---
title: "How a Black Hole Bends Light Interactive Lab | Sandbox Physics"
description: "Why can one thin accretion disk appear both above and below the black-hole shadow? Spacetime bends light around the black hole."
canonical_url: "https://sandboxphysics.com/labs/black-hole-light/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/black-hole-light/"
last_modified: "2026-10-29"
---

General relativity · gravitational lensing

# Black Hole Light Lab

**Why can one thin accretion disk appear both above and below the black-hole shadow?** Spacetime bends light around the black hole. Light from the far side of the disk curves over the top and under the bottom of the hole on its way to us, so the same thin disk shows up as several images around the shadow.

Every pixel launches a ray from the observer and integrates it backward through a nonspinning Schwarzschild spacetime. A ray can fall through the horizon, cross the accretion disk, or escape toward a gravitationally distorted celestial sphere.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

This is a teaching ray integrator for a nonspinning black hole; it does not simulate a Kerr black hole or a GRMHD accretion flow. The disk texture and temperature structure are stylized. Light bending, the black-hole shadow, gravitational redshift and relativistic Doppler beaming follow the model parameters.

Physics tutorial

## Imaging a black hole: the horizon is not what we see

**Background** A black hole gives off no light of its own. A telescope records light from distant sources and from hot surrounding matter, arriving from directions that curved spacetime has bent. The dark center is therefore not a photograph of the horizon surface; it is the black-hole shadow, cast by light paths that are captured.

**Why it matters** Telling apart the shadow, the photon sphere and the multiple disk images turns a spectacular picture into a measurement of spacetime geometry.

Start with the essentials

- **Focus question**: Why can a geometrically thin, nearly edge-on accretion disk appear above, below, and close to the center of the black-hole shadow?
- **One-sentence intuition**: Each pixel on the screen matches one null geodesic arriving at the observer. Tracing it backward tells you whether the light came from the celestial sphere, crossed the disk or fell through the horizon.

### Core mathematical model

#### Null geodesic of light

$$
k^\nu\nabla_\nu k^\mu=0
$$

The photon four-wavevector is parallel transported along itself. Integrating the spatial projection of this equation numerically gives the bent path for every pixel.

#### Schwarzschild black-hole shadow

$$
d_{\mathrm{sh}}=6\sqrt{3}\,r_g\approx10.39\,r_g
$$

Here $r_g=GM/c^2$. The shadow is larger than the event horizon because critical rays are strongly bent and captured before they reach it.

#### Observed frequency-shift factor

$$
g=\frac{\sqrt{1-2r_g/r}}{\gamma\left(1-v_{\mathrm{los}}/c\right)}
$$

The numerator gives the gravitational redshift, and the denominator gives the relativistic Doppler shift from orbital motion. The approaching side is usually brighter and bluer.

#### Innermost stable circular orbit

$$
r_{\mathrm{ISCO}}=6\,r_g
$$

For a nonspinning Schwarzschild black hole, no stable circular orbit exists inside this radius, so the default disk begins here.

### Common difficulties

#### The dark region is not a horizon photograph

**Typical misconception** The rim of the central dark circle is the event horizon, so measuring it directly gives the horizon size.

**Better mental model** The dark circle is a shadow formed by critical light paths. For a Schwarzschild black hole its diameter is about ten point four gravitational radii, substantially larger than the horizon diameter.

#### The bright ring is not a fixed material loop

**Typical misconception** The narrow light around the shadow is a physical tube of glowing matter at one fixed location.

**Better mental model** Rays close to the critical path travel around the black hole longer and can pick up light from the background or the disk more than once. The narrow brightening comes mainly from this structure of light paths, not from a ring of matter.

### Run the experiment

1. 01

   #### Begin with a grazing view

   Choose Grazing cinema view and compare the direct disk image with the higher-order images lifted above and below the shadow.

   **What to observe:** One flat disk seems to wrap around the black hole because light from its far side bends into the observer’s line of sight.

2. 02

   #### Raise the viewing inclination

   Increase the inclination until the disk is seen more directly.

   **What to observe:** The upper and lower arcs merge toward the direct image, and relativistic Doppler beaming makes the approaching side brighter than the receding side.

3. 03

   #### Move the disk inner edge

   Move $r_{\mathrm{in}}$ outward from the innermost stable circular orbit.

   **What to observe:** The center gets dimmer and a wider dark gap opens between the disk and the critical curve, but the shadow size, which the geometry sets, stays fixed.

Physical conclusion

A black-hole image is not a surface photograph. It is a map of light paths: the shadow records the directions whose light is captured, and the multiple images record how spacetime bends the rays that still escape.

## Related experiments and articles

Astronomy and gravity · Reading path

### Gravity leaves a trace

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why collapse does not need a perfectly spherical star**](https://sandboxphysics.com/stories/astronomy-gravity/penrose-trapped-surfaces/)
2. [Lab **Unilluminable Room** Find the corners a candle cannot light](https://sandboxphysics.com/labs/unilluminable-room/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)