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Einstein's derivation of the gravitational field equations was delayed because of the hole argument which he created in 1913. [1] However the problem was not as given in the section above. By 1912, the time Einstein started what he called his "struggle with the meaning of the coordinates", [ 2 ] he already knew to search for tensorial equations ...
The issue of whether covariance is a real restriction and if so in what sense appears in various contributions to the philosophical debate concerning Einstein's "hole argument." This argument initially had led Einstein in 1913 for a time to reject generally covariant theories, because a region of space/time without forces would undermine ...
As its name suggests, it was a sketch of a theory, less elegant and more difficult than general relativity, with the equations of motion supplemented by additional gauge fixing conditions. After more than two years of intensive work, Einstein realized that the hole argument was mistaken [247] and abandoned the theory in November 1915.
At the urging of Tullio Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument".
The astronomers' discovery proves Einstein's predictions right over a century later. Scientists have seen light from behind a black hole for the first time ever. The astronomers' discovery proves ...
[Einstein's] eventual derivation of the equations was a logical development of his earlier arguments—in which, despite all the mathematics, physical principles invariably predominated. His approach was thus quite different from Hilbert's, and Einstein's achievements can, therefore, surely be regarded as authentic.
Einstein also recognized another element of the definition of an exact solution: it should be a Lorentzian manifold (meeting additional criteria), i.e. a smooth manifold. But in working with general relativity, it turns out to be very useful to admit solutions which are not everywhere smooth; examples include many solutions created by matching ...
For the first time ever, scientists have seen the light from behind a