Horizon wave function for single localized particles: GUP and quantum black-hole decay (original) (raw)
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Horizon Wave-Function: From Particles to Black Holes
2016
Localised Quantum Mechanical particles are described by wave packets in position space, regardless of their energy. From a General Relativistic point of view, when a particle’s energy density is larger than a certain threshold, the particle should be a black hole. We combine these two pictures by introducing a horizon wavefunction determined by the particle wave-function in position space, which is used to compute the probability that the particle is a black hole. The sources are modelled as simple Gaussian wave-packets and using the horizon wave-function formalism we calculate the probability for these particles to be Schwarzschild black holes, respectively Reissner-Nordstrom black holes (in the case of charged particles). We also derive an effective Generalised Uncertainty Principle (GUP), which is obtained by adding the uncertainties coming from the two wave-functions associated to the particle.
Black Hole Production in the Presence of a Maximal Momentum in Horizon Wave Function Formalism
International Journal of Geometric Methods in Modern Physics
We study the Horizon Wave Function (HWF) description of a generalized uncertainty principle (GUP) black hole in the presence of two natural cutoffs as a minimal length and a maximal momentum. This is motivated by a metric which allows the existence of sub-Planckian black holes, where the black hole mass [Formula: see text] is replaced by [Formula: see text]. Considering a wave-packet with a Gaussian profile, we evaluate the HWF and the probability that the source might be a (quantum) black hole. By decreasing the free parameter, the general form of probability distribution, [Formula: see text], is preserved, but this resulted in reducing the probability for the particle to be a black hole accordingly. The probability for the particle to be a black hole grows when the mass is increasing slowly for larger positive [Formula: see text], and for a minimum mass value it reaches to [Formula: see text]. In effect, for larger [Formula: see text] the magnitude of [Formula: see text] and [Form...
Generalized uncertainty principle and black hole thermodynamics
General Relativity and Gravitation, 2014
In the current standard viewpoint small black holes are believed to emit black body radiation at the Hawking temperature, at least until they approach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncertainty principle prevents the hydrogen atom from total collapse: the collapse is prevented, not by symmetry, but by dynamics, as a minimum size and mass are approached. *Winner of 3rd place in the 2001 Gravity Research Foundation essay competition *Work supported by DOE Contract DE-AC03-76SF00515.
Horizon quantum mechanics: A hitchhiker’s guide to quantum black holes
International Journal of Modern Physics D, 2016
It is congruous with the quantum nature of the world to view the spacetime geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the spacetime manifold as a purely theoretical arena, where quantum states are defined, with the additional freedom of changing coordinates like any other symmetry. Observables, including positions and distances, should then be described by suitable operators acting on such quantum states. In principle, the top-down (canonical) quantization of Einstein–Hilbert gravity falls right into this picture, but is notoriously very involved. The complication stems from allowing all the classical canonical variables that appear in the (presumably) fundamental action to become quantum observables acting on the “superspace” of all metrics, regardless of whether they play any role in the description of a specific physical system. On can instead revisit the more humble “minisuperspace” approach and choose ...
Generalized Uncertainty Principle and Self-dual Black Holes
Arxiv preprint arXiv:1107.0708, 2011
The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the black hole event horizon ...
Sub-Planckian black holes and the Generalized Uncertainty Principle
Journal of High Energy Physics, 2015
The Black Hole Uncertainty Principle correspondence suggests that there could exist black holes with mass beneath the Planck scale but radius of order the Compton scale rather than Schwarzschild scale. We present a modified, self-dual Schwarzschild-like metric that reproduces desirable aspects of a variety of disparate models in the sub-Planckian limit, while remaining Schwarzschild in the large mass limit. The self-dual nature of this solution under M ↔ M −1 naturally implies a Generalized Uncertainty Principle with the linear form ∆x ∼ 1 ∆p + ∆p. We also demonstrate a natural dimensional reduction feature, in that the gravitational radius and thermodynamics of sub-Planckian objects resemble that of (1 + 1)-D gravity. The temperature of sub-Planckian black holes scales as M rather than M −1 but the evaporation of those smaller than 10 −36 g is suppressed by the cosmic background radiation. This suggests that relics of this mass could provide the dark matter.
Speculation about the Black Hole Final State: Resolving Singularity by Quantum Gravity
Proceedings of The International Conference on Beyond Standard Model: From Theory To Experiment, 2021
The interior of the black hole can be described by anisotropic cosmology. By quantizing the metric function, we can obtain the Wheeler-DeWitt equation for inside the horizon. In order to interpret the wave function consistently, one needs to impose a boundary condition. In this paper, we introduce a prescription for the Euclidean analytic continuation inside the horizon and the corresponding wave function solution.
Wave function of the quantum black hole
Physics Letters B, 2012
We show that the Wald Noether charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation we extend the Wheeler-DeWitt equation to a Schrödinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2π indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.
Towards a Theory of Quantum Black Holes
International Journal of Modern Physics A, 2002
We describe some specific quantum black hole model. It is pointed out that the origin of a black hole entropy is the very process of quantum gravitational collapse. The quantum black hole mass spectrum is extracted from the mass spectrum of the gravitating source. The classical analog of quantum black hole is constructed.
Journal of Cosmology and Astroparticle Physics, 2013
We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible.