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Black holes are stars that are so massive, that when they die, they become so dense that not even light can escape. That means that a black hole is costantly adding mass and energy and thus making its gravitational force even stronger. If this is what happens, black holes should live forever right? Is there a mechanism that reduces their mass and energy so as to finally evaporate?

To sum up, do black holes exist forever?

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I'm no expert but there is a mechanism that causes black holes to lose mass called Hawking radiation. To understand it, there is a thing in quantum mechanics called the uncertainty principle that basically means that if you know the exact (or nearly exact) position of a particle then you can not know the momentum of that particle to the same degree of accuracy, this then means that a particle can not be totally still, because if it was, you could know the position and the momentum, which would be zero. Since particles are excitations of quantum fields, this means that the fields can not be exactly still either and therefore have to "ripple" a bit, therefore causing excitations and therefore particles to be created. These are called virtual particles and they are always created in pairs (one particle and one anti particle). When they are created, they move out from each other semi-elliptically and then curve back into each other, "destroying" one another. This has to happen because according to the universal conservation of mass you can not create mass or energy. So when these particles are created near or basically on the event horizon of a black hole, they move out from one another, but instead of destroying each other one of them is "sucked" into the black hole. This means that the other one has just been left to roam the universe forever. This defies the conservation of mass and means that the black hole has to lose mass equal to the mass of the "free" particle. Over time this output of Hawking radiation will be more than the input of other mass from stars and planets etc. and therefore cause the black hole to evaporate. So a straight forward answer: No, black holes are not immortal.

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Black holes are not immortal and are theorised (by Stephen Hawking) to radiate Hawking radiation, which is a quantum mechanical effect. The section "Emission Process" in the Wiki article has quite a good summary of how this happens: by the equivalence principle, one can compute the physics for an observer hovering near the black hole's Schwarzschild horizon as being equivalent (at least locally) to that of an accelerated observer in flat Minkowsky space. In flat space, if we have a quantum field in its ground state, an accelerated observer actually sees the ground state as being thermalised, i.e. it is a black body radiator with temperature proportional to the acceleration: this is the Unruh effect. Qualitatively, you can understand this as the quantum ground state producing fleetingly lived virtual photon pairs, but some of these pairs must be observed by the hovering observer, i.e. they become real. If there is radiation observered by the hovering observer, then there must be a redshifted version of this radiation infinitely far away from the black hole.

This process begets an energy loss from the black hole, and the latter will slowly vanish. The black hole temperature, in Planck units, is $T=\frac{1}{8\pi\,M}$, where $M$ is the black hole mass. So the hole becomes hotter as it gets smaller, and, by the Stefan Boltzmann law, the radiation power is proportional to the fourth power of the inverse mass. So, at the end of its life, this hole not so much evaporates as explodes.

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To add a minor complexity to the two answers citing Hawking radiation. A black hole will only lose mass due to Hawking radiation once its temperature is greater than the background temperature of the universe. A stellar mass black hole has a temperature ~10^-7 K, whereas the current background temperature is ~2.7 K. So at present, all massive black holes will actually be getting heavier. Only when the universe has expanded sufficiently that its background temperature drops to typical black hole temperatures, will the holes start to evaporate. And that is unlikely to happen for 10^80-10^100 years or more (uncertain of specific magnitude). So you would have a very long wait to see it happen.

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I'm of course not an expert in this matter, but a black hole radiates thermal radiation according to the Hawking radiation, of course to fully understand this one must have some knowledge of Quantum Field Theory and General Relativity, plus a little of statistical mechanics, In Wald's book QFT in Curved Spacetime and Black Hole Thermodynamics we find on page 177 a formula which states that a black hole reaches the planck mass in the finite time of $t=M_o^3/3\alpha$, where $\alpha$ is in the order of unit in planck units

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