Quasinormal modes of BTZ black hole and Hawking‐like radiation in graphene

Abstract

The Bañados-Teitelboim-Zanelli (BTZ) black hole model corresponds to a solution of (2+1)-dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Beltrami trumpet shaped graphene sheets have been predicted to emit Hawking radiation that is experimentally detectable by a scanning tunnelling microscope. Here, for the first time we present an analytical algorithm that allows variational solutions to the Dirac Hamiltonian of graphene pseudoparticles in BTZ black hole gravitational field by using an approach based on the formalism of pseudo-Hermitian Hamiltonians within a discrete-basis-set method. We show that our model not only reproduces the exact results for the real part of quasinormal mode frequencies of (2+1)-dimensional spinless BTZ black hole, but also provides analytical results for the real part of quasinormal modes of spinning BTZ black hole, and also offers some predictions for the observable effects with a view to gravity-like phenomena in a curved graphene sheet.PACS numbers: 04.62.+v, 72.80.Vp,04.70.Dy After the work of Unruh[1] who first pointed out that quantum fluid systems can be used to create an analogue of a black hole in the laboratory, various analogue gravity systems from superfluid 3 He to ultracold fermions (see e.g. [2]) have been proposed to mimic the Hawking radiation emitted by a black hole. Recently, in a series of papers [3][4][5][6][7] Iorio and Lambiase proposed a Beltrami trumpet shaped graphene as a tabletop experiment for the quantum simulation of a black hole, i.e., an analogue black hole to detect the Hawking-Unruh radiation by a scanning tunneling microscope (STM). The Beltami trumpet shaped graphene can be thought as a deformed graphene that have been wrapped up into a hyperbolic pseudosphere with a constant negative curvature.(2+1)-dimensional (3D) BTZ black hole model[8] with a negative cosmological constant Λ = −1/l 2 exhibits similar thermodynamical properties to those of (3+1)-dimensional Kerr black holes due to having mass (M), angular momentum (J), and inner and outer horizons. Since it was shown by Cvetič and Gibbons [9] that the metric of the BTZ black hole can be mapped onto the Beltrami trumpet, studying the low energy excitations of Dirac pseudoparticles in a Beltrami trumpet shaped graphene surface allows one to study quantum properties of the event horizon and Hawking-like radiation within the BTZ black hole background. The details of this proposal and its implications are discussed in a comprehensive paper of Iorio and Lambiase [7].On the gravity side, the first exact solution of quasinormal modes and associated frequencies for 3D spinless BTZ model were obtained by Cardoso and Lemos [10] and subsequently by Birmingham[11], and to our knowledge no exact or rigorous solutions for quasinormal modes are available for 3D spinning BTZ black hole. It is well known that, instead of normal modes, one should deal with qu...

Hairy BTZ black hole and its analogue model in graphene

“…Therefore, our findings are two-fold. First, the analytical results we obtained for the spinning hairy BTZ black hole do cover the well-known results for the hairless 24 and the non-rotating hairless ones 17,19,[21][22][23] , and thus they are fully consistent with those found in the literature. Here, it is important to note that our results for the real part of QNMs of hairless BTZ black hole obtained an analytical scheme proposed here are fully consistent with those found by Cardaso et al 17 and Birmingham et al 19 even though they used different physical approaches to calculate QNMs of hairless BTZ black hole.…”

“…Therefore, our findings are two-fold. First, the analytical results we obtained for the spinning hairy BTZ black hole do cover the well-known results for the hairless 24 Additionally, due to the conformal relation between the metric of the BTZ black hole and the low energy excitations of Dirac pseudo-particles in a Beltrami shaped graphene, our model developed here allows us to propose an experimental scheme to observe Hawking-like effect in a graphene sheet in the presence of uniform magnetic and electric fields together with a gap opening term. Consequently, we showed theoretically that different electrical and magnetic field profiles induce different hairy black hole regimes, and they can be used experimentally to mimic quantum properties of a 3D BTZ black hole in a laboratuary.…”

“…(1), we plot the dimensionless spin dependence of the resulting mass-like term, i.e., half gap for different values of l which are chosen as to be compatible with those in Ref. [24], and for various of B = 100/ √ M ℓ. It is easy to see from the figure that the resulting gap can be controlled via dimensionless spin.…”

“…In our recent work 24 , we find quasinormal modes of BTZ black hole and proposed a variational approach to the solutions for the associated Dirac Hamiltonian of graphene pseudo-particles in BTZ black hole background. The approach introduced is an attempt to address how the complicated aspects of (2+1)-dimensional gravity can be simulated in a Beltrami trumpet shaped graphene.…”

Quasinormal modes of a Schwarzschild black hole immersed in an electromagnetic universe

“…( 31) that ISBH admits pure imaginary QNMs, which are in good agreement with the QNM result for the Schwarzschild black hole with a global monopole [74]. On the other hand, although it is valid for n → ∞, the QNM result of Hod [80] (see also [81]), which was analytically obtained by the continued-fraction argument method [82] supports also our result (31).…”