Recent content by Haorong Wu

Thanks, @Demystifier, @PeterDonis, @Sagittarius A-Star. Below is my attempt to understand this question. In the exponential, ##e^{-i\omega x^0}## of a mode function, the factor ##\omega## before the time coordinate ##x^0## had better be (or at least be related to) the frequency (energy)...

I am reading a paper, A Pedagogical Review of Black Holes, Hawking Radiation and the Information Paradox. On page 17, it reads that and I am not convinced that the two sets of coordinates are associated with different observers. I think the coordinate systems are independent of observers...

Thanks, @Philip Koeck and @pasmith. I will try to demonstrate the first expression. Suppose ##F(\omega)## is the Fourier transform of ##f(Q)##, i.e., ##f(Q)=(2\pi)^{-1/2} \int d\omega F(\omega) e^{-i\omega Q}##. Then the integral \begin{align} &~~\lim_{r\rightarrow \infty} \int_0^\infty dQ f(Q)...

Hi, there. I am reading this thesis. On page 146, it reads that I do not know how to calculate the limits when they are viewed as distributions. I am trying to integrate a test function with the limits. So I try (##Q## is defined as ##Q>0##) $$\lim_ {r\rightarrow \infty} \int_{0}^\infty dQ...

@Ibix Sorry, I thought that is not important, so I did not mention it. Here are the parameters (all are in Cartesian coordinates): mass of BH is ##1.988\times10^{30}~\rm{kg}=1.47\times10^3~\rm{m}## ; angular momentum per unit mass is ##0.9## (along z-axis); position of BH is ##(0,~0,~0)##...

Hi. I use Matlab to simulate that two parallel light rays pass near a Kerr BH. The angular momentum of the BH points to the ##z## direction. The ##z## components of the start points of the two rays are ## 1\times 10^3 ~\rm{m}## and ##- 1\times 10^3 ~\rm{m}##, respectively. The result, as shown...

Thanks, @vanhees71 From the identification of ##\dot x^i=k^i## (suppose I have performed the 3+1 decomposition of spacetime and I focus only on the space part), I have $$\frac {d}{d\lambda}=\frac {dx^i}{d\lambda}\frac{d}{dx^i}=k \frac{d}{dx^3}, $$ where ##\mathbf k## is assumed to be along the...

@PeterDonis I am sorry I could not find the paper on arxiv, and I think it is inappropriate to post the pdf file here. The "path length" is not defined before this paragraph. But later, the author wrote that "the unit wave vector ##\mathbf n_k=\nabla s##." It appears that the direction of...

Hi, @PeterDonis. I am reading this article, Phase evolution of the photon in Kerr spacetime . In the first paragraph of Section IV, the author wrote "Under the geometrical optics approximation, the wave function of a photon depends only on its propagating path length. Let ##C## be the integral...

Thanks, @PeterDonis . I used a wrong concept. I should say let ##C## be the integral curve of ##\mathbf k##. It is the curve along which the light propagates.

Hi, there. I am doing differentiation with respect to an affine parameter ##s##, I am not sure whether my idea is right or wrong. Let ##C## be a geodesic for light and the path length ##s## on it be the affine parameter. Now I need to calculate ##\frac {\partial f}{\partial s}##, with ##f##...

Thanks! I will dig into it.

@Drakkith @hutchphd @berkeman Thanks for your help. I study the phase distribution on the wavefront of light. It has been reported that light emitted from an accretion disk surrounding a rotating black hole can carry a phase distribution on the wavefront (here and here). What about I divide...

Hi. I am studying the wavefront evolution of light from a star. In the papers I have read, the star is often treated as a point source and the light is approximated as a line (geodesics), but this approximation is not very useful when I study the wavefront evolution, so I want to extend the...

I think I have solved it partially. From the EOM of photons in Kerr spacetime, \begin{align} \rho^2 k^r=&\pm \sqrt{R(r)},\\ \rho^2 k^\theta=&\pm \sqrt{\Theta(\theta)},\\ \rho^2 k^\phi=&-(aE-\frac{L_z}{\sin^2 \theta})+\frac a \Delta P(r), \end{align} where at large ##r##, ##R(r)\rightarrow...