Parikh-Wilczek tunnelling framework, which treats Hawking radiation as a tunnelling process, is investigated again. As the first order correction, the log-corrected entropy-area relation naturally emerges in the tunnelling picture if we consider the emission of a spherical shell. The second order correction of the emission rate for the Schwarzschild black hole is calculated too. In this level, the result is still in agreement with the unitary theory, however, the entropy of the black hole will contain three parts: the usual Bekenstein-Hawking entropy, the logarithmic term and the inverse area term. In our results the coefficient of the logarithmic term is -1. Apart from a coefficient, Our correction to the black hole entropy is consistent with that of loop quantum gravity.
The remnants are investigated by fermions' tunnelling from a 4-dimensional charged dilatonic black hole and a 5-dimensional black string. Based on the generalized uncertainty principle, effects of quantum gravity are taken into account. The quantum numbers of the emitted fermions affects the Hawking temperatures. For the black hole, the quantum gravity correction slows down the increase of the temperature, which leads to the remnant left in the evaporation. For the black string, the existence of the remnant is determined by the quantum gravity correction and effects of the extra compact dimens…
Hawking's calculation is unable to predict the final stage of the black hole evaporation. When effects of quantum gravity are taken into account, there is a minimal observable length. In this paper, we investigate fermions' tunnelling from the charged and rotating black strings. With the influence of the generalized uncertainty principle, the Hawking temperatures are not only determined by the rings, but also affected by the quantum numbers of the emitted fermions. Quantum gravity corrections slow down the increases of the temperatures, which naturally leads to remnants left in the evaporation…
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.
Hawking radiation of black ring solutions to 5-dimensional Einstein-Maxwell-dilaton gravity theory is analyzed by use of the Parikh-Wilczek tunnelling method. To get the correct tunnelling amplitude and emission rate, we adopted and developed the Angheben-Nadalini-Vanzo-Zerbini covariant approach to cover the effects of rotation and electronic discharge all at once, and the effect of back reaction is also taken into account. This constitute a unified approach to the tunnelling problem. Provided the first law of thermodynamics for black rings holds, the emission rate is proportional to the expo…
In this paper, using Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. Base on the generalized uncertainty principle, we introduce the influence of quantum gravity. After solving the equation of motion of the spin 1/2 field, we derive the corrected Hawking temperature. It turns out that the correction depends not only on the black hole's mass but also on the mass (energy) of emitted fermions. It is of interest that, in our calculation, the quantum gravity correction decelerates the temperature increase during the radiation explicitly. Thi…
Considered is quantum tunnelling in anisotropic spin systems in a magnetic field perpendicular to the anisotropy axis. In the domain of small field the problem of calculating tunnelling splitting of energy levels is reduced to constructing the perturbatio n series with degeneracy, the order of degeneracy being proportional to a spin value. Partial summation of this series taking into account ''dangerous terms'' with small denominators is performed and the value of tunnelling splitting is calculated with allowance for the first correction with respect to a magnetic field.
Experiments on tunneling into fractional quantum Hall droplets systematically found tunneling exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory. In this note, by considering the effects of a smooth boundary, we propose a modification of the theory that predicts a reduced exponent, in qualitative agreement with experiments. Such modification consists on a self-interaction cubic term, containing higher derivatives of the chiral boson field, that provides a non-universal one loop correction to the propagator.
