"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 to find the analytical solution of the gravitational field equation......"

As he spoke, Pang Xuelin picked up a marker pen and wrote 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 take this equation as an example.

This equation looks simple, but when it is expanded, there are 10 simultaneous second-order nonlinear partial differential equations.

If you want to solve the exact solution of this equation with this equation, it is complex enough that anyone can change color.

Offstage, Tan Hao immediately understood Pang Xuelin's thoughts.

"Professor Xiao Pang wants to climb a mountain to prove the superiority of Ponzi geometry theory in solving nonlinear partial differential equations!"

Tan Hao's eyes showed a hint of shock.

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, which fundamentally tells you why Ponzi geometry can find analytical solutions to nonlinear partial differential equations.

This kind of thesis seems to be very difficult for mathematicians in general, let alone scholars in other fields.

Therefore, it would undoubtedly be more convincing if a classical and extremely difficult nonlinear partial differential equation could be directly solved by the method of Ponzi geometry at the presentation site.

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 Schwarzschild solutions, Resler-Norstrem solutions, Kerr solutions, and Tob-NUT solutions, each of which corresponds to a specific type of black hole model. In addition, there are Friedman-Lemaître-Robertson-Volcker solutions, Gödel universes, Desit universes, anti-Desitt spaces, etc., each of which corresponds to an expanded model of the universe.

If Pang Xuelin can really find the analytical solution of Einstein's gravitational field equation, doesn't that mean that most of the exact solutions of the equation can be solved analytically?

Although not every exact solution of Einstein's gravitational field equation has practical 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.

For a while, the entire auditorium hall was noisy, and everyone was talking.

"Professor Pang chose what is not good, why choose Einstein's gravitational field equation, this equation is extremely difficult to solve, let alone find its analytical solution."

"Yes, it's too risky to do this, and once the derivation process gets stuck, it's going to be troublesome!"

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

……

Pang Xuelin didn't care about all this, he coughed dryly, and continued: "As we all know, the basic view of general relativity is that the structure of space-time depends on the movement and distribution of matter. Einstein's gravitational field equation deduces that the moving matter and its distribution determine the surrounding space-time properties, and the form of the field equation does not change for arbitrary coordinate transformations. And in the case of weak field, it corresponds to the Poisson equation of Newton's gravitational force. Thus, Einstein's gravitational field equation actually encompasses the entirety of general relativity, and we begin to formally analyze the equation below......"

Pang Xuelin held a marker pen and said while analytically solving Einstein's gravitational field equation on the whiteboard.

……

[Assuming that the gravitational field is uniform on the spatiotemporal scale, Guv is a tensor that depends only on the gauge and the first and second derivatives, with symmetrical conservation, and in the weak field, the energy-momentum tensor Tuv is proportional to the Guv expression.] Guv=-8πGTuv

It can be obtained: (1) Guv = 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 derived, and the Einsteinian action equation can be strictly derived from the principle of minimum action, which fundamentally reflects the essence of physical laws.

……

[Let the gravitational field and the amount of matter be Sg and Sm, respectively, Sg=∫R√-gdΩ, and δSg=0, which must be satisfied, and Ω the entire four-dimensional space-time region.] Then there is?? ∫R√-gdΩ=δ∫Ruvguv√-gdΩ……】

……

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

All eyes are focused on the whiteboard.

As the minutes passed, the whiteboard was gradually filled with formulas.

Ponzi geometry is beginning to show its analytical power.

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

……

"I see!"

Offstage, Shinichi Mochizuki slapped his thighs one by one, and his eyes showed joy.

In the past few days, he has been studying the paper on Ponzi geometry to solve nonlinear partial differential equations, but that paper is too theoretical and conceptual, and when he reads it, Shinichi Mochizuki always feels a little foggy.

It was not until today that Pang Xuelin explained it in combination with practical cases that he truly understood the core idea of Ponzi geometry to solve nonlinear partial differential equations.

In contrast, Perelman, who has been immersed in the N-S equation problem for more than ten years, obviously understood Pang Xuelin's train of thought for a long time, and he smiled lightly: "Ponzi geometry is too inclusive, it reconstructs the system of nonlinear partial differential equations by deconstructing algebraic clusters, ignoring its nonlinear factors at different stages, and only seeking solutions under linear conditions." This trip to Jiangcheng was not in vain. Professor Pang did not disappoint me. ”

On the other side, Schultz picked up the water glass on the table, took a sip 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 foggy, but I didn't expect to combine the analysis of actual cases to find that I can analyze nonlinear partial differential equations in this way! ”

Stix nodded, and said with some emotion: "It's true, and I don't know if it's our misfortune or our luck to live in the same era as such a genius!" However, I think that in the future, our students may be miserable, and Ponzi geometry is likely to become a compulsory course for most science and engineering students at the graduate level......"

Schultz was stunned and almost didn't squirt out of his mouth.

……

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

"Oh my God, that's still going to be like this!"

"Ponzi geometry, Ponzi geometry again!"

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

"I really didn't expect that this guy really solved the problem of solving nonlinear partial differential equations."

"As it stands, most of the problems of nonlinear partial differential equations can be solved by Ponzi geometry...... At present, there are many classical nonlinear partial differential equations in the academic world......"

The last sentence made the surrounding circle of people quiet.

The eyes of many mathematicians lit up.

Pang Xuelin: This is a big treasure for everyone.

As long as the core idea of Ponzi geometry is understood as soon as possible, wouldn't it be possible to use any system of nonlinear partial differential equations for a water paper?

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

Because every time you find an analytical solution to a classical nonlinear partial differential equation, it has the potential to have a significant impact on the scientific and engineering communities!

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