BLACK HOLES, THE GENERALIZED UNCERTAINTY PRINCIPLE AND HIGHER DIMENSIONS

2013 ◽  
Vol 28 (03) ◽  
pp. 1340011 ◽  
Author(s):  
B. J. CARR
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Uncertainty Principle ◽  
Black Hole Solution ◽  
Generalized Uncertainty Principle ◽  
Black Hole Mass ◽  
Compton Wavelength ◽  
Planck Mass ◽  
Spatial Dimensions

We propose a new way in which black holes connect macrophysics and microphysics. The Generalized Uncertainty Principle suggests corrections to the Uncertainty Principle as the energy increases towards the Planck value. It also provides a natural transition between the expressions for the Compton wavelength below the Planck mass and the black hole event horizon size above it. This suggests corrections to the event horizon size as the black hole mass falls towards the Planck value, leading to the concept of a Generalized Event Horizon. Extrapolating this expression below the Planck mass suggests the existence of a new kind of black hole, whose size is of order its Compton wavelength. Recently it has been found that such a black hole solution is permitted by loop quantum gravity, its unusual properties deriving from the fact that it is hidden behind the throat of a wormhole. This has important implications for the formation and evaporation of black holes in the early Universe, especially if there are extra spatial dimensions.

Thermodynamic studies of 5D Myers–Perry black holes: General uncertainty principle approach

2019 ◽  
Vol 35 (07) ◽  
pp. 2050029
Author(s):  
Amritendu Haldar ◽  
Ritabrata Biswas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Uncertainty Principle ◽  
Black Hole Solution ◽  
Generalized Uncertainty Principle ◽  
Stability Criteria ◽  
Temperature Growth

In this paper, we consider the five-dimensional Myers–Perry black hole solution to study the thermodynamic properties and compare this with the thermodynamic behaviors of generalized uncertainty principle (GUP)-induced Myers–Perry solution. We study the existence of remnant quantities. Stability criteria are studied by observing the natures of temperature growth and sign changes in specific heat. We try to locate phase transitions. Moreover, we study the corresponding physical range for the GUP parameter and try to justify the value with the data predicted by different observations.

scholarly journals Does Compton–Schwarzschild duality in higher dimensions exclude TeV quantum gravity?

2018 ◽  
Vol 27 (16) ◽  
pp. 1930001 ◽  
Author(s):  
Matthew J. Lake ◽  
Bernard Carr
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Wave Function ◽  
Quantum Gravity ◽  
Extra Dimensions ◽  
Planck Length ◽  
Compton Wavelength ◽  
Planck Mass ◽  
Higher Dimensional ◽  
Spatial Dimensions

In three spatial dimensions, the Compton wavelength [Formula: see text]) and Schwarzschild radius [Formula: see text]) are dual under the transformation [Formula: see text], where [Formula: see text] is the Planck mass. This suggests that there could be a fundamental link — termed the Black Hole Uncertainty Principle or Compton–Schwarzschild correspondence — between elementary particles with [Formula: see text] and black holes in the [Formula: see text] regime. In the presence of [Formula: see text] extra dimensions, compactified on some scale [Formula: see text] exceeding the Planck length [Formula: see text], one expects [Formula: see text] for [Formula: see text], which breaks this duality. However, it may be restored in some circumstances because the effective Compton wavelength of a particle depends on the form of the [Formula: see text]-dimensional wave function. If this is spherically symmetric, then one still has [Formula: see text], as in the [Formula: see text]-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function of a particle is asymmetric and has a scale [Formula: see text] in the extra dimensions, then [Formula: see text], so that the duality between [Formula: see text] and [Formula: see text] is preserved. In this case, the effective Planck length is increased even more but the Planck mass is unchanged, so that TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below [Formula: see text]. Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from [Formula: see text]-particle scattering amplitudes.

scholarly journals Horizon Wavefunction of Generalized Uncertainty Principle Black Holes

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Luciano Manfredi ◽  
Jonas Mureika
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Free Parameter ◽  
Generalized Uncertainty Principle ◽  
Minimum Mass ◽  
Black Hole Mass ◽  
General Shape ◽  
Quantum Black Hole ◽  
Horizon Radius

We study the Horizon Wavefunction (HWF) description of a Generalized Uncertainty Principle inspired metric that admits sub-Planckian black holes, where the black hole mass m is replaced by M=m1+β/2MPl2/m2. Considering the case of a wave-packet shaped by a Gaussian distribution, we compute the HWF and the probability PBH that the source is a (quantum) black hole, that is, that it lies within its horizon radius. The case β<0 is qualitatively similar to the standard Schwarzschild case, and the general shape of PBH is maintained when decreasing the free parameter but shifted to reduce the probability for the particle to be a black hole accordingly. The probability grows with increasing mass slowly for more negative β and drops to 0 for a minimum mass value. The scenario differs significantly for increasing β>0, where a minimum in PBH is encountered, thus meaning that every particle has some probability of decaying to a black hole. Furthermore, for sufficiently large β we find that every particle is a quantum black hole, in agreement with the intuitive effect of increasing β, which creates larger M and RH terms. This is likely due to a “dimensional reduction” feature of the model, where the black hole characteristics for sub-Planckian black holes mimic those in (1+1) dimensions and the horizon size grows as RH~M-1.

