Sunday, November 5, 2023

A globally stationary point which is not locally stationary

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Suppose that we have a wall-to-wall carpet in a room, but the carpet is slightly too large and there is an annoying wrinkle in it.          ...
Saturday, November 4, 2023

Magically adding more charge to the Coulomb field

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Let us study the following problem. We have a magic device which can create an electric charge from nothing. We have a spherically symmetric...
Thursday, November 2, 2023

Einstein-Hilbert action: a flat metric is not a stationary point?

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UPDATE November 3, 2023: If we add an infinitesimal mass dM into empty Minkowski space, the change of the metric g is infinitesimal at any o...
Tuesday, October 31, 2023

"Conservation of pressure" in general relativity?

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Our previous blog post brought up a possibility that general relativity actually has a "conservation of pressure" principle. Any v...
Saturday, October 28, 2023

Changing pressure in a spherical mass breaks Birkhoff's theorem?

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We today completed the blog entry dated to October 19, 2023. The crucial observation was that the "focusing" property of mass-ener...
Tuesday, October 24, 2023

Tolman's paradox: the gravity of pressure

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We corrected the calculations of September 9 and October 11, 2023. Now it looks like that gravity satisfies Gauss's law, at least in cer...
Thursday, October 19, 2023

What a failure of Birkhoff's theorem means?

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Let us assume that we really can affect the gravity attraction of a spherical mass M by manipulating the pressure within it. Let us analyze ...