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• Mayur Pawar

# Do you know: How do Blackhole evaporate?

Updated: Jan 28

It is quite strange to digest that the astronomical body which sucks everything in it even light; how could it evaporate? The myth has existed ever since the first reference of a black hole in the scientific community. But it has broken by Stephen Hawking after he theorized in 1974 that black holes radiate small numbers of particles (mainly photons), a process known as “Hawking Radiation”. This “evaporation” process can lead the black hole to shrink over time and ultimately to vanish completely. However, it is a staggeringly slow process: it would take about 10^67 years for a black hole the mass of the Sun to evaporate, significantly longer than the 14 billion years the Universe has existed. Black holes appear to have the capability of losing mass-energy by the Hawking radiation process that takes place by the polarization of the vacuum and which can be treated by describing the black hole’s gravitational field by classical general relativity while the surrounding vacuum space-time is described by quantum field theory. When black holes lose energy by Hawking radiation (by the emission of neutrinos, photons, gravitons, etc.), the power can be calculated, and the thermal emission turns out to be small for large black holes and large for small black holes, as it depends inversely on the square of the mass. An evaporation time can be calculated from the emitted power under the assumption that the amount of any simultaneous infalling matter or radiation is negligible. This lifetime depends on the cube of the initial mass of the black hole and is temperature-dependent in that it reflects the number of degrees of freedom in the emission process. An estimate of this evaporation time is given by the equation:

tev = 640π^2G^2Mo^3 /hc^4 ..(1)

where Mo is the initial mass of the black hole undergoing evaporation by the emission of mass-energy.

Next, we can evaluate the evaporation time or lifetime of a black hole having the threshold mass. Inserting the expression for the threshold mass. We find for the evaporation time of a black hole having an initial mass equal to the threshold mass:

tevth = 40π/Ho ..(2)

Thus, the evaporation time of a black hole of threshold mass is directly related to the Hubble constant, and thus to the Hubble time. Using a value of the Hubble constant of 2.3x10^-18 per second, we find for the evaporation time value of roughly 10^12 years, somewhat longer than the time since the Big Bang.

Somewhat differing estimates of evaporation lifetimes exist in the literature. It is pointed out that a black hole with a mass of the order of 10^15 grams (the mass of a typical asteroid) and corresponding Schwarzschild radius of the order of 10^-13 cm. (about the size of a nucleon) will have an evaporation lifetime of the order of the age of our universe.

A related estimate of the evaporation time for black holes from the literature gives:

tev ≈ 10^10 years (Mo/10^15 grams)^3

This tells us that only those black holes with masses less than or comparable to 10^15 grams have the evaporation times shorter than the age of the universe. Use of this estimate for a threshold mass 2x10^12 kilograms would lead to an evaporation time estimate of 80 billion years, longer than but within an order of magnitude of the lifetime of the visible universe.

Thus, depending on the estimates used, the threshold mass for a black hole may be only moderately above the mass of a black hole having an evaporation time comparable to the time since the Big Bang.

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