handle trajectory singularity: delete photons causing error

Question

I am coding a black hole (actually photons orbiting a black hole) and I need to handle an exception for radius values that are smaller than the limit distance

I've tried using if and while True

def Hamiltonian(r, pt, pr, pphi):
    H = (-((1-rs/r)**-1)*(pt**2)/2 + (1-rs/r)*(pr**2)/2 + (pphi**2)/(2*         (r**2)))
    if np.amax(H) < 10e-08:
        print("Your results are correct")
    else:
        print("Your results are wrong")
    return(H)    

def singularity(H, r):
    if (r).any < 1.5*rs:
        print(H)
    else:
        print("0")
        return(H, r)

print(Hamiltonian(r00, pt00, pr00, pphi00))   

I'd like to handle the case r < 1.5*rs so that I don't have the division error message and weird orbits anymore. So far my code doesn't change anything to the problem, I still get this error message :

"RuntimeWarning: divide by zero encountered in true_divide
  H = (-((1-rs/r)**-1)*(pt**2)/2 + (1-rs/r)*(pr**2)/2 + (pphi**2)/(2*(r**2)))"

and my orbits are completely wrong (for example my photon should go right in the black hole, but since there's a singularity at r < 1.5*rs, they go in and leave again and so on)

I'd like to delete the photons causing the problem but I don't know how, can anyone please help me?

Answer 1

I think you mention that we do not know exactly what goes on at a singularity. Any answer provided here most likely would not be accurate, but let's just assume that you know the behavior/dynamics at the near 0 neighborhood. I do not know how you are calling the Hamiltonian function but I can imagine you are doing it one of two ways.

1. You have a pre-defined loop that loops through each value you are passing into the function and outputting the resulting H for each value in that pre-defined loop.

2. You are passing in vectors of the same length and doing element by element math in the H function.

In the first case, you could either do a pre-check and write a new function for the near 0 behavior and call that new function if you are in the near zero neighborhood. You could also just have the check in the hamiltonian function itself and call the new function if you are in the near 0 neighborhood. This latter method is what I would prefer as it keeps the front-end (the best word I have for it) fairly clean and encapsulates the logic/math in your Hamiltonian function. In your comments you say you want to delete the photon within some radius, and that would be extremely easy to do with this method by just terminating the for loop by breaking out at that time step and plotting what you had until that time step.

In the second case, you would have to manually build the new vector by having checks throughout your vectors if they fall within the singularity neighborhood. This would be a little more difficult and would depend on the shape of your inputs and doing element by element math is more difficult to debug in my opinion.