Massive fermion emission from higher dimensional black holes

Abstract

We study the effect of extra dimensions on the process of massive Dirac fermion emission in the spacetime of (4 + n)-dimensional black hole, by examining the Dirac operator in arbitrary spacetime dimension. We comment on both bulk and brane emission and find absorption cross section and luminosity of Hawking radiation in the low-energy approximation.PACS numbers: 04.50.+h, 04.70.Dy I. INTRODUCTIONScientists have devoted many years to the ongoing quest to unify the forces in Nature. Higher-dimensional theories provide a promising framework for the unification of gravitation with other fundamental forces. In this context braneworld models [1,2] with large extra dimensions point us the way out of the long standing hierarchy problem by lowering the fundamental scale of gravity down to order of TeV. It has been also argued that mini black holes might be created through high-energy particle collisions at TeV-energy scales. These objects are expected to evaporate through Hawking radiation both in the bulk as well as on the brane. Mini black holes created in high-energy collisions will undergo a number of phases, i.e. balding phase when black hole will emit mainly gravitational radiation, spindown phase during which black hole will loose its angular momentum through emission of Hawking radiation and Schwarzschild phase in which black hole will lose its actual mass by Hawking radiation. Finally in Planck phase quantum gravity theory is needed to study its behaviour. The TeV scale gravity opens up the possibility of producing black holes and observing their decay product. The aforementioned range of energy will be soon achieved by CERN Large Hadron Collider. One hopes that it proves or merely restricts the parameter range (e.g., number or size of extra dimensions) of higher dimensional theories.Studies of particle emission from multidimensional black hole have their own long history. Namely, in Ref.[3] massless scalar emission were studied in the spacetime of (4 + n)-dimensional Schwarzschild black hole while the case of massless spinor and gauge particles was treated in [4]. Then, radiation emitted from higher-dimensional black holes were considered both analytically and numerically (see, e.g., Refs.[5]-[8] for a non-exhaustive sampling of this widely treated subject). On the other hand, graviton emission in the bulk from a higher dimensional Schwarzschild black hole was elaborated in Refs. [9], where it was established that the low-energy emission rate decreases with the number of extra-dimensions as was previously found for the case of bulk massless scalar field.The complexity of the aforementioned problem in the background of a rotating (4 + n)-dimensional black hole was revealed in Refs. [10]. The argument of the effect of mass on the emission spectrum in four-dimensions was quoted in [11] (see also [12] where the particle and light motion in the vicinity of five-dimensional rotating black hole was investigated). In Ref.[13] the scalar massless Hawking emission into the bulk by a higher dimensional rotating black hole...

Fermionic greybody factors of two and five-dimensional dilatonic black holes

“…For this spacetime it was also revealed that the absorption probability depended on mass of the emitted field, that is, the absorption probability decreases or increases depending on the range of energy when the mass of the field increases. Also, was observed that the absorption probability increases for higher radius of the event horizon [29].…”

“…As we mentioned, the reflection and transmission coefficients depend on the behaviour of the radial function both, at the horizon and at the asymptotic infinity and they are defined by (28) where F is the flux, and is given by (29), and yields…”

“…The factors that modify the spectrum emitted by a black hole are known as greybody factors and can be obtained through the classical scattering; therefore its study allows to increase the semiclassical gravity dictionary, and also permits to gain insight into the quantum nature of black holes and, thus, of quantum gravity, for an excellent review about this topic see [26]. Also, see for instance [27][28][29], for decay of Dirac fields in higher dimensional black holes. In the present work, the reflection and the transmission coefficients, and the greybody factors of two-dimensional stringy black holes ( [1,30]) and five-dimensional black holes [2] for fermionic fields are computed.…”

Greybody factors of massive charged fermionic fields in a charged two-dimensional dilatonic black hole

“…For this spacetime, it was also revealed that the absorption probability depended on the mass of the emitted field, that is, the absorption probability decreases or increases depending on the range of energy when the mass of the field increases. Also, it has been observed that the absorption probability increases for higher radii of the event horizon [29]; see for instance [30,31] for the decay of Dirac fields in higher-dimensional black holes. For further reference, massive charged scalar field perturbations of the Kerr-Newman black hole background were studied in [32,33], the absorption of photons and fermions by black holes in four-dimensions in [34], the fermion absorption cross section of a Schwarzschild black hole in [35], and charged fermionic perturbations in the Reissner-Nordstrom anti-de Sitter black hole background in [36].…”

New modes for massive Dirac field in higher-dimensional black holes

“…[28,29,30] by solving the massive Dirac equation in the background of a Schwarzschild (4 + n) higher-dimensional black hole, using a different gauge technique than the ones used there. We chose to work in the so called Cartesian gauge proposed some time ago in Ref.…”