1. What is Black Hole Time Dilation?

Time dilation near a black hole describes how time appears to pass at different rates for observers at different distances from the black hole's event horizon. This effect is predicted by Einstein's theory of general relativity.

2. How Does the Calculator Work?

The calculator uses the time dilation equation:

Where:

• \( \Delta t' \) — Time interval for observer near black hole (seconds)
• \( \Delta t \) — Time interval for distant observer (seconds)
• \( r_s \) — Schwarzschild radius (event horizon) of black hole (meters)
• \( r \) — Radial coordinate of observer (distance from center) (meters)

Explanation: The equation shows that time appears to slow down as an observer approaches the event horizon (r → rₛ).

3. Importance of Time Dilation

Details: Understanding time dilation is crucial for astrophysics, GPS satellite operations, and testing general relativity. Near black holes, these effects become extreme.

4. Using the Calculator

Tips: Enter time interval in seconds, Schwarzschild radius in meters (2GM/c²), and observer's distance in meters. Observer must be outside event horizon (r > rₛ).

5. Frequently Asked Questions (FAQ)

Q1: What happens at the event horizon?
A: At r = rₛ, time dilation becomes infinite (Δt' → 0), meaning time appears frozen to distant observers.

Q2: How is Schwarzschild radius calculated?
A: rₛ = 2GM/c², where G is gravitational constant, M is black hole mass, and c is speed of light.

Q3: Does this affect real observations?
A: Yes, astronomers observe these effects in light from matter falling into black holes.

Q4: What about rotating black holes?
A: The Kerr metric is needed for rotating black holes, which is more complex than this Schwarzschild solution.

Q5: Can humans experience this effect?
A: While measurable near Earth (GPS accounts for it), extreme effects require proximity to massive black holes.