42k views

### How to calculate scalar curvature, Ricci tensor and Christoffel symbols in Mathematica?

I am seeking a convenient and effective way to calculate such geometric quantities. I've used packages like TensoriaCalc, but they don't work at all time. Sometimes,...
446 views

### Optimization of ODE with respect to the initial condition

One has a (system) of ODEs with a one-parameter family of initial conditions. For example, ...
405 views

### A fraught with incorrect results ODE

I mean the following ODE $$y''(x)+y'(x)=\exp (-2 x) y(x)^3.$$ Trying to solve it in version 13.1 on Windows 10 by ...
515 views

### Solving elliptic integrals in Mathematica

I have an integral $$\int_{a2}^{a1}\frac{dx}{\sqrt{(a1 -x)(a2 - x)(a3 - x)}}$$ And I'm trying to integrate it with ...
304 views

### Transforming implicit solutions of an ODE involving InverseFunction to an explicit form

When I DSolve a nonlinear differential equation: ...
1 vote
1k views

### How do I get the Schwarzschild solution from the Einstein Equations?

Consider the Schwartzchild-like metric $$ds^2=-A(r)dt^2+B(r)dr^2+r^2(d\theta^2+\sin^2\theta d\phi^2).$$ The Einstein field equations for this metric reduce to $$R_{\mu\nu}=0,$$ which is also known as ...
1 vote
304 views

### Integrating and plotting solutions of a nonlinear dynamical system

So I have an ODE $k^2\; u'(\theta)^2 = -\frac{1}{3}u^3 + \frac{\omega}{k}u^2-2B\;u+2A$ where $B,A$ are constants. I attempted to directly integrate in Mathematica with ...
1 vote
449 views

### Confluent Heun function

Does the confluent Heun function exist in Mathematica? I try to evaluate the following, ...
209 views

### First order Differential equation with boundary condition

I'm wondering why it is not solving with the Mathematica?? ...
173 views

### Get the trajectory of an object in a gravitational field

Given the initial position and velocity, I want get the trajectory of an object in a gravitational field. Instead of using Kepler's Laws, I want to solve the following differential equations: ...
1 vote
249 views

### Solving Geodesics from Christoffel Symbols

I am somewhat new to using Mathematica and I am facing difficulties with a specific problem related to the geodesics of Einstein's field equation in a vacuum. The metric I am working with is derived ... 