In this paper, we study the thermodynamics of black holes using a generalized uncertainty principle (GUP) with a correction term linear order in the momentum uncertainty. The mass-temperature relation and heat capacity are calculated from which critical and remnant masses are obtained. The results are exact and are found to be identical. The entropy expression gives the famous area theorem upto leading order corrections from GUP. In particular, the linear order term in GUP leads to a $\sqrt{A}$ correction to the area theorem. Finally, the area theorem can be expressed in terms of a new variable termed as reduced horizon area only when the calculation is done to the next higher order correction from GUP.
The idea of black hole remnants for RG modified Schwarzschild solution constructed in papers [hep-th/0002196; hep-th/0602159] depends essentially on the positiveness of a parameter that enters the running Newton constant. The positiveness of this parameter was established by comparing the large distance expansion of RG modified Schwarzschild solution with the Donoghue's original result about the one-loop correction to the Newtonian potential [gr-qc/9310024; gr-qc/9405057]. But since the appearance of paper [gr-qc/0207118] by Khriplovich and Kirilin it became widely appreciated that the sign of…
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 construct a Hilbert space representation of minimum-length deformed uncertainty relation in presence of extra dimensions. Following this construction, we study corrections to the gravitational potential (back reaction on gravity) with the use of correspondingly modified propagator in presence of two (spatial) extra dimensions. Interestingly enough, for $r \rightarrow 0$ the gravitational force approaches zero and the horizon for modified Schwarzschild-Tangherlini space-time disappears when the mass approaches quantum-gravity energy scale. This result points out to the existence of zero-temp…
Possible existence of black holes remnants provides a suitable candidates for dark matter. In this paper we study the possibility of existence for such remnants. We consider quantum gravitational induced corrections of black hole's entropy and temperature to investigate the possibility of such relics. Observational scheme for detection of these remnants and their cosmological constraints are discussed.
We show that although generalized uncertainty principle with negative parameter allows black holes to evaporate completely, this process takes an infinite amount time to achieve, resulting in a metastable remnant.
In the current standard viewpoint small black holes are believed to emit radiation as black bodies at the Hawking temperature, at least until they reach Planck size, after which their fate is open to conjecture. A cogent argument against the existence of remnants is that, since no evident quantum number prevents it, black holes should radiate completely away to photons and other ordinary stable particles and vacuum, like any unstable quantum system. Here we argue the contrary, that the generalized uncertainty principle may prevent their total evaporation in exactly the same way that the uncert…
It was argued in a number of papers that the gravitational potential calculated by using the modified QFT that follows from the Planck-length deformed uncertainty relation implies the existence of black-hole remnants of the order of the Planck-mass. Usually this sort of QFTs are endowed with two specific features, the modified dispersion relation, which is universal, and the concept of minimum length, which, however, is not universal. While the emergence of the minimum-length most readily leads to the idea of the black hole remnants, here we examine the behaviour of the potential that follows …
We apply the generalized uncertainty principle to the thermodynamics of a small black hole. Here we have a black hole system with the UV cutoff. It is shown that the minimal length induced by the GUP interrupts the Gross-Perry-Yaffe phase transition for a small black hole. In order to see whether the black hole remnant takes place a transition to a large black hole, we introduce a black hole in a cavity (IR system). However, we fail to show the phase transition of the remnant to the large black hole.
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations which are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make u…
Based on the micro-black hole \emph{gedanken} experiment as well as on general considerations of quantum mechanics and gravity the generalized uncertainty principle (GUP) is analyzed by using the running Newton constant. The result is used to decide between the GUP and quantum gravitational effects as a possible mechanism leading to the black hole remnants of about Planck mass.
We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dep…
We study thermodynamic quantities of an acoustic black hole and its thermodynamic stability in a cavity based on the generalized uncertainty principle. It can be shown that there is a minimal black hole which can be a stable remnant after black hole evaporation. Moreover, the behavior of the free energy shows that the large black hole is stable too. Therefore, the acoustic black hole can decay into the remnant or the large black hole.
We argue that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse. Specifically we invoke the GUP to obtain a modified Hawking temperature, which indicates that there should exist non-radiating remnants (BHR) of about Planck mass. BHRs are an attractive candidate for cold dark matter. We investigate an alternative cosmology in which primordial BHRs are the primary source of dark matter.
