# Recent content by darida

1. ### A First Variation of Jacobi Operator

<Moderator's note: Moved from a homework forum.> Homework Statement From this paper. Let ##L## be the Jacobian operator of a two-sided compact surface embedded in a three-maniold ##(M,g)##, ##\Sigma \subset M##, and defined by L(t)=\Delta_{\Sigma(t)}+ \text{Ric}( ν_{t} , ν_{t}...
2. ### Derivative of Mean Curvature and Scalar field

Further information (file attached, Appendix A, page 99): ∂_{t} = φ\vec{ν} So the derivation of φ with respect to t would be: \frac{dφ}{dt} = \frac{d}{dt} \left (\frac{1}{ν} \frac{∂}{∂t} \right ) \frac{dφ}{dt} = \frac{1}{ν} \frac{∂}{∂t} \left ( \frac{∂}{∂t} \right ) + \frac{∂}{∂t} \frac{d}{dt}...
3. ### Derivative of Mean Curvature and Scalar field

Homework Statement Page 16 (attached file) \frac{dH}{dt}|_{t=0} = Δ_{Σ}φ + Ric (ν,ν)φ+|A|^{2}φ \frac{d}{dt}(dσ_{t})|_{t=0} = - φHdσ H = mean curvature of surface Σ A = the second fundamental of Σ ν = the unit normal vector field along Σ φ = the scalar field on three manifold M φ∈C^{∞}(Σ)...
4. ### Components of The Electromagnetic Field Strength Tensor

Never mind, just found the answer
5. ### Components of The Electromagnetic Field Strength Tensor

Ok now I get confused. So, I am trying to find the radial component of the magnetic field from the Hodge-dual of the Field Tensor, but then end up like this *F_{\mu\nu}=\frac{1}{2} \epsilon_{\mu\nu\lambda\rho}F^{\lambda\rho}= \begin{bmatrix} 0 B_x B_y B_z \\ -B_x 0 -E_z...

Thank you!
7. ### Components of The Electromagnetic Field Strength Tensor

Source: http://gmammado.mysite.syr.edu/notes/RN_Metric.pdf Section 2 Page: 2 Eq. (15) The radial component of the magnetic field is given by B_r = g_{11} ε^{01μν} F_{μν} Where does this equation come from? Section 4 Page 3 Similar to the electric charges, the Gauss's flux theorem for the...
8. ### Electromagnetics in Spherical Symmetric Problem

In a spherical symmetric problem the only nonzero components of the electric and the magnetic field are Er and Br Why?
9. ### Reissner Nordstrom Metric

Ah thank you, that's so simple >_<
10. ### Reissner Nordstrom Metric

I want to derive Reissner Nordstrom solution using this paper as a guide: http://gmammado.mysite.syr.edu/notes/RN_Metric.pdf, but I get confused by the Eq. (8). Why the Enstein's equation can be rewritten in that form and what is the physical meaning of the Eq. (8)?
11. ### Integration of Ricci Scalar Over Surface

Does this integration of Ricci scalar over surface apply in general or just for compact surfaces? ∫RdS = χ(g) where χ(g) is Euler characteristic. And could anybody give me some good references to prove the formula?
12. ### Stability of Hawking Mass

For example: Source: page 8
13. ### Stability of Hawking Mass

Thank you so much for the references. I want to know what we talk about when we talk about stability of Hawking energy? How can we know the Hawking energy is stable?
14. ### Stability of Hawking Mass

So, what should I do now?
15. ### Stability of Hawking Mass

What is stability of Hawking Mass and how to calculate it? Any references will be appreciated. Thanks