# If time were frozen, gravity would also freeze

## Big Bang 8, school book

52 RG 8.1 / G 8.1 Competence Area Theory of Relativity In the vicinity of masses, time passes more slowly (Chap. 43.4, p. 43). For an observer who is very far away (strictly speaking, infinitely far), the collapse would become slower and slower until finally the star at the Schwarzschild radius freezes, as it were. That is why black holes were called frozen stars until 1967. At the same time, the redshift would also get stronger. Although the star never collapses completely from the outside, its luminosity would still drop to zero. Info: "Frozen" time Fig. 43.43: Black holes are the most powerful gravitational lenses that exist. The Milky Way in a simulation with and without a black hole in the foreground “Frozen” time The equations in Chap. 43.3 to 43.5 are approximations that apply to R S / r << 1. To show the “freezing of time” at the Schwarzschild radius, we need a more precise equation. From the SRT it follows for the time dilation (Chap. 40.2, p. 17): t q = t √ ____ 1 - v 2 __ c 2 Assume that a laboratory with v 0 = 0 approaches a central mass from an infinitely great distance. On the surface it will arrive with: v = √ ____ 2 GM ____ r - this corresponds to the escape speed. If you insert this speed into the equation for the time dilation according to the equivalence principle, you get: tq = t √ ______ 1 - 2 GM ____ c 2 rtq is the time that passes in the distance r, t the time that passes in infinite Distance passes. This equation differs from that in Chap. 43.4, p. 44, with an additional term. If you now insert RS, you get: tq = t √ __________ 1 - 2 GM ____ c 2 c 2 ____ 2 GM = 0 Compared with a clock in infinity, it says black - shield radius the time still. i But how do you find something that you can't even see? So far, black holes can only be found indirectly. They could act as gravitational lenses, for example (Fig. 43.43) and one could deduce them from distortions. Furthermore, so-called accretion disks can form around black holes (Fig. 43.44), which emit characteristic, extremely high-energy radiation. The kinematic method is also very popular. In doing so, one examines the trajectories of visible objects and then deduces the mass of the invisible ones. One suspects a gigantic black hole with several billion solar masses in the center of the galaxy M87 (chap. 42.1, p. 31). Fig. 43.44: A black hole sucks in the gas of its double star partner and a rotating gas disk is formed. The acceleration of the gas creates a characteristic radiation. Fig. 43.45: As the density of an object increases, the curvature of space also increases (a + b). In the case of black holes, it becomes infinitely large (c). The curvature of the room can be imagined as a kind of dent (chap. 43.5, p. 45). The greater the density of the object, the deeper this dent becomes. In the case of a black hole, the curvature of space becomes infinitely great. This corresponds to a funnel with vertical walls (Fig. 43.45 c). The diameter of a circular path around a black hole would be infinitely large! The two lines in Fig. 43.45c would be infinitely long! Fascinating! Of course, one dimension has been left out in all of these representations. In reality, it is not two-dimensional, but three-dimensional space that curves. However, that is beyond our imagination. If you put two such funnels together, you get what you call a wormhole. As a shortcut, wormholes could connect two distant areas of the universe (43.46 a) or, what sounds even more eerie, even two. For testing purposes only - property of the publisher öbv

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