Motivated by several approaches to quantum gravity, there is a considerable literature on generalised uncertainty principles particularly through modification of the canonical position-momentum commutation relations. Some of these modified relations are also consistent with general principles that may be supposed of any physical theory. Such modified commutators have significant observable consequences. Here we study the noisy behaviour of an optomechanical system assuming a certain commonly studied modified commutator. From recent observations of radiation pressure noise in tabletop optomecha…
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 argue that a remnant is formed for all black objects in gravity's rainbow. This will be based on the observation that a remnant depends critically on the structure of the rainbow functions, and this dependence is a model independent phenomena. We thus propose general relations for the modified temperature and entropy of all black objects in gravity's rainbow. We explicitly check this to be the case for Kerr, Kerr-Newman-dS, charged-AdS, and higher dimensional Kerr-AdS black holes. We also try to argue that a remnant should form for black Saturn in gravity's rainbow. This work extends our pr…
The Hawking radiation of static, spherically symmetric, asymptotically flat solutions in quadratic gravity, is here explored. The emitted fermions are governed by the Dirac equation in the generalized uncertainty principle (GUP) context, that probes the spacetime (quantum) nature. The Hawking thermal spectrum is scrutinized out of the tunnelling method and the WKB procedure. The Hawking flux is shown to vanish for small black holes, for a precise combination of the GUP parameter and the coupling constants that drive the gravitational interaction in quadratic gravity, yielding absolutely stable…
Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea we examine the Wheeler-DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number 'n' which coincides with Bekenstein's proposal. We also found that the mass of the black hole is directly proportional to the quantum number 'n' when quantum gravity effects are taken into consider…
In this work, we conduct a study regarding the thermodynamic evolution and the phase transition of a black hole in a finite spherical cavity subject to the generalized uncertainty principle. The results demonstrate that both the positive and negative generalized uncertainty principle parameters $β_0$ can significantly affect the thermodynamic quantities, stability, critical behavior, and phase transition of the black hole. For $β_0>0$, the black hole forms a remnant with finite temperature, finite mass, and zero local heat capacity in the last stages of evolution, which can be regarded as an e…
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…
We consider a modification of the Brans-Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans-Dicke scalar field is modified such that the equation of motion for the scalar field be modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann--Lema\^ıtre--Robertson--Walker metric. We investigate the dynamics and the cosmological evolution for the dynamical variables of the theory and we compare …
Very recently Ali et al.(2009) proposed a new generalized uncertainty principle (or GUP) with a linear term in Plank length which is consistent with doubly special relativity and string theory. The classical and quantum effects of this generalized uncertainty principle (term as modified uncertainty principle or MUP) are investigated on the phase space of a dilatonic cosmological model with an exponential dilaton potential in a flat FRW background . Interestingly, as a consequence of MUP, we found that it is possible to get a late time acceleration for this model. For the quantum mechanical des…
A consequence of adopting a modified gravitational theory (MOG) for the aLIGO GW190521 gravitational wave detection involving binary black hole sources is to fit the aLIGO strain and chirp data with lower mass, compact coalescing binary systems such as neutron star-neutron star (NS-NS), black hole - neutron star (BH-NS), and black hole-black hole (BH-BH) systems. In MOG BH - BH component masses can be smaller than the component masses $m_1=85M_\odot$ and $m_2=66M_\odot$ inferred from the aLIGO GW190521 gravitational wave event. This reduces the mass of the final remnant mass $M_f=150M_\odot$ a…
In this paper, we have investigated the thermodynamics of Schwarzschild black holes using the symmetric generalized uncertainty principle which contains correction terms involving momentum and position uncertainty. We obtain the mass-temperature relation and the heat capacity of the black hole using which we compute the critical and remnant masses. The entropy is found to satisfy the area law upto leading order corrections from the symmetric generalized uncertainty principle.
Accounting for detector calibration uncertainty in black-hole ringdown analysis
The Australian National University（澳大利亚国立大学）；The University of Tokyo（东京大学）；Monash University（蒙纳士大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring…
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in Ali et al. (2009) [5] in simple quantum mechanical systems and study its thermodynamic properties. We have assumed that the quantum particles follow Maxwell-Boltzmann statistics with no spin. We compare our results with the results found in the GUP and polymer quantum mechanical frameworks. Interestingly we find that the corrected thermodynamic entities are exactly same compared to the polymer results but the length scale considered has a theoretically different origin. Hence we express the need of further…
In this paper, we study the effects of Generalized Uncertainty Principle(GUP) and Modified Dispersion Relations(MDRs) on the thermodynamics of ultra-relativistic particles in early universe. We show that limitations imposed by GUP and particle horizon on the measurement processes, lead to certain modifications of early universe thermodynamics.
