scholarly journals Effective GUP-modified Raychaudhuri equation and black hole singularity: four models

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Keagan Blanchette ◽  
Saurya Das ◽  
Saeed Rastgoo
Keyword(s):  
Black Hole ◽  
Proper Time ◽  
Generalized Uncertainty Principle ◽  
Rate Of Change ◽  
Conjugate Points ◽  
Raychaudhuri Equation ◽  
Schwarzschild Black Hole ◽  
Effective Dynamics ◽  
Singularity Theorems ◽  
Black Hole Singularity

Abstract The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.

scholarly journals Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals BLACK HOLE THERMODYNAMICS AND MODIFIED GUP CONSISTENT WITH DOUBLY SPECIAL RELATIVITY

2012 ◽  
Vol 27 (39) ◽  
pp. 1250227 ◽  
Author(s):  
K. ZEYNALI ◽  
F. DARABI ◽  
H. MOTAVALLI
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Black Hole Thermodynamics ◽  
Schwarzschild Black Hole ◽  
Commutation Relations ◽  
Doubly Special Relativity ◽  
Correction Terms

We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of Modified Generalized Uncertainty Principle suggested by Doubly Special Relativity.

scholarly journals Geodesic stability and quasi normal modes via Lyapunov exponent for Hayward black hole

2020 ◽  
Vol 35 (30) ◽  
pp. 2050249
Author(s):  
Monimala Mondal ◽  
Parthapratim Pradhan ◽  
Farook Rahaman ◽  
Indrani Karar
Keyword(s):  
Black Hole ◽  
Lyapunov Exponent ◽  
Time Scale ◽  
Proper Time ◽  
Normal Modes ◽  
Schwarzschild Black Hole ◽  
Coordinate Time ◽  
Stability And Instability ◽  
The Stability ◽  
Asymptotic Observers

We derive proper time Lyapunov exponent [Formula: see text] and coordinate time Lyapunov exponent [Formula: see text] for a regular Hayward class of black hole. The proper time corresponds to [Formula: see text] and the coordinate time corresponds to [Formula: see text], where [Formula: see text] is measured by the asymptotic observers both for Hayward black hole and for special case of Schwarzschild black hole. We compute their ratio as [Formula: see text] for time-like geodesics. In the limit of [Formula: see text] that means for Schwarzschild black hole this ratio reduces to [Formula: see text]. Using Lyapunov exponent, we investigate the stability and instability of equatorial circular geodesics. By evaluating the Lyapunov exponent, which is the inverse of the instability time scale, we show that, in the eikonal limit, the real and imaginary parts of quasi-normal modes (QNMs) is specified by the frequency and instability time scale of the null circular geodesics. Furthermore, we discuss the unstable photon sphere and radius of shadow for this class of black hole.

scholarly journals THERMODYNAMICS OF NONCOMMUTATIVE SCHWARZSCHILD BLACK HOLE

2007 ◽  
Vol 22 (38) ◽  
pp. 2917-2930 ◽  
Author(s):  
KOUROSH NOZARI ◽  
BEHNAZ FAZLPOUR
Keyword(s):  
Black Hole ◽  
String Theory ◽  
Final Stage ◽  
Generalized Uncertainty Principle ◽  
Black Hole Thermodynamics ◽  
Maximum Temperature ◽  
Evaporation Process ◽  
Zero Temperature ◽  
Schwarzschild Black Hole ◽  
Space Noncommutativity

We investigate the effects of space noncommutativity and the generalized uncertainty principle on the thermodynamics of a radiating Schwarzschild black hole. We show that evaporation process is in such a way that black hole reaches a maximum temperature before its final stage of evolution and then cools down to a nonsingular remnant with zero temperature and entropy. We compare our results with more reliable results of string theory. This comparison shows that GUP and space noncommutativity are similar concepts at least from the viewpoint of black hole thermodynamics.

scholarly journals MICROSCOPIC BLACK HOLE AND UNCERTAINTY PRINCIPLE WITH MINIMAL LENGTH AND MOMENTUM

2013 ◽  
Vol 28 (10) ◽  
pp. 1350029 ◽  
Author(s):  
M. M. STETSKO
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Emission Rate ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Schwarzschild Black Hole ◽  
Evaporation Time ◽  
Thermodynamical Functions

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained.

scholarly journals Bardeen regular black hole as a quantum-corrected Schwarzschild black hole

2019 ◽  
Vol 28 (03) ◽  
pp. 1950048 ◽  
Author(s):  
R. V. Maluf ◽  
Juliano C. S. Neves
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Upper Bounds ◽  
Nonlinear Electrodynamics ◽  
Schwarzschild Black Hole ◽  
Regular Black Hole ◽  
Cosmological Observations ◽  
New Interpretation

Bardeen regular black hole is commonly considered as a solution of general relativity coupled to a nonlinear electrodynamics. In this paper, it is shown that the Bardeen solution may be interpreted as a quantum-corrected Schwarzschild black hole. This new interpretation is obtained by means of a generalized uncertainty principle applied to the Hawking temperature. Moreover, using the regular black hole of Bardeen, it is possible to evaluate the quantum gravity parameter of the generalized uncertainty principle or, assuming the recent upper bounds for such a parameter, to verify an enormous discrepancy between a cosmological constant and that measured by recent cosmological observations [Formula: see text].

scholarly journals The geodesics structure of Schwarzschild black hole immersed in an electromagnetic universe

2017 ◽  
Vol 26 (14) ◽  
pp. 1750169 ◽  
Author(s):  
A. Al-Badawi ◽  
M. Q. Owaidat ◽  
S. Tarawneh
Keyword(s):  
Black Hole ◽  
Analytical Solution ◽  
Exact Analytical Solution ◽  
Proper Time ◽  
Massive Particle ◽  
Schwarzschild Black Hole ◽  
Circular Orbits ◽  
Schwarzschild Metric ◽  
Effective Potentials ◽  
Em Field

The geodesic equations are considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic (em) field. Due to the em field horizon shrinks and geodesics are modified. By analyzing the behavior of the effective potentials for the massless and massive particle we study the radial and circular trajectories. Radial geodesics for both photons and particles are solved exactly. It is shown that a particle that falls toward the horizon in a finite proper time slows down so that the particle reaches the singularity slower than Schwarzschild case. Timelike and null circular geodesics are investigated. We have shown that, there are no stable circular orbits for photons, however stable and unstable second-kind orbits exist for the massive particle. An exact analytical solution for the innermost stable circular orbits (ISCO) has been obtained. It has been shown that the radius of the ISCO shrinks due to the presence of the em field.

scholarly journals SPACE–TIMES WITH INTEGRABLE SINGULARITY: BLACK–WHITE HOLES AND ASTROGENIC UNIVERSES

2013 ◽  
Vol 28 (02) ◽  
pp. 1350007 ◽  
Author(s):  
VLADIMIR N. LUKASH ◽  
VLADIMIR N. STROKOV
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Phenomenological Approach ◽  
Space Time ◽  
Schwarzschild Black Hole ◽  
White Hole ◽  
Black Hole Singularity

We use the phenomenological approach to study properties of space–time in the vicinity of the Schwarzschild black-hole singularity. Requiring finiteness of the Schwarzschild-like metrics we come to the notion of integrable singularity that is, in a sense, weaker than the conventional singularity and allows the (effective) matter to pass to the white-hole region. This leads to a possibility of generating a new universe there. Thanks to the gravitational field of the singularity, this universe is already born highly inflated ("singularity-induced inflation") before the ordinary inflation starts.

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