In model units G=c=1 and mass M=3, find the Schwarzschild radius.
Answer and explanation
6
rs=2M=6 in these geometric units.
Subjects
Relativistic astrophysics
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Sample exercises
In the Schwarzschild model, mass quadruples. Find the horizon-radius factor.
Answer and explanation
4
rs is proportional to mass.
Which object is not the event horizon itself?
- The boundary beyond which outward escape fails
- The Schwarzschild radius surface for the stated geometry
- A bright accretion disk
- The causal boundary in the model
Answer and explanation
A bright accretion disk
The disk is luminous matter outside the horizon, not the horizon itself.
Why does the phrase black holes suck everything nearby misrepresent gravity?
Answer and explanation
At a given large distance, gravity depends on mass and spacetime, not a universal suction mechanism. Matter with suitable angular momentum can orbit rather than immediately fall in.
Credit mass dependence and orbital motion.
Which restriction belongs to rs=2GM/c² as a horizon-radius formula?
- Nonrotating and uncharged Schwarzschild model
- Only ordinary planets
- Only zero mass
- Every rotating geometry unchanged
Answer and explanation
Nonrotating and uncharged Schwarzschild model
The simple formula has specific spacetime assumptions.
Explain why observing emission near a black hole does not contradict its definition.
Answer and explanation
The emission can originate outside the horizon and escape. The no-escape property concerns signals from within the horizon.
Credit location and causal distinction.
Study notes
Black holes, horizons and observable environments
For a nonrotating uncharged black hole, the horizon radius is rs=2GM/c². Rotation and charge require a different spacetime description.
Advanced universityBlack holes, horizons and observable environments · revision notes
For a nonrotating uncharged black hole, the horizon radius is rs=2GM/c². Rotation and charge require a different spacetime description.
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