In this paper, considering the influence of the principle of generalized uncertainty (GUP), the phase transition of a Schwarzschild black hole with global monopole is discussed. First, we use the generalized Dirac equation to obtain corrected Hawking temperature, local temperature, black hole residue, black hole entropy, thermal capacity, and other thermodynamic quantities. Then, we use images to analyze the effects of generalized uncertainty parameters on phase transitions and the effects of magnetic monopole parameters on phase transitions. Finally, we study the thermodynamic stability and phase change structure under the influence of the principle of generalized uncertainty. The results show that, in the black hole with global monopole, there are first-order and second-order phase transitions. In addition, the general uncertainty parameters and monopole parameters will affect the black hole residues.
The fragmentation of black hole containing $f(R)$ global monopole under GUP is studied. We focus on that the black hole breaks into two parts. We derive the entropies of the initial black hole and the broken parts while the generalization of Heisenberg's uncertainty principle is introduced. We find that the $f(R)$ global monopole black hole keeps stable instead of breaking because the entropy difference is negative without the generalization. The fragmentation of the black hole will happen if the black hole entropies are limited by the GUP and the considerable deviation from the general relati…
We consider quantum corrections for the Schwarzschild black hole metric by using the generalized uncertainty principle (GUP) to investigate quasinormal modes, shadow and their relationship in the eikonal limit. We calculate the quasinormal frequencies of the quantum-corrected Schwarzschild black hole by using the sixth-order Wentzel-Kramers-Brillouin (WKB) approximation, and also perform a numerical analysis that confirms the results obtained from this approach. We also find that the shadow radius is nonzero even at very small mass limit for finite GUP parameter.
In this paper we have implemented quantum corrections for the Schwarzschild black hole metric using the generalized uncertainty principle (GUP) in order to investigate the scattering process. We mainly compute, at the low energy limit, the differential scattering and absorption cross section by using the partial wave method. We determine the phase shift analytically and verify that these quantities are modified by the GUP. We found that due to the quantum corrections from the GUP the absorption is not zero as the mass parameter goes to zero. A numerical analysis has also been performed for arb…
We investigate the thermodynamics of the Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle (GUP). The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of the Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of the black hole approaches the order of Planck scale, it stops radiating and leads to black hole remnant. Meanwhile, the Planck scale remnant can be con…
Quantum gravity has exciting peculiarities on the Planck scale.The effect of generalized uncertainty principle (GUP) to the entangled scalar/fermion particles' tunneling from a Schwarzschild black hole immersed in an electromagnetic Universe is investigated by the help of semi-classical tunneling method. The quantum corrected Hawking temperature of this black hole with an external parameter "a" modifies the Hawking temperature for the entangled particles.
In this paper we study through tunneling formalism, the effect of noncommutativity to Hawking radiation and the entropy of the noncommutative Schwarzschild black hole. In our model we have considered the noncommutativity implemented via the Lorentzian distribution. We obtain non-commutative corrections to the Hawking temperature using the Hamilton-Jacobi method and the Wentzel-Kramers-Brillouin (WKB) approximation. In addition, we found corrections of the logarithmic and other types due to noncommutativity and quantum corrections from the generalized uncertainty principle (GUP) for the entropy…
We find the entropy of Kehagias-Sfetsos black hole in the deformed Hořava-Lifshitz gravity by using the first law of thermodynamics. When applying generalized uncertainty principle (GUP) to Schwarzschild black hole, the entropy $S=A/4+(π/ω)\ln(A/4)$ may be interpreted as the GUP-inspired black hole entropy. Hence, it implies that the duality in the entropy between the Kehagias-Sfetsos black hole and GUP-inspired Schwarzschild black hole is present.
The greybody factor of massless scalar fields in the four-dimensional Schwarzschild spacetime involving an $f(R)$ global monopole is derived. We show how the monopole parameter and the deviation from the standard general relativity adjust the greybody factor. We also demonstrate that the effects from the global monopole and $f(R)$ gravity theory are manifest in the energy emission rate and the generalized absorption cross section of the scalar fields.
Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg Uncertainty Principle near the Plank scale, known as the Generalized Uncertainty Principle (GUP). Here we study the effects of GUP which preserves the rotational symmetry of the spacetime, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild-de Sitter spacetime with the resulted value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the spacetime. Now, if th…
Motivated by a recent work of Scardigli, Lambiase and Vagenas (SLV), we derive the GUP parameter, i.e. $α_0$, when the GUP has a linear and quadratic term in momentum. The value of the GUP parameter is obtained by conjecturing that the GUP-deformed black hole temperature of a Schwarzschild black hole and the modified Hawking temperature of a quantum-corrected Schwarzschild black hole are the same. The leading term in both cases is the standard Hawking temperature and since the corrections are considered as thermal, the modified and deformed expressions of temperature display a slight shift in …
We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle. The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of black hole approach to the order of Planck scale, it stops radiating and leads to black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through th…
In this paper we study the effects of the Generalized Uncertainty Principle (GUP) on canonical quantum gravity of black holes. Through the use of modified partition function that involves the effects of the GUP, we obtain the thermodynamical properties of the Schwarzschild black hole. We also calculate the Hawking temperature and entropy for the modification of the Schwarzschild black hole in the presence of the GUP.
Diverse theories of Quantum Gravity expect modification of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle.It was shown by some authors that the Generalized uncertainty principle gives rise to corrections to Schrodinger,Klien-Gordon and Dirac equations.By solving the Generalized uncertainty principle corrected equations,the authors arrived at quantization not only of energy but also of box length,area and volume. We extend the above result to the case of curved Space-Time(Schwarzschild metric). We showed that we arrived at the Quantiz…
It is discussed that the Ernst--Schwarzschild metric describing a nonrotating black hole in the external magnetic field admits the solutions of the Dirac monopole types for the corresponding Maxwell equations. The given solutions are obtained in explicit form and a possible influence of the conforming Dirac monopoles on Hawking radiation is also outlined.
An algorithm for numerical computation of the barrier transparency for the potentials surrounding Schwarzschild black holes is described for massive spinor particles. It is then applied to calculate the total (including electronic neutrino and the contributions of twisted field configurations connected with Dirac monopoles) luminosity for the electron-positron Hawking radiation from a Schwarzschild black hole with mass $M=10^{15}$ g. It is found that the contribution due to monopoles can be of order 12% of the total electron-positron luminosity.
We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, $T^0_0 - T^i_i = 0$. This property was however known for the global monopole spacetime while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos - Zannias scalar field solution is dual to flat space.
We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.
Hawking flux from the Schwarzschild black hole with a global monopole is obtained by using Robinson and Wilczek's method. Adopting a dimension reduction technique, the effective quantum field in the (3+1)--dimensional global monopole background can be described by an infinite collection of the (1+1)--dimensional massless fields if neglecting the ingoing modes near the horizon, where the gravitational anomaly can be cancelled by the (1+1)--dimensional black body radiation at the Hawking temperature.
This paper is based on the study of the paper of Scardigli and Casadio [Eur. Phys. J. C (2015) 75:425] where the authors computed the light deflection and perihelion precession for the Generalized Uncertainty Principle (GUP) modified Schwarzschild metric. In the present work, we computed the gravitational tests such as Shapiro time delay, gravitational redshift, and geodetic precession for the GUP modified Schwarzschild metric. Using the results of Solar system experiments and observations, we obtain upper bounds for the GUP parameter $β$. Finally, we compare our bounds with other bounds in th…
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 to 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 view point of black hole thermodynamics.
