MATLAB Can Light Rays Cross Near a BH? - Simulated w/ Matlab

AI Thread Summary
The discussion centers on simulating the behavior of two parallel light rays passing near a Kerr black hole (BH) using Matlab. The rays start symmetrically above and below the equatorial plane, with specified initial positions and wave vectors. The mass of the BH is approximately 1.988 x 10^30 kg, with an angular momentum parameter of 0.9 along the z-axis. The simulation results show that the rays cross each other, ending at distinct z-coordinates of -667 m and 667 m. Concerns are raised about the accuracy of the model, particularly regarding the increase in wave number, which may stem from potential errors in the ode45 algorithm used for calculations. The discussion highlights the need for clarification on initial conditions and parameters to validate the simulation outcomes, emphasizing the phenomenon of gravitational lensing.
Haorong Wu
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When I simulate that two parallel light rays pass near a Kerr BH, the result shows that they cross each other. Is it possible?
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 in the figure, indicates that the rays cross each other. In the end, the ##z## components of the two rays are ##-667~\rm{m}## and ##667~\rm{m}##, respectively.

I am not sure if this is possible or not. Maybe there are some errors in my model. How can I check if my result is correct or not?

Thanks.
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You haven't really explained your initial conditions, so it's hard to comment. I think your rays start symmetrically above and below the equatorial plane. What are their initial directions, and what are the mass and angular momentum parameters of the hole?
 
@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)##;
initial positions of rays are ##(-1\times 10^4,~2\times 10^4,~1\times 10^3)## and ##(-1\times 10^4,~2\times 10^4,~-1\times 10^3)##, respectively;
both initial wave vectors are ##(1.03\times 10^7 ,~1.82\times 10^6 , ~ 0)##;

The results are:
the final positions of rays are ##(9.12\times 10^4,~1.55\times 10^3,~-667)## and ##(9.12\times 10^4,~1.55\times 10^3,~667)##, respectively;
the final wave vectors are ##(1.05\times 10^7,~-2.28\times 10^6,~-1.90\times 10^5)## and ##(1.05\times 10^7,~-2.28\times 10^6,~1.90\times 10^5)##, respectively.

The wave number is increased by ##2.36\times10^5~\rm{m^{-1}}##, but I think that is due to the calculation error of the ode45 algorithm.
 
Last edited:
This is gravitational lensing.
 

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