Figure 4 - uploaded by Yvo Petkov

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# Computer plot: comparison of radial components of plunge velocities experienced by different in-fallers who drop from rest (so with L = 0) at a great distance from Schwarzschild and extreme Kerr black holes.

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## Contexts in source publication

**Context 1**

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Figure 4 compares the magnitude of the square root of this expression with the magnitude of the velocity of the stone dropped from rest at a great distance in the Schwarzschild case (equation [32], page 3-22): [26. = 0 ...

**Context 2**

... Penrose devised a scheme for milking energy from a spinning black hole. This scheme is called the Penrose process (see references). The Penrose process depends on the prediction that in some orbits inside the ergosphere a particle can have negative total energy. Before we detail the Penrose process, we need to describe negative total energy. What can negative total energy possibly mean? Negative energy is nothing new. In Newtonian mechanics the potential energy of a particle at rest far from Sun is usually taken to be zero by convention. Then a particle at rest near Sun has zero kinetic energy and negative potential energy, yielding a total energy less than zero. But in Newtonian mechanics the zero point of potential energy is arbitrary, and all reasonable choices of this zero point lead to the same description of motion. In contrast, special relativity determines the rest energy of a free material particle in flat spacetime, setting its rest energy equal to its mass. So the arbitrary choice of a zero point for energy is lost, and a particle far from a center of gravitational attraction always has an energy that is positive. For Schwarzschild geometry the physical system differs from Newtonian. A particle at rest near the horizon of a nonspinning black hole has zero total energy (from equation [18] in Sample Problem 1, page 3-12). The meaning? That it takes an energy equal to its rest energy (= m ) to remove this particle to rest at a large distance from the black hole (where it has the energy m ). As a consequence, if the particle drops into the black hole from its stationary position next to the horizon, then the mass of the combined black-hole-particle system (measured by a far-away observer, Figure 4, page 3-11) does not change. For Kerr geometry the physical system differs from that in Schwarzschild geometry. A particle can have a negative energy near a spinning black hole. The meaning? An energy greater than its rest energy (greater than m ) is required to remove such a particle to rest at a great distance from the black hole. If the particle with negative energy is captured by the spinning black hole, the black hole’s mass and angular momentum decrease. (See Section 11.) This process can be repeated until the black hole has zero angular momentum. Then it becomes a “dead” Schwarzschild black hole, from which only Hawking radiation can extract energy (box page ...