Black holes as self-sustained quantum states and Hawking radiation (original) (raw)
Related papers
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.
Annihilation-to-nothing: a quantum gravitational boundary condition for the Schwarzschild black hole
JCAP 11 (2020) 002, 2020
The interior of a static Schwarzschild metric can be written in terms of two functions, similar to some models of anisotropic cosmology. With a suitable choice of canonical variables, we solve the Wheeler-DeWitt equation (WDW) inside the horizon of a Schwarzschild black hole. By imposing classicality near the horizon, and requiring boundedness of the wave function, we get a rather generic solution of the WDW equation, whose steepest-descent solution, i.e., the ridge of the wave function, coincides nicely with the classical trajectory. However, there is an ambiguity in defining the arrow of time which leads to two possible interpretations — (i) if there is only one arrow of time, one can infer that the steepest-descent of the wave function follows the classical trajectory throughout: coming from the event horizon and going all the way down to the singularity, while (ii) if there are two different arrows of time in two separate regimes, it can be inferred that the steepest- descent of the wave function comes inwards from the event horizon in one region while it moves outwards from the singularity in the other region, and there exists an annihilation process of these two parts of the wave function inside the horizon. Adopting the second interpretation could shed light on the information loss paradox: as time goes on, probabilities for histories that include black holes and singularities decay to zero and eventually only trivial geometries dominate.
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.
Quantum Black Hole Model and Hawking's Radiation", Preprint INR 0916/96, e-print gr-qc/9602020
2013
The black hole model with a self-gravitating charged spherical symmetric dust thin shell as a source is considered. The Schroedinger-type equation for such a model is derived. This equation appeared to be a finite differences equation. A theory of such an equation is developed and general solution is found and investigated in details. The discrete spectrum of the bound state energy levels is obtained. All the eigenvalues appeared to be infinitely degenerate. The ground state wave functions are evaluated explicitly. The quantum black hole states are selected and investigated. It is shown that the obtained black hole mass spectrum is compatible with the existence of Hawking’s radiation in the limit of low temperatures both for large and nearly extreme Reissner-Nordstrom black holes. The above mentioned infinite degeneracy of the mass (energy) eigenvalues may appeared helpful in resolving the well known information paradox in the black hole physics. 1 I.Introduction. The fate of black ...
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.
Quantum Mechanical Black Holes: Towards a Unification of Quantum Mechanics and General Relativity
1998
In this paper, starting from vortices we are finally lead to a treatment of Fermions as Kerr-Newman type Black Holes wherein we identify the horizon at the particle's Compton wavelength periphery. A naked singularity is avoided and the singular processes inside the horizon of the Black Hole are identified with Quantum Mechanical effects within the Compton wavelength. Inertial mass, gravitation,
Quantum oscillations in the black hole horizon
Theoretical and Mathematical Physics, 2022
By applying Rosen's quantization approach to the historical Oppenheimer and Snyder gravitational collapse and by setting the constraints for the formation of the Schwarzschild black hole (SBH), in a previous paper [1] two of the Authors (CC and FF) found the gravitational potential, the Schrödinger equation, the solution for the energy levels, the area quantum and the quantum representation of the ground state at the Planck scale of the SBH. Such results are consistent with previous ones in the literature. It was also shown that the traditional classical singularity in the core of the SBH is replaced by a quantum oscillator describing a non-singular two-particle system where the two components, named the "nucleus" and the "electron", strongly interact with each other through a quantum gravitational interaction. In agreement with the de Broglie hypothesis, the "electron" is interpreted in terms of the quantum oscillations of the BH horizon. In other words, the SBH should be the gravitational analogous of the hydrogen atom. In this paper, it is shown that these results allow us to compute the SBH entropy as a function of the BH principal quantum number in terms of Bekenstein-Hawking entropy and three sub-leading corrections. In addition, the coefficient of the formula of Bekenstein-Hawking entropy is reduced to a quarter of the traditional value. Then, it is shown that, by performing a correct rescaling of the energy levels, the semi-classical Bohr-like approach to BH quantum physics, previously developed by one of the Authors (CC), is consistent with the obtained results for large values of the BH principal quantum number. After this, Hawking radiation will be analysed by discussing its connection with the BH quantum structure. Finally, it is shown that the time evolution of the above mentioned system solves the BH information paradox.
Classical analogue of a quantum Schwarzschild black hole: “Standard model” and beyond
Theoretical and Mathematical Physics, 2012
We build a model in which the main global properties of classical and semiclassical black holes become local: these are the event horizon, "no-hair," temperature, and entropy. Our construction is based on the features of a quantum collapse, discovered when studying some particular quantum black hole models. But our model is purely classical, and this allows using the Einstein equations and classical (local) thermodynamics self-consistently and, in particular, solving the "puzzle of log 3.
Black Hole as a Quantum Field Configuration
Universe, 2020
We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation G μ ν = 8 π G ⟨ ψ | T μ ν | ψ ⟩ and quantum matter fields in a self-consistent manner. As the matter fields, we consider N massless free scalar fields (N is large). We find a spherically symmetric self-consistent solution of the metric g μ ν and the state | ψ ⟩ . Here, g μ ν is locally A d S 2 × S 2 geometry, and | ψ ⟩ provides ⟨ ψ | T μ ν | ψ ⟩ = ⟨ 0 | T μ ν | 0 ⟩ + T μ ν ( ψ ) , where | 0 ⟩ is the ground state of the matter fields in the metric and T μ ν ( ψ ) consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure ⟨ 0 | T θ θ | 0 ⟩ due to the vacuum fluctuation of the bound modes with large angular momenta l ≫ 1 . This describes the interior of the black hole when the back reaction of the evaporation is taken into account. In this...
Universe
We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.