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In equations, Hawking showed that if one denotes the creation and annihilation operators at a frequency for a quantum field propagating in the black-hole background by and † then the expectation value of the product of these operators in the state formed by the collapse of a black hole would satisfy † = / where k is the Boltzmann constant ...
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.
By dimensional analysis, the life span of a black hole can be shown to scale as the cube of its initial mass, [15] [16]: 176–177 and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 10 12 kg would have evaporated completely by the present day. [17]
Stephen Hawking never stopped trying to unravel the mysteries surrounding black holes -- in fact, he was still working to solve one of them shortly before his death. Now, his last research paper ...
Stephen Hawking may have come up with an answer to a long-running debate among scientists—the fate of information that enters a black hole. The challenge has been to reconcile the paradox ...
Before Stephen Hawking came up with the concept of Hawking radiation, the question of black holes having entropy had been avoided. However, this concept demonstrates that black holes radiate energy, which conserves entropy and solves the incompatibility problems with the second law of thermodynamics. Entropy, however, implies heat and therefore ...
In physics, black hole thermodynamics [1] is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons.As the study of the statistical mechanics of black-body radiation led to the development of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the ...
In 1974, Stephen Hawking predicted that black holes might not be the bottomless pits we imagine them to be. According to Hawking's calculations, some information might escape black holes in the ...