We probe both the unidimensional quartic harmonic oscillator and the double well potential through a numerical analysis of the Functional Renormalization Group flow equations truncated at first order in the derivative expansion. The two partial differential equations for the potential V_k(varphi) and the wave function renormalization Z_k(varphi), as obtained in different schemes and with distinct regulators, are studied down to k=0, and the energy gap between lowest and first excited state is computed, in order to test the reliability of the approach in a strongly non-perturbative regime. Our …
The paper deals with non-thermal radiation spectrum by tunnelling mechanism with correction due to the generalized uncertainty principle (GUP) in the background of non-commutative geometry. Considering the reformulation of the tunnelling mechanism by Banerjee and Majhi, the Hawking radiation spectrum is evaluated through the density matrix for the outgoing modes. The GUP corrected effective temperature and the corresponding GUP corrected effective metric in non-commutative geometry are determined using Hawking's periodicity arguments. Thus, we obtain further corrections to the non-strictly the…
Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the instanton physics, first, explicit instanton solutions are found and next, quantities like Pontryagin index and the semiclassical approximation to the inter-vacua tunnelling amplitude are evaluated. The Atiyah-Patodi-Singer index theorem is checked as well by constructing explicitly the normalizable fermion zero modes in this de Sitter spacetime instanton b…
We compute logarithmic corrections to the entropy of a magnetically charged extremal black hole in AdS4 x S7 using the quantum entropy function and discuss the possibility of matching against recently derived microscopic expressions.
We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections to various quantum phenomena. We compute such corrections to the Lamb Shift, the Landau levels and the tunnelling current in a Scanning Tunnelling Microscope (STM). We show that these corrections can be interpreted in two ways: (a) either that they are exceedingly small, beyond the reach of current experiments, or (b) that they predict upper bounds on the qu…
We use holographic techniques to calculate the first thermal correction to the entanglement entropy of a cap-like region of a CFT defined on a sphere, successfully reproducing the field theory result. Since this is an order-one correction to the entropy in the large-$N$ expansion, quantum corrections to the holographic entanglement entropy formula are essential. The bulk calculation is made tractable using the same technical machinery recently used to derive the linearized Einstein equations in the bulk from the first law of entanglement entropy in the CFT.
Using a relation between the thermodynamics of local horizons and the null energy condition, we consider the effects of quantum corrections to the gravitational entropy. In particular, we find that the geometric form of the null energy condition is not affected by the inclusion of logarithmic corrections to the Bekenstein-Hawking entropy.
We study higher derivative corrections to the statistical entropy function and the statistical entropy for five dimensional BMPV black holes by doing the asymptotic expansion of the partition function. This enables us to evaluate entropy for a large range of charges, even out of Cardy (Farey tail) limit.
The quantum corrections to the entropy of charged black holes are calculated. The Reissner-Nordstrem and dilaton black holes are considered. The appearance of logarithmically divergent terms not proportional to the horizon area is demonstrated. It is shown that the complete entropy which is sum of classical Bekenstein-Hawking entropy and the quantum correction is proportional to the area of quantum-corrected horizon.
We calculate the correction to the Bekenstein-Hawking entropy formula for five dimensional AdS-Schwarzschild black holes due to thermodynamic fluctuations. The result is then compared with the boundary gauge theory entropy corrections via AdS/CFT correspondence. We then further generalise our analysis for the rotating black hole in five dimensional AdS space.
Using Rindler method we derive the logarithmic correction to the entanglement entropy of a two dimensional BMS-invariant field theory (BMSFT). In particular, we present a general formula for extraction of the logarithmic corrections to both the thermal and the entanglement entropies. We also present a CFT formula related to the logarithmic correction of the BTZ inner horizon entropy which results in our formula after taking appropriate limit.
We present subleading corrections to the N=2 supersymmetric black hole entropy. These subleading contributions correspond to instanton corrections of the Type II string theory. In particular we consider an axion free black hole solution of low-energy effective Type II string theory. We present a procedure to include successively all instanton corrections. Expanding these corrections at particular points in moduli space yields polynomial and logarithmic instanton corrections to the classical black hole entropy. We comment on a microscopic interpretation of these instanton corrections and find t…
We study the leading $α^\prime$ corrections to the entropy of certain black holes with AdS$_5\times S^5$ asymptotics. We find that, in the supersymmetric limit, the entropy does not receive $α^\prime$ corrections. This result strengthens recent calculations that match the index of $\mathcal{N}=4$ Super-Yang-Mills with the corresponding partition function in the supersymmetric limit. In the small temperature regime, we find that the entropy corrections are concordant with the weak gravity conjecture.
