Black holes as particle accelerators

Wormhole Hunter
3 min readDec 29, 2016

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The schematic figure of particle collision for which the Center of Mass (CM) energy can be very large. The arrow denotes the direction of the spin of the black hole. For arbitrarily high CM energy to be achieved, the critical particle orbits the black hole arbitrarily large number of times with arbitrarily long proper time.

The existence of black holes is strongly suggested by astrophysical observations. However, it is not so clear whether the observed objects are really identical with what we know as black holes predicted in general relativity. It is necessary to understand the physics of black hole horizons for the direct observational confirmation of black holes. What do black holes as particle accelerators mean?

Before asking this question, let us ask what it means that terrestrial particle accelerators, such as the Large Hadron Collider, accelerate particles. In most of terrestrial particle accel- erators, the kinetic energy of particles is increased through the work exerted on the particles by electromagnetic force. For the proton-proton collision in the Large Hadron Collider, the energy Ecm measured by an observer who is at rest with respect to the centre of mass frame, which is called centre-of-mass (CM) energy and denoted as Ecm, becomes as high as 14 tera electron volts (TeV). This is 15,000 times the rest mass energy of proton approximately.

Black holes have gravitational force strong enough to trap light rays. The boundary behind which no light ray can escape to infinity is called an event horizon. Since gravitational force acts on both charged and neutral particles, black holes can accelerate not only charged particles but also neutral particles. From such a consideration, it can be regarded as natural that black holes accelerate particles. However, for the Schwarzschild black hole, which is a static spherically symmetric black hole, the CM energy Ecm of two particles of equal rest mass m which have been at rest at infinity can be 2√5mc2 at most, which corresponds to γ = 9 in terms of the relative velocity, and hence it cannot be regarded as a high energy particle accelerator.

In 2009, Ban ̃ados, Silk and West found that Ecm can be arbitrarily high for rotating black holes in the context of dark matter particle annihilation at the galactic centre. It should be noted that the unboundedly high Ecm of particle collision had already been noticed in a different context.. Because of the equivalence principle of general relativity, not only microscopic particles such as electrons, protons, neutrons, ions and molecules but also macroscopic objects such as black holes and compact stars can be accelerated by a rotating black hole with the same gamma factor if the size and mass of those objects are sufficiently small compared to the those of the central black hole.

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