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Astronomy & space · Advanced university

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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Prerequisites

Relativity, gravity and radiation.

Study notes

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

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

rs=2M=6 in these geometric units.

6

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

rs is proportional to mass.

4

Check your understanding

  1. Which object is not the event horizon itself?

    1. The boundary beyond which outward escape fails
    2. The Schwarzschild radius surface for the stated geometry
    3. A bright accretion disk
    4. The causal boundary in the model

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

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

    1. Nonrotating and uncharged Schwarzschild model
    2. Only ordinary planets
    3. Only zero mass
    4. Every rotating geometry unchanged

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

Answers and marking guidance

Answers and marking notes
  1. A bright accretion disk

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

  2. 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.

  3. Nonrotating and uncharged Schwarzschild model

    The simple formula has specific spacetime assumptions.

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

    Credit location and causal distinction.

Further reading and review references

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