# Search results

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

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)...
3. ### 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...
4. ### 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?
5. ### 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)?
6. ### 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?
7. ### Stability of Hawking Mass

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

Ansatz metric of the 4 dimensional spacetime: ds^2=a^2 g_{ij}dx^i dx^j + du^2 (1) where: Signature: - + + + Metric g_{ij} \equiv g_{ij} (x^i) describes 3 dimensional AdS spacetime i,j = 0,1,2 = 3 dimensional curved spacetime indices a(u)= warped factor u = x^D =...
9. ### Christoffel Symbol

Ansatz metric of the four dimensional spacetime: ds^2=a^2 g_{ab}dx^a dx^b - du^2 where: a,b=0,1,2 a(u)=warped factor Christoffel symbol of a three dimensional AdS spacetime: \Gamma^{c}_{ab}= \frac{1}{2} g^{cd}(∂_b g_{da} + ∂_a g_{bd} - ∂_d g_{ba}) Now how to find \Gamma^{a}_{b}?
10. ### Weak field Geodesic equation

Geodesic equation: m_{0}\frac{du^{\alpha}}{d\tau}+\Gamma^{\alpha}_{\mu\nu}u^{\mu}u^{\nu}= qF^{\alpha\beta}u_{\beta} Weak-field: ds^{2}= - (1+2\phi)dt^{2}+(1-2\phi)(dx^{2}+dy^{2}+dz^{2}) Magnetic field, B is set to be zero. I want to find electric field, E, but don't know where to start, so...
11. ### Poisson Bracket

Homework Statement Show that Q_{1}=\frac{1}{\sqrt{2}}(q_{1}+\frac{p_{2}}{mω}) Q_{2}=\frac{1}{\sqrt{2}}(q_{1}-\frac{p_{2}}{mω}) P_{1}=\frac{1}{\sqrt{2}}(p_{1}-mωq_{2}) P_{2}=\frac{1}{\sqrt{2}}(p_{1}+mωq_{2}) (where mω is a constant) is a canonical transformation by Poisson bracket test. This...
12. ### Generating Function in Physics

Could anybody give me some examples of generating function in physics, it's application, and it's use? Thank you
13. ### Maple Maple - Error (in plots:-display)

I tried this on maple: eps1 := [0, 1/5, 2/5, 3/5, 4/5, 1]: start1 := 2.3: base1 := 1.1: for i from 1 to 6 do R := start1*base1**0: points1[i] := [R, evalf(eval(mH, {M=1, r=R, epsilon = eps1[i]}))]: for a from 1 to 20 do R := start1*base1**a: points1[i] := points1[i], [R, evalf(eval(mH, {M=1...
14. ### Hawking Mass in Schwarzschild Spacetime

Homework Statement Metric signature: - + + + Schwarzschild metric: dS^{2}=-(1-\frac{2M}{r})dt^{2}+(1-\frac{2M}{r})^{-1}dr^{2}+r^{2}d\theta^{2}+r^{2}(sin\theta)^{2}d\phi^{2} Second fundamental form: h_{ij}=g_{kl}\Gamma^{k}_{ij}n^{l} where: i=1,2 j=1,2...