scholarly journals Rainbow Gravity Corrections to the Entropic Force

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong-Wen Feng ◽  
Shu-Zheng Yang
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Quantum Gravity ◽  
Gravity Model ◽  
Einstein Field Equation ◽  
Friedmann Equation ◽  
Quantum Corrections ◽  
Entropic Force ◽  
Planck Length ◽  
Multifunctional Properties

The entropic force attracts a lot of interest for its multifunctional properties. For instance, Einstein’s field equation, Newton’s law of gravitation, and the Friedmann equation can be derived from the entropic force. In this paper, utilizing a new kind of rainbow gravity model that was proposed by Magueijo and Smolin, we explore the quantum gravity corrections to the entropic force. First, we derive the modified thermodynamics of a rainbow black hole via its surface gravity. Then, according to Verlinde’s theory, the quantum corrections to the entropic force are obtained. The result shows that the modified entropic force is related not only to the properties of the black hole but also to the Planck length lp and the rainbow parameter γ. Furthermore, based on the rainbow gravity corrected entropic force, the modified Einstein field equation and the modified Friedmann equation are also derived.

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.

scholarly journals Newman-Janis Ansatz for rotating wormholes

2021 ◽  
Vol 2081 (1) ◽  
pp. 012005
Author(s):  
A C Gutiérrez-Piñeres ◽  
N H Beltrán ◽  
C S López-Monsalvo
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Field Equation ◽  
Einstein Equation ◽  
Open Problem ◽  
Einstein Field Equation ◽  
Kerr Black Hole ◽  
Rotating Fluids ◽  
Anisotropic Pressures ◽  
Interior Solutions

Abstract A central problem in General Relativity is obtaining a solution to describe the source’s interior counterpart for Kerr black hole. Besides, determining a method to match the interior and exterior solutions through a surface free of predefined coordinates remains an open problem. In this work, we present the ansatz formulated by the Newman-Janis to generate solutions to the Einstein field equation inspired by the mention problems. We present a collection of independent classes of exact interior solutions of the Einstein equation describing rotating fluids with anisotropic pressures. Furthermore, we will elaborate on some obtained solutions by alluding to rotating wormholes.

Thermodynamics from field equations for charged radiating rotating black hole near horizon

2020 ◽  
Vol 35 (19) ◽  
pp. 2050092
Author(s):  
Uma Papnoi ◽  
Sushant G. Ghosh
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Field Equation ◽  
Thermodynamic Parameters ◽  
Apparent Horizon ◽  
Einstein Field Equation ◽  
Axially Symmetric ◽  
Field Equations ◽  
Rotating Black Hole

It is well known that near horizon black hole space–times show a resemblance to thermodynamic systems, it is easy to associate the thermodynamic parameters like temperature and entropy with them. In this paper, we study the connection between gravitational dynamics of the horizon and thermodynamics for the case of charged radiating rotating axially symmetric black holes. It is shown that Einstein field equation near apparent horizon can be interpreted in the form of thermodynamic law, i.e. [Formula: see text].

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Mathematical Model ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Zero Point ◽  
Space Time ◽  
Planck Length ◽  
Exclusion Zone ◽  
Curvature Perturbation

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GeUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GeUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GeUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

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 Black hole corrections due to minimal length and modified dispersion relation

2015 ◽  
Vol 30 (12) ◽  
pp. 1550059 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Gravity ◽  
Specific Heat ◽  
Friedmann Equation ◽  
Considerable Change ◽  
Standard Entropy ◽  
De Sitter ◽  
Modified Dispersion Relation ◽  
Early Case

The generalized uncertainty principles (GUP) and modified dispersion relations (MDR) are much like two faces for one coin in research for the phenomenology of quantum gravity which apparently plays an important role in estimating the possible modifications of the black hole thermodynamics and the Friedmann equations. We first reproduce the horizon area for different types of black holes and investigate the quantum corrections to Bekenstein–Hawking entropy (entropy-area law). Based on this, we study further thermodynamical quantities and accordingly the modified Friedmann equation in four-dimensional de Sitter–Schwarzschild, Reissner–Nördstrom and Garfinkle–Horowitz–Strominger black holes. In doing this, we applied various quantum gravity approaches. The MDR parameter relative to the GUP one is computed and the properties of the black holes are predicted. This should play an important role in estimating response of quantum gravity to the various metric-types of black holes. We found a considerable change in the thermodynamics quantities. We find that the modified entropy of de Sitter–Schwarzshild and Reissner–Nördstrom black holes starts to exist at a finite standard entropy. The Garfinkle–Horowitz–Strominger black hole shows a different entropic property. The modified specific heat due to GUP and MDR approaches vanishes at large standard specific heat, while the corrections due to GUP result in different behaviors. The specific heat of modified de Sitter–Schwarzshild and Reissner–Nördstrom black holes seems to increase, especially at large standard specific heat. In the early case, the black hole cannot exchange heat with the surrounding space. Accordingly, we would predict black hole remnants which may be considered as candidates for dark matter.

