WORLD-CRYSTAL UNCERTAINTY PRINCIPLE AND MICRO BLACK HOLES

2011 ◽  
Vol 20 (10) ◽  
pp. 2003-2007 ◽  
Author(s):  
PETR JIZBA ◽  
HAGEN KLEINERT ◽  
FABIO SCARDIGLI
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Lattice Spacing ◽  
Uncertainty Relation ◽  
Rest Mass ◽  
Uncertainty Relations ◽  
Planck Length ◽  
Temperature Relation ◽  
Black Hole Evaporation ◽  
Mass Temperature

We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of order of Planck length — a "world crystal". For energies near the border of the Brillouin zone, i.e. for Planckian energies, the uncertainty relation for position and momentum does not pose any lower bound. We apply these results to micro black holes physics, where we derive a new mass–temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass–temperature formula predicts both a finite Hawking's temperature and a zero rest-mass remnant at the end of the black hole evaporation.

scholarly journals BLACK HOLE UNCERTAINTIES

1993 ◽  
Vol 08 (20) ◽  
pp. 1925-1941
Author(s):  
ULF H. DANIELSSON
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Wave Functions ◽  
Uncertainty Relations ◽  
Two Dimensional ◽  
Black Hole Mass ◽  
Dilaton Black Holes

In this work the quantum theory of two-dimensional dilaton black holes is studied using the Wheeler-De Witt equation. The solutions correspond to wave functions of the black hole. It is found that for an observer inside the horizon, there are uncertainty relations for the black hole mass and a parameter in the metric determining the Hawking flux. Only for a particular value of this parameter can both be known with arbitrary accuracy. In the generic case there is instead a relation that is very similar to the so-called string uncertainty relation.

scholarly journals Black hole evaporation in Hořava–Lifshitz gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Hao Xu ◽  
Yen Chin Ong
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Lorentz Invariance ◽  
Detailed Balance ◽  
Einstein Gravity ◽  
Zero Temperature ◽  
Black Hole Mass ◽  
Black Hole Evaporation ◽  
Higher Derivative ◽  
Temperature State

Abstract Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter $$0\leqslant \epsilon ^2\leqslant 1$$0⩽ϵ2⩽1. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $$d=4,5$$d=4,5 behave differently from $$d\geqslant 6$$d⩾6. For the case of $$\epsilon =0$$ϵ=0, in $$d=4,5$$d=4,5, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As $$d\geqslant 6$$d⩾6, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of $$\ell ^{d-1}$$ℓd-1, similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to $$\epsilon ^2=1$$ϵ2=1), though for the latter this holds for all $$d\geqslant 4$$d⩾4. The case of $$0<\epsilon ^2<1$$0<ϵ2<1 is also qualitatively similar with $$\epsilon =0$$ϵ=0.

Hawking radiation of charged fermions from accelerating and rotating black holes with generalized uncertainty principle

2019 ◽  
Vol 28 (08) ◽  
pp. 1950102
Author(s):  
Muhammad Rizwan ◽  
Khalil Ur Rehman
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Hawking Temperature ◽  
Black Hole Evaporation ◽  
Rotating Black Holes ◽  
Gravity Effects ◽  
Made In

By considering the quantum gravity effects based on generalized uncertainty principle, we give a correction to Hawking radiation of charged fermions from accelerating and rotating black holes. Using Hamilton–Jacobi approach, we calculate the corrected tunneling probability and the Hawking temperature. The quantum corrected Hawking temperature depends on the black hole parameters as well as quantum number of emitted particles. It is also seen that a remnant is formed during the black hole evaporation. In addition, the corrected temperature is independent of an angle [Formula: see text] which contradicts the claim made in the literature.

scholarly journals INFORMATION STORAGE IN BLACK HOLES

2005 ◽  
Vol 14 (12) ◽  
pp. 2251-2255 ◽  
Author(s):  
M. D. MAIA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Information Loss ◽  
Information Storage ◽  
Evaporation Process ◽  
Black Hole Evaporation ◽  
Information Loss Paradox

The information loss paradox for Schwarzschild black holes is examined, using the ADS/CFT correspondence extended to the M6(4, 2) bulk. It is found that the only option compatible with the preservation of the quantum unitarity is when a regular remnant region of the black hole survives to the black hole evaporation process, where information can be stored and eventually retrieved.