The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy. Independently, due to quantum gravity effects the Heisenberg uncertainty principle has been extended to a Generalized Uncertainty Principle (GUP). In this work, we show that GUP has been derived from considering non-extensive entropies, proposed by one of us. We found that the deformation parameters associated with $S_{+}$ and $S_-$ entropies are negative and posit…
In this paper, we explore the quantum spacetimes that are potentially connected with the generalized uncertainty principles. By analyzing the gravity-induced quantum interference pattern and the Gedanken for weighting photon, we find that the generalized uncertainty principles inspire the effective Newton constant as same as our previous proposal. A characteristic momentum associated with the tidal effect is suggested, which incorporates the quantum effect with the geometric nature of gravity. When the simplest generalized uncertainty principle is considered, the minimal model of the regular b…
Motivated by the recently derived new form of generalized uncertainty principle we obtain the corresponding dispersion relation which is now modified. This modification can be interpreted as a possible mechanism that makes particles more massive. In addition, the modified velocity of photons is obtained and indicates that photons' propagation depends on their energy, thus superluminal photons are permitted due to generalized uncertainty principle. Furthermore, we derive and solve the two-dimensional Klein-Gordon equation in the presence of GUP corrections, and therefore the GUP-corrected emiss…
Recently Ali et.al.(2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner-Nordstrom black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlie…
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, $[\hat{X},\hat{P}] = i \hbar (1+βp^2)$, may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified commutator. This provides guidance when constructing GUP models since it distinguishes those GUPs that have a minimal length sc…
Based on the universality of the entropy-area relation of a black hole, and the fact that the generalized uncertainty principle (GUP) adds a logarithmic correction term to the entropy in accordance with most approaches to quantum gravity, we argue that the GUP-corrected entropy-area relation is universal for all black objects. This correction to the entropy produces corrections to the thermodynamics. We explicitly calculate these corrections for three types of black holes: Reissner--Nordström, Kerr, and charged AdS black holes, in addition to spinning black rings. In all cases we find that the…
We study the Hawking radiation from the five-dimensional charged static squashed Kaluza-Klein black hole by the tunneling of charged scalar particles and charged fermions. In contrast to the previous studies of Hawking radiation from squashed Kaluza-Klein black holes, we consider the phenomenological quantum gravity effects predicted by the generalized uncertainty principle with the minimal measurable length. We derive corrections of the Hawking temperature to general relativity, which are related to the energy of the emitted particle, the size of the compact extra dimension, the charge of the…
Wald's entropy formula allows one to find the entropy of black holes' event horizon within any diffeomorphism invariant theory of gravity. When applied to general relativity, the formula yields the Bekenstein-Hawking result but, for any other gravitational action that departs from the Hilbert action, the resulting entropy acquires an additional multiplicative factor that depends on the global geometry of the background spacetime. On the other hand, the generalized uncertainty principle (GUP) has extensively been recently used to investigate corrections to the Bekenstein-Hawking entropy formula…
A modified formulation of energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such modification will give corrections to both the temperature and the entropy of black holes. In particular this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaching the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter.
We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of the order of Planck length -- "world crystal". In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our 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-te…
In this Letter we study the effects of the Modified Uncertainty Principle as proposed in [8] on the inflationary dynamics of the early universe in both standard and Randall-Sundrum type II scenarios. We find that the quantum gravitational effect increase the amplitude of density fluctuation, which is oscillatory in nature, with an increase in the tensor-to-scalar ratio.
In this manuscript, we investigate the effects of a modified dispersion relation on the thermodynamics of Schwarzschild black hole surrounded by the quintessence matter. We find that the MDR-correction states the same lower bound on the horizon, while the quintessence matter specifies the upper bound to the horizon depending on the state parameter. Due to MDR-correction and quintessence matter presence, we observe modifications in equation of state and specific heat functions of black hole. We show that a remnant can occur according to quintessence matter, and the black hole's stability depend…
The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General Relativity. These corrections generically violate the Equivalence Principle. The GUP has also been indirectly applied to the gravitational source by relating the GUP modified Hawking temperature to a deformation of the background metric. Such a deformed background metric determines new geodesic motions without violating the Equivalence Principle. We point out her…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for testing the modified Heisenberg principle at high energies.In this paper, we formulate a relativistic Generalized Uncertainty Principle. We then use this to write the modified Klein-Gordon, Schrödinger and Dirac equations, and compute quantum gravity corrections to the relativistic hydrogen atom, particle in a box, and the linear harmonic oscillator.
The generalized uncertainty principle (GUP) corrected modified relativistic particle model has been derived in curved space-time. From this modified model, the equation of motion (EM) has been constructed relativistically in terms of the affine parameter ($λ$) or proper time ($τ$) and nonrelativistically in terms of coordinate time ($t$). In this context, the constraint analysis technique has been applied to get the EM. Interestingly, the EM obtained in both cases is the usual one. This result clearly indicates an important fact, that is, consistency of the equivalence principle in the GUP fra…
The standard Hawking formula predicts the complete evaporation of black holes. Taking into account effects of quantum gravity, we investigate fermions' tunnelling from a 5-dimensional rotating black string. The temperature is determined not only by the string, but also affected by the quantum number of the emitted fermion and the effect of the extra spatial dimension. The quantum correction slows down the increase of the temperature, which naturally leads to the remnant in the evaporation.
