Equation of Motion for Gravitational Field with D'Alembertian Operator

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In summary, the conversation focused on finding the equation of motion in a gravitational field using the potential V and the D'alembertian D. The equation is V DV = 4 pi T, where T is the trace of the stress energy tensor. The individual asking for help is a college student and is not familiar with certain terms, so they requested for detailed explanations. However, the responder stated that this topic is beyond the scope of the forum and advised the individual to seek help from their professor or a mathematician specializing in general relativity.
  • #1
Jitu18
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Hi. I am new in here. So i am not fully sure whether i should post it here. But please help me if u can.
Let V be the potential of gravitational field and i will write d'alembertian as D the equation is:
V DV = 4 pi T
here T is the trace of the stress energy tensor. Now how can i find the equation of motion in these field. I have used the lagrangian equation but to no avail. And i should also mention to u that i am not even a university student. I am a college student. So please try to elaborate it if u can. And please also give a detail about the term u may use. Because i may not know them.
 
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  • #2
I'm sorry, but this is beyond the scope of this forum. You should ask your professor or a mathematician who specializes in general relativity for help on this question.
 

What is a d'Alembertian operator?

The d'Alembertian operator, denoted as ∇² or □, is a mathematical operator in the field of differential equations. It is defined as the sum of the second-order partial derivatives of a function with respect to its spatial coordinates.

What is the significance of the d'Alembertian operator in physics?

In physics, the d'Alembertian operator is used to describe the wave equation, which is a fundamental equation in the study of waves and oscillations. It is also used in the theory of relativity, where it represents the wave equation for massless particles.

How is the d'Alembertian operator used in solving differential equations?

The d'Alembertian operator is used to simplify and solve partial differential equations, particularly in the case of wave equations. It allows for the separation of variables and reduces the problem to a set of ordinary differential equations, which are easier to solve.

What are the properties of the d'Alembertian operator?

The d'Alembertian operator is a linear operator, meaning that it follows the rules of linearity. It is also a self-adjoint operator, which means that its adjoint is the same as itself. Additionally, it is a second-order operator, as it involves second-order derivatives.

What are some applications of the d'Alembertian operator?

The d'Alembertian operator has various applications in physics, engineering, and mathematics. It is used in the study of waves, such as acoustic, electromagnetic, and gravitational waves. It is also used in fields like fluid dynamics, elasticity, and quantum mechanics.

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