Microscopic Black Holes as a Source of Ultrahigh Energy γ-rays

We investigate the idea that ultrahigh energy γ-rays (E > 10TeV) can be produced when charged particles are accelerated by microscopic black holes. We begin by showing that microscopic black holes may exist as remnants of primordial black holes or as products of the collisions in the large extra dimensions scenario of high energy cosmic rays with atmospheric particles. We then solve Maxwell’s equations on curved spacetime backgrounds in 4, 5 and 6 dimensions and use the solutions to calculate the energy distributions. From the latter we obtain the black hole parameters needed to produce the energies of the observed γ-rays. INTRODUCTION The existence of cosmological black holes with masses of 10−108 solar masses is now an accepted fact. The existence of microscopic black holes with masses of 1−10 Planck masses has not been established, but their existence is of great theoretical interest. If they do exist, there is the possibility that they could be probed experimentally to obtain information about quantum gravity. One possible source of such microscopic black holes is primordial black holes, which have reached Planck-size masses during the present epoch through emission of Hawking radiation. Another possible source is microscopic black hole production. The recent proposal of the existence of large extra dimensions [1] and the consequent lowering of the fundamental energy scale to 1 TeV implies that microscopic black holes can be created in accelerators [2] whose center of mass energies are above the fundamental energy scale. Microscopic black holes would also be produced in the collisions of ultrahigh energy cosmic rays with the Earth’s atmosphere [3]. In this talk we describe one of the signatures of black holes impinging upon the Earth’s atmosphere: ultrahigh energy γ-rays. As of yet there is no firm evidence that such emissions are occurring in our atmosphere, but there is some evidence for γ-rays with energies greater than 100 TeV at the 1.6 σ -level from unknown sources within the galatic plane[4]. A charged particle being accelerated by a black hole can produce γ-rays with energies in the multi-TeV range before the particle passes beyond the horizon radius provided that the curvature gradient of the space around the black hole is large enough. Such curvature gradients occur in quantum black holes, black holes whose masses are of the order the Planck mass. A calculation taking into account special relativity (but not general relativity) shows us that to produce γ-ray energies in the 10 TeV range a single electronic charge would have to be accelerated by a black hole with a mass equal to five times that of the Planck mass. The microscopic black holes needed to produce ultrahigh γ-rays may be the remnants of primordial black holes. Such black holes can be produced by • Inflationary horizon-scale fluctuations • Density fluctuations at phase transitions and bubble formation and collapse • Baryon isocurvature fluctuations on small scales. Large-mass primordial black holes (M > 1015 gm) decaying via Hawking radiation [5] as described by the canonical ensemble in 4 space-time dimensions, (dM/dt)∼−M−2, would have decayed to a Planck-size mass in the present epoch. Microscopic black holes produced in this manner could be stable if quantum gravity effects terminate the decay process. Copious microscopic black hole production can also occur if large extra dimensions exist. In this scenario black hole production can occur as the result of the collision of particles with total center of mass energy above the effective Planck scale, which can be as low as the electroweak scale mew ∼ 1TeV. Black holes could thus be produced in collisions of high energy cosmic rays with the Earth’s atmosphere. As we show in the next Section, such black holes may live long enough to create ultrahigh γ-rays even without taking quantum gravity effects into account. BLACK HOLES AND LARGE EXTRA DIMENSIONS In a 4-dimensional space-time, a black hole might emerge from the collision of two particles only if its center of mass energy exceeds the Planck mass mp (lp will denote the Planck length). In fact, the Compton wavelength lM = lp (mp/M) of a point-like particle of mass M < mp would be smaller than the gravitational radius RH = 2GN M = 2(lp/mp)M and the very (classical) concept of a black hole would lose its meaning. However, since the fundamental mass scale is shifted down to mew in the models under consideration, black holes with M ≪ mp can now exist as classical objects provided lp (mp/M) ≪ RH ≪ L , (1) where L is the scale at which corrections to the Newtonian potential become effective. The left hand inequality ensures that the black hole behaves semiclassically, and one does not need a full-fledged theory of quantum gravity, while the right hand inequality guarantees that the black hole is small enough that its gravitational field can depart from the Newtonian behavior without contradicting present experiments. The luminosity of a black hole in D space-time dimensions is given by L (D)(M) = (D) ∫ ∞ 0 S ∑ s=1 n (D) (ω)Γ (s) (D) (ω)ωD−1 dω (2) where A (D) is the horizon area in D space-time dimensions, Γ (s) (D) the corresponding grey-body factor and S the number of species of particles that can be emitted. For the sake of simplicity, we shall approximate ∑s Γ(s) (D) as a constant. The distribution n(D) is the microcanonical number density [6, 7, 8] n(D)(ω) = C [[M/ω]] ∑ l=1 exp [ SE (D)(M− l ω)−S E (D)(M) ]