The Science Fiction World of Xueba

"Next, I will take Einstein's gravitational field equation as an example to show you how to analyze the gravitational field equation through Ponzi geometry, so as to find the analytical solution of the gravitational field equation..."

As he spoke, Pang Xuelin picked up a marker pen and wrote down the formula of Einstein's gravitational field equation on the whiteboard.

Ruv-1/2guvR=8πG/c^4×Tuv

There was a buzzing sound in the venue.

Einstein's gravitational field equation?

No one expected that Pang Xuelin would use this equation as an example.

This equation looks very simple, but after expanding it, you will get 10 simultaneous second-order nonlinear partial differential equations.

Trying to find an exact solution to this equation through this equation is complex enough to make anyone turn pale.

In the audience, Tan Hao immediately understood Pang Xuelin's thoughts.

"Professor Pang wants to prove the superiority of Ponzi's geometric theory in solving nonlinear partial differential equations by climbing a mountain!"

There was a hint of shock in Tan Hao's eyes.

Tan Hao has read Pang Xuelin's paper on solving nonlinear partial differential equations through Ponzi geometry, but that paper is a purely theoretical article, fundamentally telling everyone why Ponzi geometry can solve the analysis of nonlinear partial differential equations untie.

That kind of paper seems to be very difficult for ordinary professional mathematicians, let alone scholars in other fields.

Therefore, it will undoubtedly be more convincing if you can directly solve a classic and extremely difficult nonlinear partial differential equation through the method of Ponzi geometry at the report meeting.

But the question is, can Einstein's gravitational field equation really find an analytical solution?

At present, scientists have only found the exact solution of the gravitational field equation under certain conditions, and only part of the solution has physical significance.

These include the Schwarzschild solution, the Ressler-Nostrum solution, the Kerr solution, the Taub-NUT solution, each corresponding to a particular type of black hole model; there is also the Friedmann-Lemay T-Robertson-Wolcker solution, Gödel universe, de Sitter universe, anti-de Sitter space, etc., each solution corresponds to an expanding universe model.

If Pang Xuelin can really find out the analytical solution of Einstein's gravitational field equation,

Doesn't that mean that most of the exact solutions to this equation can be found analytically?

Although not every exact solution of Einstein's gravitational field equation has actual physical significance, there is no doubt that once Pang Xuelin successfully finds the analytical solution of the gravitational field equation, it will be of great significance to the entire physics community.

All of a sudden, the entire hall of the auditorium became noisy, and everyone talked about it.

"Professor Pang didn't choose a good choice. Why did he choose Einstein's gravitational field equation? It is extremely difficult to solve this equation, let alone find its analytical solution."

"Yeah, it's too risky to do this. Once the derivation process gets stuck, it will be troublesome then!"

"I can only say that Professor Pang is too courageous, but if he is really asked to find the analytical solution of Einstein's field equations, the entire physics community will probably be boiling."

...

Pang Xuelin didn't care about all this. He coughed dryly and continued: "As we all know, the basic idea of ​​general relativity is that the structure of space-time depends on the motion and distribution of matter. The gravitational field equation proposed by Einstein embodies the moving matter and its The distribution determines the surrounding space-time properties. For any coordinate transformation, the form of the field equation remains unchanged. In the case of a weak field, it corresponds to the Poisson equation of Newton's gravity. Therefore, Einstein's gravitational field equation actually contains all of the general theory of relativity content, below, we begin to formally analyze the equation..."

Holding a marker pen, Pang Xuelin analyzed and solved Einstein's gravitational field equation on the whiteboard while talking.

...

[Assuming that the gravitational field is uniform on the space-time scale, Guv is a tensor that only depends on the metric and the first-order and second-order derivatives, and has symmetric conservation. In the weak field, the energy-momentum tensor Tuv is proportional to the expression of Guv. Guv=-8πGTuv

Available: ①Guv=Ruv-1/2guvR

②Ruv-1/2guvR+λguv=-8πGTuv

The constant λ is zero, so that the form of Einstein’s gravitational field equation can be obtained, and the Einstein’s action equation can be strictly derived from the principle of least action that fundamentally reflects the essence of physical laws]

...

[Assume that the gravitational field and the action of matter are Sg and Sm respectively, and Sg=∫R√-gdΩ must satisfy δSg=0, and Ω is the entire four-dimensional space-time region. Then there is ?∫R√-gdΩ=δ∫Ruvguv√-gdΩ……]

...

Pang Xuelin's nib was brushing on the whiteboard, and the noise in the auditorium gradually calmed down.

All focus on the whiteboard.

Time passed by, and the whiteboard was gradually filled with various formulas.

Ponzi geometry began to show its powerful analytical ability.

[We can find that in this equation, all quantities have Rik=0 for time derivatives, by (X^0, X^1, X^2, X^3)=(ct, R, θ, Φ), α , β, γ are functions about r, e^γ=1, e^α=1, e^β=r^2, then there are...]

...

"I see!"

Under the stage, Mochizuki slapped his thighs one by one, with joy in his eyes.

In the past few days, he has been studying the paper on solving nonlinear partial differential equations with Ponzi geometry, but that paper is too theoretical and conceptual. When reading it, Mochizuki always feels a little foggy.

It was not until today that Pang Xuelin explained in combination with actual cases that he really understood the core idea of ​​Ponzi geometry for solving nonlinear partial differential equations.

In contrast, Perelman, who has been immersed in N-S equations for more than ten years, obviously understood Pang Xuelin's thinking long ago. He said with a faint smile: "The inclusiveness of Ponzi geometry is really too strong. It passes The method of deconstructing algebraic varieties, re-architecting nonlinear partial differential equations, ignoring its nonlinear factors at different stages, and only seeking solutions under its linear conditions. This trip to Jiangcheng was not in vain. Professor Pang really did not make me feel disappointment."

On the other side, Schultz picked up the water glass on the table, sipped lightly and said:

"This guy, I really don't know how his brain grows? When I read his paper two days ago, I still felt a little confused. I didn't expect to combine it with the actual case analysis, and I found out that it's not bad. This is how to solve nonlinear partial differential equations!"

Stix nodded, and said with emotion: "That's true, and I don't know whether it is our misfortune or our luck to live in the same age as such a genius! But I think our students may be miserable in the future, Pang Geometry is likely to become a compulsory course for most science and engineering students at the graduate level..."

Schultz was taken aback for a moment, and almost spit out the water from his mouth.

...

In addition to Mochizuki Shinichi, Perelman, Schultz, Stix and others, at the press conference, more and more mathematicians gradually understood Pang Xuelin's solution ideas.

"My God, it's still possible to do this!"

"Ponzi geometry, Ponzi geometry again!"

"I seem to see the figure of Pope Grothendieck in Algebraic Geometry!"

"Unexpectedly, this guy really solved the problem of solving nonlinear partial differential equations."

"Based on the current situation, most nonlinear partial differential equation problems should be solved by Ponzi geometry... There are quite a few classic nonlinear partial differential equations in academia..."

The last sentence made the surrounding people quiet.

The eyes of many mathematicians lit up immediately.

Pang Xuelin has opened up a great treasure for everyone.

As long as you understand the core idea of ​​Ponzi geometry as soon as possible, isn't it true that any problem of nonlinear partial differential equations can be used for water papers?

And the posture of this kind of water paper is not low at all.

Because every time an analytical solution of a classical nonlinear partial differential equation is found, it may have a significant impact on the scientific and engineering circles!