# 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.

Course: [Astrophysics, cosmology and inference](https://studybrix.com/en/courses/astrophysics-and-cosmology/index.md)
Level: advanced
Prerequisites: Relativity, gravity and radiation.

## 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.

## Practice questions

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

Answer: 6

Explanation: rs=2M=6 in these geometric units.

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

Answer: 4

Explanation: rs is proportional to mass.

### 3. Which object is not the event horizon itself?

A. The boundary beyond which outward escape fails
B. The Schwarzschild radius surface for the stated geometry
C. A bright accretion disk
D. The causal boundary in the model

Answer: A bright accretion disk

Explanation: 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 / 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.

Explanation: Credit mass dependence and orbital motion.

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

A. Nonrotating and uncharged Schwarzschild model
B. Only ordinary planets
C. Only zero mass
D. Every rotating geometry unchanged

Answer: Nonrotating and uncharged Schwarzschild model

Explanation: The simple formula has specific spacetime assumptions.

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

Sample answer / marking guidance: The emission can originate outside the horizon and escape. The no-escape property concerns signals from within the horizon.

Explanation: Credit location and causal distinction.

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

Answer: 30 km

Explanation: Multiply the supplied approximate scale by mass in solar units.

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

Sample answer / marking guidance: Orbital dynamics of nearby stars, accretion spectra, gravitational-wave observations and horizon-scale imaging are examples.

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

## Further reading

- https://science.nasa.gov/universe/black-holes/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.