We investigate the impact of quantum gravity on accretion onto a modified Schwarzschild black hole within the context of the generalized uncertainty principle (GUP). The minimal measurable length connected to GUP modifies the Schwarzschild black hole, giving it the capacity to accommodate the correction due to quantum gravity. We look at potential critical point locations and calculate the critical speed of the matter accreting. We determine the temperature and total integrated flux correction at the event horizon for the polytropic matter using the least measurable length conjecture offered b…
Black hole radiation from an infinitesimally thin massive collapsing shell, possessing a global monopole charge, which in turn leads to a Schwarzschild black hole with a global monopole charge has been shown to be processed by a unitary evolution. The exterior metric of the collapsing shell is described by the global monopole (GM) metric. The analysis is performed using the Wheeler-deWitt formalism which gave rise to a Schrödinger-like wave equation. Existence of unitarity is confirmed from two independent lines of approach. Firstly, by showing that the trace of the square of the density matri…
In this article, close to the Planck scale, we discuss on the remnant and residue entropy from a Rutz-Schwarzschild black hole in the frame of Finsler geometry. Employing the corrected Hamilton-Jacobi equation, the tunneling radiation of a scalar particle is presented, and the revised tunneling temperature and revised entropy are also found. Taking into account generalized uncertainty principle (GUP), we analyze the remnant stability and residue entropy based on thermodynamic phase transition. In addition, the effects of the Finsler perturbation parameter, GUP parameter and angular momentum pa…
We generalize our previous studies on the Maxwell quasinormal modes around Schwarzschild-anti-de-Sitter black holes with Robin type vanishing energy flux boundary conditions, by adding a global monopole on the background. We first formulate the Maxwell equations both in the Regge-Wheeler-Zerilli and in the Teukolsky formalisms and derive, based on the vanishing energy flux principle, two boundary conditions in each formalism. The Maxwell equations are then solved analytically in pure anti-de Sitter spacetimes with a global monopole, and two different normal modes are obtained due to the existe…
We study quantum corrections at the horizon scale of a black hole induced by a Generalized Uncertainty Principle (GUP) with a quadratic term in the momentum. The interplay between quantum mechanics and gravity manifests itself into a non-zero uncertainty in the location of the black hole radius, which turns out to be larger than the usual Schwarzschild radius. We interpret such an effect as a correction which makes the horizon disappear, as it happens in other models of quantum black holes already considered in literature. We name this kind of horizonless compact objects $GUP stars$. We also i…
GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）；Shanghai Frontier Science Center for Gravitational Wave Detection, School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院上海引力波探测前沿科学中心）
The quasinormal modes (QNMs) and the late-time behavior of arbitrary spin fields are studied in the background of a Schwarzschild black hole with a global monopole (SBHGM). It has been shown that the real part of the QNMs for a SBHGM decreases as the symmetry breaking scale parameter $H$ increases but imaginary part increases instead. For large overtone number $n$, these QNMs become evenly spaced and the spacing for the imaginary part equals to $-i(1-H)^{3/2}/(4M)$ which is dependent of $H$ but independent of the quantum number $l$. It is surprisingly found that the late-time behavior is domin…
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 …
In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct…
In this paper, we derive an exact black hole spacetime metric in the Einstein-Hilbert-Bumblebee (EHB) gravity around global monopole field. We study the horizon, temperature, and the photon sphere of the black hole. Using the null geodesics equation, we obtain the shadow cast by the Schwarzschild-like black hole with a topological defect in bumblebee gravity. Interestingly, the radius of shadow of the black hole increases with increase in the global monopole parameter. We also visualize the shadows and energy emission rates for different values of parameters. Moreover, using the Gauss-Bonnet t…
We study holographic superconductors in the Schwarzschild-AdS black hole with a global monopole through a charged complex scalar field. We calculate the condensates of the charged operators in the dual conformal field theories (CFTs) and discuss the effects of the global monopole on the condensation formation. Moreover, we compute the electric conductive using the probe approximation and find that the properties of the conductive are quite similar to those in the Schwarzschild-AdS black hole. These results can help us know more about holographic superconductors in the asymptotic AdS black hole…
In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalized uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters $β_0$ and $ α_0$ with $η$ which is the parameter that characterizes the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation paramet…
Using Weitzenböck Induced Matter Theory (WIMT), we study Schwarzschild wormholes performing different foliations on an extended (non-vaccuum) 5D manifold. We explore the geodesic equations for observers which are in the interior of a traversable wormhole and how these observers can detect gravito-magnetic monopoles which are dual to gravito-electric sources observed in the outer zone of some Schwarzschild Black-Hole (BH). The densities of these monopoles are calculated and quantized in the Dirac sense. This kind of duality on the extended Einstein-Maxwell equations, relates electric and magnet…
We review versions of the Generalized Uncertainty Principle (GUP) obtained in string theory and in gedanken experiments carried out in Quantum Gravity. We show how a GUP can be derived from a measure gedanken experiment involving micro-black holes at the Planck scale of spacetime. The model uses only Heisenberg principle and Schwarzschild radius and it is independent from particular versions of Quantum Gravity.
The existence of a minimal length is a common prediction of various theories of quantum gravity. This minimal length leads to a modification of the Heisenberg uncertainty principle to a Generalized Uncertainty Principle (GUP). Various studies showed that a GUP modifies the Hawking radiation of black holes. In this paper, we propose a modification of the Schwarzschild metric based on the modified Hawking temperature derived from the GUP. Based on this modified metric, we calculate corrections to the deflection of light, time delay of light, perihelion precession, and gravitational redshift. We …
We have derived a new Generalised Uncertainty Principle (GUP) based on certain general assumptions. This GUP is consistent with predictions from string theory. It is then used to study Schwarzschild black hole thermodynamics. Corrections to the mass-temperature relation, area law and heat capacity are obtained. We find that the evaporation process stops at a particular mass, referred as the remnant mass. This is instrumental in bypassing the well known singularity problem that occurs in a semiclassical approach.