We consider entanglement entropy in quantum field theories with a gravity dual. In the gravity description, the leading order contribution comes from the area of a minimal surface, as proposed by Ryu-Takayanagi. Here we describe the one loop correction to this formula. The minimal surface divides the bulk into two regions. The bulk loop correction is essentially given by the bulk entanglement entropy between these two bulk regions. We perform some simple checks of this proposal.
From the perspective of AdS/CFT correspondence, we study the gravitational Chern-Simons term correction to the holographic entanglement entropy of CFT on the conformal boundary of asymptotically AdS$_3$ spacetime using the off-shell Euclidean path integral method. We show that, like the BTZ black hole entropy, the holographic entanglement entropy is indeed modified due to the gravitational Chern-Simons term although the bulk geometry does not change.
We calculate the quantum corrections to the entropy of a very large black hole, coming from the theory of a $D$-dimensional, non-critical bosonic string. We show that, for $D >2$, as a result of modular invariance the entropy is ultraviolet finite, although it diverges in the infrared (while for $D=2$ the entropy contains both ultraviolet and infrared divergences). The issue of modular invariance in field theory, in connection with black-hole entropy, is also investigated.
The holographic entanglement entropy is computed for an entangling surface that coincides with the horizon of a boundary de Sitter metric. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. The entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. The entanglement entropy takes the expected form of the de Sitter entropy, incl…
The microscopic formula for the degeneracy of BMPV black hole microstates contains a series of exponentially suppressed corrections to the leading Bekenstein Hawking expression. We identify saddle points of the quantum entropy function for the BMPV black hole which are natural counterparts to these corrections and discuss the matching of leading and next-to-leading terms from the microscopic and macroscopic sides in a limit where the black hole charges are large.
It has been shown by A. Sen that logarithmic corrections to the black hole area-entropy law are entirely determined macroscopically from the massless particle spectrum. They therefore serve as powerful consistency checks on any proposed enumeration of quantum black hole microstates. Sen's results include a macroscopic computation of the logarithmic corrections for a five-dimensional near extremal Kerr-Newman black hole. Here we compute these corrections microscopically using a stringy embedding of the Kerr/CFT correspondence and find perfect agreement.
Recently, Guica, Huang, Li, and Strominger considered an R^2 correction to the entropy of a black ring, and found a mismatch between supergravity and the CFT. However, such a comparison should take into account the subtle distinction between the asymptotic charges of the black ring and the charges entering the CFT description. We show that using the correct charges yields perfect agreement.
We compute logarithmic corrections to the twisted index $B^g_6$ in four-dimensional $\mathcal{N}=4$ and $\mathcal{N}=8$ string theories using the framework of the Quantum Entropy Function. We find that these vanish, matching perfectly with the large--charge expansion of the corresponding microscopic expressions.
We study thermodynamical aspects of string theory in the limit in which it corresponds to Noncommutative Yang-Mills. We confirm, using the AdS/CFT correspondence, that for general Dp branes the entropy in the planar approximation depends neither on the value of the background magnetic field B nor on its rank. We find 1/N corrections to the planar entropy in the WKB approximation. For all appropriate values of p these corrections are much softer than the corresponding corrections for the B=0 case, and vanish altogether in the high temperature limit.
In a $d$-dimensional conformal field theory, it has been known that a relevant deformation operator with the conformal dimension, $Δ=\frac{d+2}{2}$, generates a logarithmic correction to the entanglement entropy. In the large 't Hooft coupling limit, we can investigate such a logarithmic correction holographically by deforming an AdS space with a massive scalar field dual to the operator with $Δ=\frac{d+2}{2}$. There are two sources generating the logarithmic correction. One is the metric deformation and the other is the minimal surface deformation. In this work, we investigate the change of t…
We calculate the statistical entropy of a quantum field with an arbitrary spin propagating on the spherical symmetric black hole background by using the brick wall formalism at higher orders in the WKB approximation. For general spins, we find that the correction to the standard Bekenstein-Hawking entropy depends logarithmically on the area of the horizon. Furthermore, we apply this analysis to the Schwarzschild and Schwarzschild-AdS black holes and discuss our results.
We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".