In this paper, we present a theoretical and numerical analysis of the free expansion of a Bose-Einstein condensate, where we assume that the single particle energy spectrum is deformed due to a possible quantum structure of spacetime. Also, we consider the presence of interparticle interactions in order to study more realistic and specific scenarios. The modified free velocity expansion of the condensate leads in a natural way to a modification of the uncertainty principle, which allows us to investigate some possible features of the Planck scale regime in low-energy earth-based experiments.
Motivated by the endeavors of Li Xiang and You-Gen Shen on naked singularities, we investigate the validity of the cosmic censorship conjecture in the context of generalized uncertainty principle. In particular, upon considering both linear and quadratic terms of momentum in the uncertainty principle, we first compute the entropy of a massless charged black hole in de Sitter spacetime at a given modified temperature. Then, we compute the corresponding modified cosmological radius and express the black hole electric charge in terms of this modified cosmological radius and, thus, in terms of the…
We consider quintessence scalar field cosmology in which the Lagrangian of the scalar field is modified by the Generalized Uncertainty Principle. We show that the perturbation terms which arise from the deformed algebra are equivalent with the existence of a second scalar field, where the two fields interact in the kinetic part. Moreover, we consider a spatially flat Friedmann-Lema\^ıtre-Robertson-Walker spacetime (FLRW), and we derive the gravitational field equations. We show that the modified equation of state parameter $w_{GUP}$ can cross the phantom divide line; that is $w_{GUP}<-1$. Furt…
It is often argued that quantum gravitational correction to the Heisenberg's uncertainty principle leads to, among other things, a black hole remnant with finite temperature. However, such a generalized uncertainty principle also seemingly removes the Chandrasekhar limit, i.e., it permits white dwarfs to be arbitrarily large, which is at odds with astrophysical observations. We show that this problem can be resolved if the parameter in the generalized uncertainty principle is negative. We also discuss the Planck scale physics of such a model.
It is shown that polymer quantization leads to a modified uncertainty principle similar to that obtained from string theory and non-commutative geometry. When applied to quantum field theory on general background spacetimes, corrections to the uncertainty principle acquire a metric dependence. For Friedmann-Robertson-Walker cosmology this translates to a scale factor dependence which gives a large effect in the early universe.
There are good indications that fundamental physics gives rise to a modified space-momentum uncertainty relation that implies the existence of a minimum length scale. We implement this idea in the scalar field theory that describes density perturbations in flat Robertson-Walker space-time. This leads to a non-linear time-dependent dispersion relation that encodes the effects of Planck scale physics in the inflationary epoch. Unruh type dispersion relations naturally emerge in this approach, while unbounded ones are excluded by the minimum length principle. We also find red-shift induced modifi…
We consider a new mass scale $M_{T}=(\hbar^{2}\sqrtΛ/G)^{1/3}$ constructed from dimensional analysis by using $G$, $\hbar$ and $Λ$ and discuss its physical interpretation. Based on the Generalized Uncertainty Relation, a black hole with age comparable to the universe would stop radiating when the mass reaches a new mass scale $M'_{T}=c(\hbar/G^{2}\sqrtΛ)^{1/3}$ at which its temperature corresponds to the mass $M_{T}$. Black hole remnants could have masses ranging from a Planck mass to a trillion kilograms. Holography persists even when the uncertainty relation is modified to the Minimum Length…
In this paper, we investigate a novel implication of the non-negligible spacetime curvature at large distances when its effects are expressed in terms of a suitably modified form of the Heisenberg uncertainty relations. Specifically, we establish a one-to-one correspondence between such modified uncertainty principle and the Standard Model Extension (SME), a string-theoretical effective field theory that accounts for both explicit and spontaneous breaking of Lorentz symmetry. This tight correspondence between string-derived effective field theory and modified quantum mechanics with extended un…
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…
Multiple approaches are required to study the evolution of black-hole binaries. While the post-Newtonian approximation is sufficient to describe the early inspiral (even from infinitely large orbital separation), only numerical relativity can capture the full complexity of the dynamics near merger. We combine multi-timescale post-Newtonian integrations with numerical-relativity surrogate models, thus mapping the entire history of the binary from its asymptotic configuration at past-time infinity to the post-merger remnant. This approach naturally allows us to assess the impact of the precessio…
The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts to a theory of quantum gravity and predicts the existence of a minimum length in Nature. In this work, we consider two cosmological models arising from Friedmann equations modified by the GUP (in its linear and quadratic formulations) and compare them with observational data. Our aim is to derive constraints on the GUP parameter and discuss the viability and physical implications of such models. We find for the parameter in the quadratic formulation the constraint $α^{2}_{Q}<10^{59}$ (tighter than most of those obtain…
