Einstein's solution in general form. Who will undertake the verification ?, Solution of the Einstein equation for a scalar field in general form.
I would like to make publicly available the solution of the Einstein equation in general form for a scalar field. I solved this equation around 1998 while working at the Sarov nuclear center. Serious help in mathematics was provided to me by my senior colleague M. V. Gorbatenko. There would be no solution without him.
The history of the issue is as follows. In 1997, I solved and published in collaboration with my boss (V. D. Selemir) the problem of the propagation of electromagnetic radiation in a rapidly growing gravitational field. Here is a link to download the article (Izvestiya VUZov, Physics series, 1997):
cloud.mail.ru/public/3r6D/VTZgjsjhr
This article shows that when passing through a region of space with a rapidly growing gravitational potential, the frequency of electromagnetic radiation changes - decreases, i.e. the wavelength grows, and under certain conditions the frequency can decrease to zero and even become negative. However, in these extreme conditions, the approximation used in the article does not work, so the turn of the arrow of time should not occur.
Reflecting on overcoming the limitations of the model used, I came to the conclusion that for this it is necessary to solve the Einstein equation for the propagation of an electromagnetic wave, taking into account its own gravitational potential (very small, but in that article I showed that the wave is not affected by the magnitude of the potential of the gravitational field, but only its rate of change affects).
So the task was set. I formulated it as follows: in empty space we select an imaginary plane through which an electromagnetic wave begins to pass at the zero moment of time. The observer of the wave is this imaginary plane. Since the speed of propagation of gravity is equal to the speed of light, the gravitational potential at the zero moment of time is equal to zero. And then, as the electromagnetic wave passes through the imaginary plane (i.e., through the observer), on this plane the gravitational potential begins to grow, moreover, with the maximum possible speed in nature.
However, it soon became clear that for a vector field (which is the electromagnetic field) the components of the Einstein equation do not decouple, which makes it impossible to solve it analytically, therefore (at the suggestion of a colleague Gorbatenko) Einstein's equation for a scalar field was formulated. As a result, the components were disengaged, which made it possible to solve the problem to the end. Here is a link to a scan of the manuscript:
cloud.mail.ru/public/2m1W/bEumkYx2G
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If there are specialists here who are able to check this solution, I will be glad if they do it and publish it in scientific journals. I myself have not worked in science for a long time (I had to feed my family in times of crisis) and have forgotten everything, so I ask the current specialists in general relativity to take this task into their own hands.
Best regards, Nizhegorodtsev Yu. B.