We investigate the gravitational lensing effect in the strong field background around the Schwarzschild black hole with extremely small mass and solid deficit angle subject to the global monopole by means of the strong field limit issue. We obtain the angular position and magnification of the relativistic images and show that they relate to the global monopole parameter $η$. We discuss that with the increase of parameter $η$, the minimum impact parameter $u_{m}$ and angular separation $s$ increase and the relative magnification $r$ decreases. We also find that $s$ grows extremely greatly as th…
Quasinormal modes and late time tails of perturbation fields on a Schwarzschild-like black hole with a global monopole in the Einstein-bumblebee theory
We study the Schwarzschild and Reissner-Nordström black hole thermodynamics using the simplest form of the generalized uncertainty principle (GUP) proposed in the literature. The expressions for the mass-temperature relation, heat capacity and entropy are obtained in both cases from which the critical and remnant masses are computed. Our results are exact and reveal that these masses are identical and larger than the so called singular mass for which the thermodynamics quantities become ill-defined. The expression for the entropy reveals the well known area theorem in terms of the horizon area…
We propose a physically sensible formulation of initial value problem for black hole perturbations in higher-order scalar-tensor theories. As a first application, we study monopole perturbations around stealth Schwarzschild solutions in a shift- and reflection-symmetric subclass of degenerate higher-order scalar-tensor (DHOST) theories. In particular, we investigate the time evolution of the monopole perturbations by solving a two-dimensional wave equation and analyze the Vishveshwara's classical scattering experiment, i.e., the time evolution of a Gaussian wave packet. As a result, we confirm…
We will discuss some analogies between internal gauge theories and gravity in order to better understand the charge concept in gravity. A dimensional analysis of gauge theories in general and a strict definition of elementary, monopole, and topological charges are applied to electromagnetism and to teleparallelism, a gauge theoretical formulation of Einstein gravity. As a result we inevitably find that the gravitational coupling constant has dimension $\hbar/l^2$, the mass parameter of a particle dimension $\hbar/l$, and the Schwarzschild mass parameter dimension l (where l means length). Thes…
Static solutions in spherical symmetry are found for gravitating global monopoles. Regular solutions lacking a horizon are found for $η< 1/\sqrt{8π}$, where $η$ is the scale of symmetry breaking. Apparently regular solutions with a horizon are found for $1/\sqrt{8π} \le η\alt \sqrt{3/8π}$. Though they have a horizon, they are not Schwarzschild. The solution for $η= 1/\sqrt{8π}$ is argued to have a horizon at infinity. The failure to find static solutions for $η> \sqrt{3/8π} \approx 0.3455$ is consistent with findings that topological inflation begins at $η\approx 0.33$.
Within the framework of the recent Eddington-inspired Born-Infeld (EiBI) theory we study gravitational field around an $SO(3)$ global monopole. The solution also suffers from the deficit solid angle as in the Barriola-Vilenkin metric but shows a distinct feature that cannot be transformed away unless in the vanishing EiBI coupling constant, $κ$. When seen as a black hole eating up a global monopole, the corresponding Schwarzschild horizon is shrunk by $κ$. The deficit solid angle makes the space is globally not Euclidean, and to first order in $κ$ (weak-field limit) the deflection angle of lig…
We derive the formula of the black hole entropy with a minimal length of the Planck size by counting quantum modes of scalar fields in the vicinity of the black hole horizon, taking into account the generalized uncertainty principle (GUP). This formula is applied to some intriguing examples of black holes - the Schwarzschild black hole, the Reissner-Nordstrom black hole, and the magnetically charged dilatonic black hole. As a result, it is shown that the GUP parameter can be determined by imposing the black hole entropy-area relationship, which has a Planck length scale and a universal form wi…
The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically-corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existenc…
The neutrino behavior in the Einstein$\text{-}$Hilbert$\text{-}$Bumblebee gravity around global monopole field
College Pharmacy, Guizhou University of Traditional Chinese Medicine（贵州中医药大学药学院）；School of Science, Guiyang University（贵阳学院理学院）；College of Physics, Guizhou University（贵州大学物理学院）
We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and ex…
