Black Hole Evaporation Calculator

Black Hole Evaporation Equation:

\[ t = \frac{5120 \pi G^2 M^3}{\hbar c^4} \]

Black Hole Mass (M):

Gravitational Constant (G):

m³/kg·s²

Reduced Planck Constant (ħ):

J·s

Speed of Light (c):

m/s

Evaporation Time (t):

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1. What is Black Hole Evaporation?

Black hole evaporation is a process predicted by quantum mechanics where black holes lose mass over time by emitting Hawking radiation. This phenomenon was first proposed by Stephen Hawking in 1974.

2. How Does the Calculator Work?

The calculator uses the black hole evaporation equation:

\[ t = \frac{5120 \pi G^2 M^3}{\hbar c^4} \]

Where:

\( t \) — Evaporation time (seconds)
\( G \) — Gravitational constant (m³/kg·s²)
\( M \) — Black hole mass (kg)
\( \hbar \) — Reduced Planck constant (J·s)
\( c \) — Speed of light (m/s)

Explanation: The equation shows that the evaporation time is proportional to the cube of the black hole's mass and inversely proportional to fundamental constants of nature.

3. Importance of Evaporation Time Calculation

Details: Calculating evaporation time helps understand the lifespan of black holes and the nature of Hawking radiation, which has implications for quantum gravity theories and the ultimate fate of black holes.

4. Using the Calculator

Tips: Enter the black hole mass in kilograms and the fundamental constants. Default values are provided for G, ħ, and c based on standard physical constants.

5. Frequently Asked Questions (FAQ)

Q1: How long would a black hole take to evaporate?
A: For a solar-mass black hole (2×10³⁰ kg), the evaporation time is about 2×10⁶⁷ years - far longer than the current age of the universe.

Q2: What happens at the end of black hole evaporation?
A: As the black hole nears complete evaporation, it's theorized to emit a final burst of high-energy radiation.

Q3: Has Hawking radiation been observed?
A: No, Hawking radiation has not been directly observed yet, as the radiation from astrophysical black holes is too faint to detect with current technology.

Q4: Do all black holes evaporate?
A: In theory, yes, but for massive black holes, the timescale is so long that they effectively don't evaporate in the current age of the universe.

Q5: What affects the evaporation rate?
A: The rate increases as the black hole loses mass, making the final stages of evaporation extremely rapid compared to the initial slow process.