scholarly journals Limits to Seeing High-Redshift Galaxies Due to Planck-Scale-Induced Blurring

2015 ◽  
Vol 11 (S319) ◽  
pp. 54-54
Author(s):  
Eric Steinbring
Keyword(s):  
Random Walk ◽  
Quantum Gravity ◽  
Gravity Model ◽  
High Redshift ◽  
Planck Scale ◽  
Holographic Principle ◽  
Planck Length ◽  
High Redshift Galaxies ◽  
Cosmological Distance ◽  
Redshift Galaxies

If spacetime is “foamy” travel along a lightpath must be subject to continual, random distance fluctuations ± δ l proportional to Planck length lP ~ 10−35 m (Lieu & Hillman 2003). Although each “kick” by itself is tiny, these may accumulate. Accounting for redshifted (bluer) emitted photons, over a cosmological distance L = (1+z)LC for co-moving distance LC, the resultant phase perturbations Δ φ = 2π δ l/λ at observed wavelength λ could grow independently of telescope diameter D to a maximum of Δφmax=(1+z)Δφ0 (Steinbring 2007) where Δφ0=2π a0 (lPα/λ)L1 - α follows Ng et al. (2003). Here a0 ~ 1 and α specifies the quantum-gravity model: 1/2 implies a random walk and 2/3 is consistent with the holographic principle; a vanishingly small ΔφP=Δφmax/[(1 + z) a0 (L/lP)1 - α]=2π lP/λ is approached when α=1.

scholarly journals Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle

2021 ◽  
Author(s):  
David Escors ◽  
Grazyna Kochan
Keyword(s):  
Mathematical Model ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Zero Point ◽  
Space Time ◽  
Planck Length ◽  
Exclusion Zone ◽  
Curvature Perturbation

General relativity is a theory for gravitation based on Riemannian geometry, difficult to compatibilize with quantum mechanics. This is evident in relativistic problems in which quantum effects cannot be discarded. For example in quantum gravity, gravitation of zero-point energy or events close to a black hole singularity. Here, we set up a mathematical model to select general relativity geodesics according to compatibility with the uncertainty principle. To achieve this, we derived a geometric expression of the uncertainty principle (GUP). This formulation identified proper space-time length with Planck length by a geodesic-derived scalar. GUP imposed a minimum allowed value for the interval of proper space-time which depended on the particular space-time geometry. GUP forced the introduction of a “zero-point” curvature perturbation over flat Minkowski space, caused exclusively by quantum uncertainty but not to gravitation. When applied to the Schwarzschild metric and choosing radial-dependent geodesics, our mathematical model identified a particle exclusion zone close to the singularity, similar to calculations by loop quantum gravity. For a 2 black hole merger, this exclusion zone was shown to have a radius that cannot go below a value proportional to the energy/mass of the incoming black hole multiplied by Planck length.

Quantum corrections to thermodynamics of BTZ black hole

2019 ◽  
Vol 34 (11) ◽  
pp. 1950063 ◽  
Author(s):  
Nadeem-ul-islam ◽  
Prince A. Ganai
Keyword(s):  
Black Hole ◽  
Comparative Analysis ◽  
String Theory ◽  
Quantum Gravity ◽  
Loop Quantum Gravity ◽  
Quantum Corrections ◽  
Leading Order ◽  
Btz Black Hole ◽  
Thermodynamic Variables

The motivation behind this study is to enumerate the leading order corrections to the thermodynamics of BTZ black hole (named after three scientists; Banados, Teitelboim, and Zanelli). We first analyze the effect of quantum corrections (motivated from string theory and loop quantum gravity) on various thermodynamic variables for uncharged and stationary BTZ black hole. We, later on, endow charges and rotations to the same black hole and rederive all the expressions once again. The comparative analysis is done between the corrected and uncorrected thermodynamics via plots.

scholarly journals A Review on Black hole solutions in General Relativity

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Monika Sati ◽  
K.C. Petwal
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Schwarzschild Solution ◽  
Penrose Diagram ◽  
Static Solutions ◽  
Spherical Mass ◽  
Black Hole Solutions

In the present manuscript, we endeavour to review and develop the black hole solutions in general relativity. We emphasize here the Schwarzschild solution in Einstein’s field equation, which describes the gravitational field outside a spherical mass. The paper aims to obtain certain results, including the description of the Einstein field equation with stationary and static solutions and components of the metric that turns out to be time independent, some experiments on the Schwarzschild - Penrose diagram, the Kerr-Newman solution for rotating black holes, and the Reissner- Nordstrom solution for static and charged black holes.

Sign in / Sign up

Export Citation Format

Share Document