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 The shadow of M87∗ black hole within rational nonlinear electrodynamics

2020 ◽  
Vol 35 (35) ◽  
pp. 2050291
Author(s):  
S. I. Kruglov
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Event Horizon ◽  
Magnetic Charge ◽  
Nonlinear Electrodynamics ◽  
Black Hole Mass

We consider rational nonlinear electrodynamics with the Lagrangian [Formula: see text] ([Formula: see text] is the Lorentz invariant), proposed in Ref. 63, coupled to General Relativity. The effective geometry induced by nonlinear electrodynamics corrections are found. We determine shadow’s size of regular non-rotating magnetic black holes and compare them with the shadow size of the super-massive M87[Formula: see text] black hole imaged by the Event Horizon Telescope collaboration. Assuming that the black hole mass has a pure electromagnetic nature, we obtain the black hole magnetic charge. The size of the shadow obtained is very close to the shadow size of non-regular neutral Schwarzschild black holes. As a result, we can interpret the super-massive M87[Formula: see text] black hole as a regular (without singularities) magnetized black hole.

scholarly journals Thermodynamics of a Non-Stationary Black Hole Based on Generalized Uncertainty Principle

2017 ◽  
Vol 1 (2) ◽  
pp. 127
Author(s):  
Mustari Mustari ◽  
Yuant Tiandho
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Correction Term ◽  
Apparent Horizon ◽  
Generalized Uncertainty Principle ◽  
Minimum Length ◽  
Theory Of Relativity ◽  
Stationary Black Hole ◽  
Gravitational Fields

In the general theory of relativity (GTR), black holes are defined as objects with very strong gravitational fields even light can not escape. Therefore, according to GTR black hole can be viewed as a non-thermodynamic object. The worldview of a black hole began to change since Hawking involves quantum field theory to study black holes and found that black holes have temperatures that analogous to black body radiation. In the theory of quantum gravity there is a term of the minimum length of an object known as the Planck length that demands a revision of Heisenberg's uncertainty principle into a Generalized Uncertainty Principle (GUP). Based on the relationship between the momentum uncertainty and the characteristic energy of the photons emitted by a black hole, the temperature and entropy of the non-stationary black hole (Vaidya-Bonner black hole) were calculated. The non-stationary black hole was chosen because it more realistic than static black holes to describe radiation phenomena. Because the black hole is dynamic then thermodynamics studies are conducted on both black hole horizons: the apparent horizon and its event horizon. The results showed that the dominant correction term of the temperature and entropy of the Vaidya-Bonner black hole are logarithmic.

scholarly journals Minimal length and the flow of entropy from black holes

2018 ◽  
Vol 27 (14) ◽  
pp. 1847028 ◽  
Author(s):  
Ana Alonso-Serrano ◽  
Mariusz P. Da̧browski ◽  
Hussain Gohar
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Hawking Radiation ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Evaporation Process ◽  
Black Hole Evaporation ◽  
The Impact

The existence of a minimal length, predicted by different theories of quantum gravity, can be phenomenologically described in terms of a generalized uncertainty principle. We consider the impact of this quantum gravity motivated effect onto the information budget of a black hole and the sparsity of Hawking radiation during the black hole evaporation process. We show that the information is not transmitted at the same rate during the final stages of the evaporation, and that the Hawking radiation is not sparse anymore when the black hole approaches the Planck mass.

scholarly journals Thermodynamics of the Schwarzschild and Reissner–Nordström black holes under the Snyder–de Sitter model

2019 ◽  
Vol 79 (11) ◽  
Author(s):  
H. Hassanabadi ◽  
E. Maghsoodi ◽  
Won Sang Chung ◽  
M. de Montigny
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
De Sitter ◽  
Schwarzschild Black Hole ◽  
Temperature Relation ◽  
Corrected Entropy ◽  
Sitter Model ◽  
De Sitter Model

AbstractThis paper examines the effects of a new form of the extended generalized uncertainty principle in the Snyder–de Sitter model on the thermodynamics of the Schwarzschild and Reissner–Nordström black holes. Firstly, we present a generalization of the minimal length uncertainty relation with two deformation parameters. Then we obtain the corrected mass–temperature relation, entropy and heat capacity for Schwarzschild black hole. Also we investigate the effect of the corrected uncertainty principle on the thermodynamics of the charged black holes. Our discussion of the corrected entropy involves a heuristic analysis of a particle which is absorbed by the black hole. Finally, we compare the thermodynamics of a charged black hole with the thermodynamics of a Schwarzschild black hole and with the usual forms, that is, without corrections to the uncertainty principle.

scholarly journals Orbifold black holes

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Muneto Nitta ◽  
Kunihito Uzawa
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Event Horizon ◽  
Black Hole Solution ◽  
Maxwell Theory ◽  
Regular Black Hole

AbstractWe construct a regular black hole solution on the orbifold $${\mathbb C}^{n}/{\mathbb Z}_{n}$$ C n / Z n in the ($$2n+1$$ 2 n + 1 )-dimensional Einstein–Maxwell theory. The event horizon is $$S^{2n-1}/{\mathbb Z}_{n}$$ S 2 n - 1 / Z n .

scholarly journals The Effects of Minimal Length, Maximal Momentum, and Minimal Momentum in Entropic Force

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang ◽  
Hui-Ling Li ◽  
Xiao-Tao Zu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Friedmann Equation ◽  
Minimal Length ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Maximal Momentum

The modified entropic force law is studied by using a new kind of generalized uncertainty principle which contains a minimal length, a minimal momentum, and a maximal momentum. Firstly, the quantum corrections to the thermodynamics of a black hole are investigated. Then, according to Verlinde’s theory, the generalized uncertainty principle (GUP) corrected entropic force is obtained. The result shows that the GUP corrected entropic force is related not only to the properties of the black holes but also to the Planck length and the dimensionless constantsα0andβ0. Moreover, based on the GUP corrected entropic force, we also derive the modified Einstein’s field equation (EFE) and the modified Friedmann equation.

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