(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The possible orbit of a particle moving around a black hole can be described using the effective potential U_{GR}(r) (in effect, potential energy per unit mass):

U_{GR}(r) = -GM/r +l^{2}/2m^{2}r^{2}- R_{s}l^{2}/2m^{2}r^{3}

where the symbols have their usual meaning and in particular R_{s}= 2GM / c^{2}is the Schwarzschild radius for the black hole. We then use the energy balance equation

K = 1/2 mr^{2}+ mU_{GR}= constant

to illustrate the main features of the possible orbits.

(a) Show that the function U_{GR}has a minimum and maximum value at r = r_{-}and r = r_{+}respectively and determine expressions for these qualities.

(b) Briefly describe the possible orbits.

2. Relevant equations

Listed above

3. The attempt at a solution

Please help.

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# Homework Help: Orbits of Particle Around a Black Hole using Effective Potential

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