How long would it take for a black hole the size of the Sun to disappear?

In one line

The rule

Black holes slowly lose mass over time by giving off energy as "Hawking radiation". The smaller the black hole, the faster it evaporates. The time it takes is proportional to the cube of its mass.

The formula for the evaporation time (lifetime) of a black hole is:

T ≈ 5120 × (G² M³) / (ħ c⁴)

Where:

• T = time to evaporate (in seconds)
• G = gravitational constant
• M = mass of the black hole
• ħ = reduced Planck constant
• c = speed of light

For a black hole with the Sun's mass, this gives about 2 × 10⁶⁷ years.

Let's understand it simply

Imagine you have a giant pressure cooker (the black hole) that is so strong, not even light can escape. But, thanks to a strange effect called Hawking radiation, the cooker leaks a tiny bit of steam (energy) over time. The bigger the cooker, the slower it leaks. If your cooker is as big as the Sun, it would take longer than you, your family, and all of India put together could ever count, for it to finally run out of steam and vanish!

Think of a huge ice block (the black hole) melting in the sun (Hawking radiation). A small ice cube melts fast, but a giant block takes ages. For a black hole the size of the Sun, the melting (evaporation) is so slow, it's almost like it never happens in our lifetime.

How it works

1. Hawking radiation: Black holes are not completely black. They emit a tiny amount of radiation due to quantum effects near their edge (event horizon).
2. Energy loss: This radiation carries away energy, which means the black hole loses mass (Einstein's E = mc²).
3. Shrinking: As the black hole loses mass, it gets smaller and emits more radiation (the process speeds up at the end).
4. Evaporation time: The time it takes for the black hole to completely vanish depends on its mass. The bigger the mass, the longer it takes.
5. For the Sun's mass: Plugging the Sun's mass into the formula gives a time of about 2 × 10⁶⁷ years.
6. Comparison: The current age of the universe is only about 1.4 × 10¹⁰ years, so the black hole lasts much, much longer.

The story behind it

The idea of black holes evaporating was first proposed by Stephen Hawking in 1974. Before this, scientists thought black holes could only grow or stay the same size. Hawking used quantum physics to show that black holes can actually lose mass and disappear over time. This was a huge surprise! Hawking's work connected gravity, quantum mechanics, and thermodynamics (the study of heat), three big areas of physics. He did his calculations while struggling with ALS, a disease that made him unable to move or speak easily, but he kept working using only his mind and a few helpers.

Where you see it in real life

• Space: Real black holes in the universe, like those formed from dying stars, are losing mass by Hawking radiation (but extremely slowly).
• Physics labs: Scientists try to create tiny "black hole analogues" using sound or light to study Hawking radiation effects.
• Science fiction: Many stories imagine black holes evaporating or being used as energy sources.
• Cosmic background: The universe's oldest, smallest black holes (if any exist) might be evaporating now, possibly giving off bursts of energy.
• Theoretical physics: The idea helps scientists understand how gravity and quantum mechanics work together.
• Black hole mergers: After two black holes merge, the new one will also slowly evaporate, but over a very long time.

Why it matters

• Connects big ideas: Hawking radiation links gravity, quantum mechanics, and thermodynamics.
• Fate of black holes: It tells us that black holes are not forever—they can disappear!
• Universe's future: In the far future, all black holes will eventually evaporate, leaving only radiation.
• Helps test theories: Studying this effect helps physicists test and improve their theories about the universe.

Worked example

Let's estimate the evaporation time for a black hole with the Sun's mass (about 2 × 10³⁰ kg):

Given: M = 2 × 10³⁰ kg (mass of Sun)
Step 1: Write the formula  T ≈ 5120 × (G² M³) / (ħ c⁴)
Step 2: Plug in values (using known constants)
Step 3: Calculate T ≈ 2 × 10⁶⁷ years

Common mistakes

• Thinking black holes last forever: They do not. They evaporate, but very slowly if they are big.
• Believing Hawking radiation is strong: For big black holes, it is extremely weak. You would not notice it.
• Confusing with normal radiation: Hawking radiation is not like sunlight or heat from a fire; it comes from quantum effects near the event horizon.
• Forgetting the time scale: The evaporation time is much, much longer than the age of the universe for stellar-mass black holes.

Remember it

A black hole the size of the Sun would take about 10⁶⁷ years to evaporate—far longer than the universe has existed.