scholarly journals Planckian physics comes into play at Planckian distance from horizon

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pei-Ming Ho ◽  
Hikaru Kawai ◽  
Yuki Yokokura
Keyword(s):  
Black Hole ◽  
Gravitational Collapse ◽  
Hawking Radiation ◽  
Effective Theory ◽  
Planck Length ◽  
Black Hole Evaporation ◽  
Higher Derivative ◽  
The Creation ◽  
Transition Amplitudes

Abstract In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow exponentially with time and become of order 1 when the collapsing matter is about a Planck length outside the horizon. As a result, the effective theory breaks down at the scrambling time, invalidating its prediction of Hawking radiation. Planckian physics comes into play to decide the fate of black-hole evaporation.

scholarly journals Back-Reaction in Canonical Analogue Black Holes

2020 ◽  
Vol 10 (24) ◽  
pp. 8868
Author(s):  
Stefano Liberati ◽  
Giovanni Tricella ◽  
Andrea Trombettoni
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Density Distribution ◽  
Hawking Radiation ◽  
Einstein Condensate ◽  
Back Reaction ◽  
Unitary Evolution ◽  
Black Hole Evaporation ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We study the back-reaction associated with Hawking evaporation of an acoustic canonical analogue black hole in a Bose–Einstein condensate. We show that the emission of Hawking radiation induces a local back-reaction on the condensate, perturbing it in the near-horizon region, and a global back-reaction in the density distribution of the atoms. We discuss how these results produce useful insights into the process of black hole evaporation and its compatibility with a unitary evolution.

scholarly journals Black hole event horizons — Teleology and predictivity

2017 ◽  
Vol 32 (34) ◽  
pp. 1750186
Author(s):  
Swastik Bhattacharya ◽  
S. Shankaranarayanan
Keyword(s):  
Boundary Condition ◽  
Black Holes ◽  
Black Hole ◽  
Black Hole Thermodynamics ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Black Hole Evaporation ◽  
Spacetime Manifold ◽  
Statistical Mechanical ◽  
Late Stages

General Relativity predicts the existence of black holes. Access to the complete spacetime manifold is required to describe the black hole. This feature necessitates that black hole dynamics is specified by future or teleological boundary condition. Here, we demonstrate that the statistical mechanical description of black holes, the raison d’être behind the existence of black hole thermodynamics, requires teleological boundary condition. Within the fluid–gravity paradigm — Einstein’s equations when projected on spacetime horizons resemble Navier–Stokes equation of a fluid — we show that the specific heat and the coefficient of bulk viscosity of the horizon fluid are negative only if the teleological boundary condition is taken into account. We argue that in a quantum theory of gravity, the future boundary condition plays a crucial role. We briefly discuss the possible implications of this at late stages of black hole evaporation.

Thermal relativity, modified Hawking radiation, and the generalized uncertainty principle

2019 ◽  
Vol 16 (10) ◽  
pp. 1950156
Author(s):  
Carlos Castro Perelman
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Black Hole Entropy ◽  
The Novel ◽  
Black Hole Information ◽  
The One ◽  
Mini Black Holes

After a brief review of the thermal relativistic corrections to the Schwarzschild black hole entropy, it is shown how the Stefan–Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do not completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald’s entropy should, in principle, determine the functional form of the modified gravitational Lagrangian [Formula: see text]. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature [Formula: see text] associated with thermal relativity and given in terms of the Hawking ([Formula: see text]) and Planck ([Formula: see text]) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of [Formula: see text]. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

scholarly journals Gravitational crystal inside the black hole

2015 ◽  
Vol 30 (37) ◽  
pp. 1550201 ◽  
Author(s):  
Hrvoje Nikolić
Keyword(s):  
Black Hole ◽  
Lattice Spacing ◽  
Planck Scale ◽  
Fluid Phase ◽  
Crystal Phase ◽  
Planck Length ◽  
Quantum Objects ◽  
Gravity Effects ◽  
Natural Mechanism ◽  
Black Hole Information

Crystals, as quantum objects typically much larger than their lattice spacing, are counterexamples to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.

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