   #copyright

Hawking radiation

2007 Schools Wikipedia Selection. Related subjects: Space (Astronomy)

   In physics, Hawking radiation is thermal radiation thought to be
   emitted by black holes due to quantum effects. It is named after
   British physicist Stephen Hawking who worked out the theoretical
   argument for its existence in 1974. Hawking's discovery became the
   first convincing insight into quantum gravity. However, the existence
   of Hawking radiation remains controversial. .

Overview

   Black holes are sites of immense gravitational attraction into which
   surrounding matter is drawn by gravitational forces. Classically, the
   gravitation is so powerful that nothing, not even radiation or light
   (hence why it is black as no light is reflecting from it), can escape
   from the black hole. However, by doing a calculation in the framework
   of quantum field theory in curved spacetimes, Hawking showed that
   quantum effects allow black holes to emit radiations in a thermal
   spectrum.

   Physical insight on the process may be gained by imagining that
   particle antiparticle radiation is emitted from just beyond the event
   horizon. This radiation does not come directly from the black hole
   itself, but rather is a result of virtual particles being "boosted" by
   the black hole's gravitation into becoming real particles.

   A more precise, but still much simplified view of the process is that
   vacuum fluctuations cause a particle-antiparticle pair to appear close
   to the event horizon of a black hole. One of the pair falls into the
   black hole whilst the other escapes. In order to fill the energy 'hole'
   left by the pair's spontaneous creation, energy tunnels out of the
   black hole and across the event horizon. By this process the black hole
   loses mass, and to an outside observer it would appear that the black
   hole has just emitted a particle.

An example

   A black hole of one solar mass has a temperature of only 60
   nanokelvins; in fact, such a black hole would absorb far more cosmic
   microwave background radiation than it emits. A black hole of
   4.5 × 10²² kg (about the mass of the Moon) would be in equilibrium at
   2.7 kelvins, absorbing as much radiation as it emits. Yet smaller
   primordial black holes would emit more than they absorb, and thereby
   lose mass.

Problems with the theory

   The trans-Planckian problem may raise doubts on the physical validity
   of Hawking's result. Hawking's original derivation employed field modes
   of arbitrarily high frequency near the black hole horizon, although
   these do not appear in the final result. In particular, he used modes
   of frequency higher than the inverse Planck time, and at these scales
   the physical laws are unknown. A number of alternative approaches to
   the Hawking radiation have appeared in order to try to overcome or
   address this problem. Some of these are in connection with the Unruh
   effect.

   The Hawking Radiation shows that the laws of black hole thermodynamics
   have a complete physical meaning.

Emission process

   A black hole emits thermal radiation at a temperature

          T_H = \frac{\kappa}{2 \pi} ,

   in natural units with G, c, \hbar and k equal to 1, and where κ is the
   surface gravity of the horizon.

   In particular, the radiation from a Schwarzschild black hole is
   black-body radiation with temperature:

          T={\hbar\,c^3\over8\pi G M k}

   where \hbar is the reduced Planck constant, c is the speed of light, k
   is the Boltzmann constant, G is the gravitational constant, and M is
   the mass of the black hole.

Black hole evaporation

   When particles escape, the black hole loses a small amount of its
   energy and therefore of its mass (recall that mass and energy are
   related by Einstein's famous equation E = mc²).

   The power emitted by a black hole in the form of Hawking radiation can
   easily be estimated for the simplest case of a nonrotating, non-charged
   Schwarzschild black hole of mass M. Combining the formulae for the
   Schwarzschild radius of the black hole, the Stefan-Boltzmann law of
   black-body radiation, the above formula for the temperature of the
   radiation, and the formula for the surface area of a sphere (the black
   hole's event horizon) we get:

          P={\hbar\,c^6\over15360\,\pi\,G^2M^2}

   where P is the energy outflow, \hbar is the reduced Planck constant, c
   is the speed of light, and G is the gravitational constant. It is worth
   mentioning that the above formula has not yet been derived in the
   framework of semiclassical gravity.

   The power in the Hawking radiation from a solar mass black hole turns
   out to be a minuscule 10^−28 watts. It is indeed an extremely good
   approximation to call such an object 'black'.

   Under the assumption of an otherwise empty universe, so that no matter
   or cosmic microwave background radiation falls into the black hole, it
   is possible to calculate how long it would take for the black hole to
   evaporate. The black hole's mass is now a function M(t) of time t. The
   time that the black hole takes to evaporate is:

          t_{\operatorname{ev}}={5120\,\pi\,G^2M_0^{\,3}\over\hbar\,c^4}

   For a black hole of one solar mass (about 2 \times 10^30 kg), we get an
   evaporation time of 10^67 years—much longer than the current age of the
   universe. But for a black hole of 10^11 kg, the evaporation time is
   about 3 billion years. This is why some astronomers are searching for
   signs of exploding primordial black holes.

   In common units,

          P = 3.563\,45 \times 10^{32}
          \left[\frac{\mathrm{kg}}{M}\right]^2 \mathrm{W}

          t_\mathrm{ev} = 8.407\,16 \times 10^{-17}
          \left[\frac{M_0}{\mathrm{kg}}\right]^3 \mathrm{s} \ \ \approx\
          2.66 \times 10^{-24} \left[\frac{M_0}{\mathrm{kg}}\right]^3
          \mathrm{yr}

          M_0 = 2.282\,71 \times 10^5
          \left[\frac{t_\mathrm{ev}}{\mathrm{s}}\right]^{1/3} \mathrm{kg}
          \ \ \approx\ 7.2 \times 10^7
          \left[\frac{t_\mathrm{ev}}{\mathrm{yr}}\right]^{1/3} \mathrm{kg}

   So, for instance, a 1 second-lived black hole has a mass of 2.28 × 10^5
   kg, equivalent to an energy of 2.05 × 10^22 J that could be released by
   5 × 10^6 megatons of TNT. The initial power is 6.84 × 10^21 W.

   Black hole evaporation has several significant consequences:
     * Black hole evaporation produces a more consistent view of black
       hole thermodynamics, by showing how black holes interact thermally
       with the rest of the universe.
     * Unlike most objects, a black hole's temperature increases as it
       radiates away mass. The rate of temperature increase is
       exponential, with the most likely endpoint being the dissolution of
       the black hole in a violent burst of gamma rays. A complete
       description of this dissolution requires a model of quantum gravity
       however, as it occurs when the black hole approaches Planck mass
       and Planck radius.
     * The simplest models of black hole evaporation lead to the black
       hole information paradox. The information content of a black hole
       appears to be lost when it evaporates, as under these models the
       Hawking radiation is random (containing no information). A number
       of solutions to this problem have been proposed, including
       suggestions that Hawking radiation is perturbed to contain the
       missing information, that the Hawking evaporation leaves some form
       of remnant particle containing the missing information, and that
       information is allowed to be lost under these conditions.

   Retrieved from " http://en.wikipedia.org/wiki/Hawking_radiation"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
