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- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Astronomy_1e_(OpenStax)/24%3A_Black_Holes_and_Curved_Spacetime/24.05%3A_Black_HolesTheory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding...Theory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding a black hole, where the escape velocity equals the speed of light, is called the event horizon, and the radius of the surface is called the Schwarzschild radius. Nothing, not even light, can escape through the event horizon from the black hole. At its center, each black hole is thought to have a si
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/06%3A_Vacuum_Solutions/6.01%3A_Event_HorizonsOne seemingly trivial way to generate solutions to the field equations in vacuum is simply to start with a flat Lorentzian spacetime and do a change of coordinates. This might seem pointless, since it...One seemingly trivial way to generate solutions to the field equations in vacuum is simply to start with a flat Lorentzian spacetime and do a change of coordinates. This might seem pointless, since it would simply give a new description (and probably a less convenient and descriptive one) of the same old, boring, flat spacetime. It turns out, however, that some very interesting things can happen when we do this.
- https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/02%3A_Schwarzschild_Geometry/2.05%3A_Spacetime_DiagramsIn Special Relativity, we constructed light cones using lines at 45 degree angles.
- https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/34%3A_Frontiers_of_Physics/34.02%3A_General_Relativity_and_Quantum_GravityWe know from "Special Relativity" that relativity is the study of how different observers measure the same event, particularly if they move relative to one another. Einstein’s theory of general relati...We know from "Special Relativity" that relativity is the study of how different observers measure the same event, particularly if they move relative to one another. Einstein’s theory of general relativity describes all types of relative motion including accelerated motion and the effects of gravity. General relativity encompasses special relativity and classical relativity in situations where acceleration is zero and relative velocity is small compared with the speed of light.
- https://phys.libretexts.org/Bookshelves/Modern_Physics/Spiral_Modern_Physics_(D'Alessandris)/3%3A_Spacetime_and_General_Relativity/3.2%3A_Schwarzchild_MetricIn General Relativity, the flatspace Minkowski metric cannot be used to describe spacetime. In fact, the metric depends (in a very complicated way) on the exact distribution of mass and energy in its ...In General Relativity, the flatspace Minkowski metric cannot be used to describe spacetime. In fact, the metric depends (in a very complicated way) on the exact distribution of mass and energy in its vicinity. This metric is referred to as the Schwarzchild metric, and describes the shape of space near a spherical mass such as (approximately) the earth or the sun, as well as the space surrounding a black hole.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Astronomy_2e_(OpenStax)/24%3A_Black_Holes_and_Curved_Spacetime/24.06%3A_Black_HolesTheory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding...Theory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding a black hole, where the escape velocity equals the speed of light, is called the event horizon, and the radius of the surface is called the Schwarzschild radius. Nothing, not even light, can escape through the event horizon from the black hole. At its center, each black hole is thought to have a si
- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/13%3A_Application_-_Orbits_and_Kepler's_Laws/13.03%3A_Weight_Acceleration_and_the_Equivalence_PrincipleHowever, if the equivalence principle is true, and physical phenomena look the same in a constantly accelerating frame as in an inertial frame with a constant gravitational field, it follows that ligh...However, if the equivalence principle is true, and physical phenomena look the same in a constantly accelerating frame as in an inertial frame with a constant gravitational field, it follows that light must also bend its path in the latter system, in much the same way as a projectile would. (I say “much the same way” because the effect is not just as simple as giving light an “effective mass”; there are other relativistic effects, such as space contraction and time dilation, that must also be r…
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/06%3A_Vacuum_Solutions/6.04%3A_Black_Holes_(Part_1)A provocative feature of the Schwarzschild metric is that it has elements that blow up at r=0 and at r=2m. If this is a description of the sun, for example, then these singularities are of no physic...A provocative feature of the Schwarzschild metric is that it has elements that blow up at r=0 and at r=2m. If this is a description of the sun, for example, then these singularities are of no physical significance, since we only solved the Einstein field equation for the vacuum region outside the sun, whereas r=2m would lie about 3 km from the sun’s center. Furthermore, it is possible that one or both of these singularities is nothing more than a spot where our coordinate system misbehaves.
- https://phys.libretexts.org/Courses/Grossmont_College/ASTR_110%3A_Astronomy_(Fitzgerald)/12%3A_The_Death_of_Stars/12.11%3A_Black_HolesTheory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding...Theory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding a black hole, where the escape velocity equals the speed of light, is called the event horizon, and the radius of the surface is called the Schwarzschild radius. Nothing, not even light, can escape through the event horizon from the black hole.
- https://phys.libretexts.org/Courses/Skidmore_College/Introduction_to_General_Relativity/05%3A_Spinning_Black_Holes/5.03%3A_The_ErgoregionFor a Schwarzschild black hole, the infinite redshift surface, the static limit surface, and the event horizon happen to have the same r-value, but that isn't necessarily the case for other black hole...For a Schwarzschild black hole, the infinite redshift surface, the static limit surface, and the event horizon happen to have the same r-value, but that isn't necessarily the case for other black holes. For a spinning black hole, the infinite redshift surface and the static limit surface are still the same, but they are different from the event horizon. The region in between the infinite redshift surface and the event horizon is called the ergoregion.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_I_-_Classical_Mechanics_(Gea-Banacloche)/10%3A_Gravity/10.02%3A_Weight_Acceleration_and_the_Equivalence_PrincipleHowever, if the equivalence principle is true, and physical phenomena look the same in a constantly accelerating frame as in an inertial frame with a constant gravitational field, it follows that ligh...However, if the equivalence principle is true, and physical phenomena look the same in a constantly accelerating frame as in an inertial frame with a constant gravitational field, it follows that light must also bend its path in the latter system, in much the same way as a projectile would. (I say “much the same way” because the effect is not just as simple as giving light an “effective mass”; there are other relativistic effects, such as space contraction and time dilation, that must also be r…
