ATRONOMY – BLACK HOLE & RELATIVITY (38) CALCULATOR
Hawking Temperature
A precise tool.
What is the Hawking Temperature & How does it work?
Stephen Hawking showed that black holes are not completely black; they emit a faint thermal radiation due to quantum effects near the event horizon. This phenomenon, known as Hawking radiation, allows a black hole to lose mass over astronomical timescales.
The temperature of this radiation depends inversely on the blackβholeβs mass: the smaller the black hole, the hotter it radiates. For stellarβmass black holes the temperature is far below the cosmic microwave background, making direct detection extremely challenging.
The Hawking temperature is given by a simple formula that combines fundamental constants β the reduced Planck constant (Δ§), the speed of light (c), the gravitational constant (G), Boltzmannβs constant (kB) β with the blackβhole mass (M). Understanding this relationship helps illustrate the deep connection between quantum mechanics, thermodynamics, and general relativity.
T = frac{hbar c^{3}}{8pi G M k_{B}}
T = Hawking temperature (K)
hbar = reduced Planck constant
c = speed of light in vacuum
G = gravitational constant
M = blackβhole mass
k_{B} = Boltzmann constant
hbar = reduced Planck constant
c = speed of light in vacuum
G = gravitational constant
M = blackβhole mass
k_{B} = Boltzmann constant
Parameters
Result
β
Frequently Asked Questions
What is Hawking radiation?
Hawking radiation is the theoretical emission of particles from black holes due to quantum effects near the event horizon.
How does the temperature of Hawking radiation relate to the mass of a black hole?
The temperature of Hawking radiation is inversely proportional to the mass of the black hole; smaller black holes emit hotter radiation.
Can we detect Hawking radiation from stellar-mass black holes?
No, for stellar-mass black holes, the Hawking radiation temperature is far below the cosmic microwave background, making direct detection impossible with current technology.
What is the formula used to calculate Hawking Temperature?
The Hawking Temperature (T) can be calculated using the formula T = (h * c^3) / (8 * Ο * G * M * k_B), where h is Planck's constant, c is the speed of light, G is the gravitational constant, M is the mass of the black hole, and k_B is Boltzmann's constant.
How does Hawking radiation affect a black hole?
Hawking radiation causes black holes to lose mass over time, leading them to evaporate completely if they have enough time.
Results are for informational purposes only and do not constitute professional advice.