causal properties collapse consider const crosses the horizon curved space curved space-times density of matter describe determine effects event horizon event Q expanding universe F and F flat space flat space-time flat-space FLRW model FLRW universe fundamental observers Geneva CERN geodesics geometry gravitational field initial singularity interval isotropic Large Hadron Collider lectures Let us look light cones Lorentz transformation massive body massive object measured metric ds2 metric form Minkowski universe model universe number of galaxies observer Oi particle horizon past light-cone proper-time Q and Q radiation radius real universe received by O2 refocusing relative motion Rindler universe rocket rotation Schwarzschild solution shown in Fig signals sin2 small universe space-sections space-time diagrams spatial sections spatially homogeneous special relativity speed sphere spherically symmetric star static observers stationary observer steady-state universe straight lines surfaces of simultaneity tends to zero time-like two-sphere universe model world lines