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Astronomy & space · lesson 3 of 4

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.

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Learn the ideas

Prerequisites: Relativity, gravity and radiation.

Schwarzschild model

For a nonrotating uncharged black hole, the horizon radius is rs=2GM/c². Rotation and charge require a different spacetime description.

Horizon

The horizon is a causal boundary, not the bright accretion disk or a solid shell. Signals from inside do not reach distant outside observers.

Evidence

Motion of nearby matter, accretion emission, gravitational waves and horizon-scale imaging constrain models through different observations.

Limits

A simple horizon-radius calculation does not describe the complete interior, accretion flow, jet or quantum-gravity problem.

Worked examples

Example 1

In model units G=c=1 and mass M=3, find the Schwarzschild radius.

rs=2M=6 in these geometric units.

6

Example 2

In the Schwarzschild model, mass quadruples. Find the horizon-radius factor.

rs is proportional to mass.

4

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

1 In model units G=c=1 and mass M=3, find the Schwarzschild radius.

Show answer and explanation

6

rs=2M=6 in these geometric units.

2 In the Schwarzschild model, mass quadruples. Find the horizon-radius factor.

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4

rs is proportional to mass.

3 Which object is not the event horizon itself?

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A bright accretion disk

The disk is luminous matter outside the horizon, not the horizon itself.

4 Why does the phrase black holes suck everything nearby misrepresent gravity?

Sample answer and marking guidance

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.

5 Which restriction belongs to rs=2GM/c² as a horizon-radius formula?

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Nonrotating and uncharged Schwarzschild model

The simple formula has specific spacetime assumptions.

6 Explain why observing emission near a black hole does not contradict its definition.

Sample answer and marking guidance

The emission can originate outside the horizon and escape. The no-escape property concerns signals from within the horizon.

Credit location and causal distinction.

7 Using rs≈3 km per solar mass as a stated rough scale, estimate rs for 10 solar masses.km

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30 km

Multiply the supplied approximate scale by mass in solar units.

8 Name two independent observational approaches to studying black-hole systems.

Sample answer and marking guidance

Orbital dynamics of nearby stars, accretion spectra, gravitational-wave observations and horizon-scale imaging are examples.

Credit two approaches without claiming each alone resolves all model uncertainties.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.