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  2. Schwarzschild metric - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_metric

    The Schwarzschild solution, taken to be valid for all r > 0, is called a Schwarzschild black hole. It is a perfectly valid solution of the Einstein field equations, although (like other black holes) it has rather bizarre properties. For r < r s the Schwarzschild radial coordinate r becomes timelike and the time coordinate t becomes spacelike. [22]

  3. Schwarzschild radius - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_radius

    The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.

  4. Eddington–Finkelstein coordinates - Wikipedia

    en.wikipedia.org/wiki/Eddington–Finkelstein...

    The regions for finite v and r < 2GM is a different region from finite u and r < 2GM. The horizon r = 2GM and finite v (the black hole horizon) is different from that with r = 2GM and finite u (the white hole horizon) . The metric in Kruskal–Szekeres coordinates covers all of the extended Schwarzschild spacetime in a single coordinate system ...

  5. Gravitational singularity - Wikipedia

    en.wikipedia.org/wiki/Gravitational_singularity

    General relativity predicts that any object collapsing beyond a certain point (for stars this is the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed. [2] The Penrose–Hawking singularity theorems define a singularity to have geodesics that cannot be extended in a smooth ...

  6. Black hole electron - Wikipedia

    en.wikipedia.org/wiki/Black_hole_electron

    The Schwarzschild radius r s of a mass m is the radius of the event horizon for a non-rotating uncharged black hole of that mass. It is given by r s = 2 G m c 2 , {\displaystyle r_{\text{s}}={\frac {2Gm}{c^{2}}},} where G is the Newtonian constant of gravitation , and c is the speed of light .

  7. Schwarzschild coordinates - Wikipedia

    en.wikipedia.org/wiki/Schwarzschild_coordinates

    The extension of the exterior region of the Schwarzschild vacuum solution inside the event horizon of a spherically symmetric black hole is not static inside the horizon, and the family of (spacelike) nested spheres cannot be extended inside the horizon, so the Schwarzschild chart for this solution necessarily breaks down at the horizon.

  8. Event horizon - Wikipedia

    en.wikipedia.org/wiki/Event_horizon

    In 1958, David Finkelstein used general relativity to introduce a stricter definition of a local black hole event horizon as a boundary beyond which events of any kind cannot affect an outside observer, leading to information and firewall paradoxes, encouraging the re-examination of the concept of local event horizons and the notion of black ...

  9. Kruskal–Szekeres coordinates - Wikipedia

    en.wikipedia.org/wiki/Kruskal–Szekeres_coordinates

    The black hole event horizon bordering exterior region I would coincide with a Schwarzschild t-coordinate of + while the white hole event horizon bordering this region would coincide with a Schwarzschild t-coordinate of , reflecting the fact that in Schwarzschild coordinates an infalling particle takes an infinite coordinate time to reach the ...