We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hole. In the extreme case the contributions from graviton, gravitino and photon to the one-loop corrections to the entropy are shown to cancel. This gives the first explicit example of the supersymmetric non-renormalization theorem for the on-shell action (entropy) for BPS configurations which admit Killing spinors. We display the residual supersymmetry of the perturbations of a general supersymmetric theory in a bosonic BPS background.
We consider charged black holes in four dimensional AdS space, in the presence of a Weyl correction. We obtain the solution including the effect of back-reaction, perturbatively up to first order in the Weyl coupling, and study its thermodynamic properties. This is complemented by a calculation of the holographic entanglement entropy of the boundary theory. The consistency of results obtained from both computations is established.
Thermal corrections to the entropy of black holes in the Lovelock gravity are calculated. As the thermodynamic behavior of the black holes of this theory falls into two classes, the thermodynamic quantities are computed in each case. Finally, the logarithmic prefactors are obtained in two different limits.
We extend earlier work on the origin of the Bekenstein-Hawking entropy to higher-dimensional spacetimes. The mechanism of counting states is shown to work for all spacetimes associated with a Euclidean doublet $(E_1,M_1)+(E_2,M_2)$ of electric-magnetic dual brane pairs of type II string-theory or M-theory wrapping the spacetime's event horizon plus the complete internal compactification space. Non-Commutativity on the brane worldvolume enters the derivation of the Bekenstein-Hawking entropy in a natural way. Moreover, a logarithmic entropy correction with prefactor 1/2 is derived.
The first quantum corrections to the free energy for an eternal 4-dimensional black hole is investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. The quadratic and logarithmic divergences as well as a finite part associated with the first quantum correction to the entropy are obtained at a generic temperature. It is argued that, at the Hawking temperature, the horizon divergences of the internal energy should cancel. Some comments on the divergences of the entropy are also presented.
In four-dimensional N=2 compactifications of string theory or M-theory, modifications of the Bekenstein-Hawking area law for black hole entropy in the presence of higher-derivative interactions are crucial for finding agreement between the macroscopic entropy obtained from supergravity and subleading corrections to the microscopic entropy obtained via state counting. Here we compute the modifications to the area law for various classes of black holes, such as heterotic black holes, stemming from certain higher-derivative gravitational Wilsonian coupling functions. We consider the extension to …
The first quantum corrections to the entropy for an eternal 4-dimensional extremal Reissner-Nordström black hole is investigated at one-loop level, in the large mass limit of the black hole, making use of the conformal techniques related to the optical metric. A leading cubic horizon divergence is found and other divergences appear due to the singular nature of the optical manifold. The area law is shown to be violated.
We compute the leading corrections to the Bekenstein-Hawking entropy of the Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the flat analogues of the BTZ black holes in AdS3. The analysis is done by a computation of density of states in the dual 2D Galilean Conformal Field Theory and the answer obtained by this matches with the limiting value of the expected result for the BTZ inner horizon entropy as well as what is expected for a generic thermodynamic system. Along the way, we also develop other aspects of holography of 3D flat spacetimes.
We present a consolidated manual of Euclidean gravity approaches for finding the logarithmic corrections to the entropy of the full Kerr-Newman family of black holes in both extremal and non-extremal limits. Seeley-DeWitt coefficients for the quadratic fluctuations of a concern gravity theory appear to be the key ingredients in this manual. Following the manual, we calculate the first three Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and non-extremal black holes in a generalized Einstein-Maxwell theory minimally-coupled to additional massless scalar, vecto…
We study one-loop covariant effective action of \say{non-minimally coupled} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional determinant of Laplacian differential operator following Seeley-DeWitt technique of heat kernel expansion in proper time. We then compute the Seeley-DeWitt coefficients obtained through the expansion. A particular Seeley-DeWitt coefficient is used for determining the logarithmic correction to Bekenstein-Hawking entropy of extremal black holes using quantum e…
Recent work that treats the Hawking radiation as a semi-classical tunnelling process from the four-dimensional Schwarzschild and Reissner-Nordstrom black holes is extended to the case of higher dimensional Reissner-Nordstrom-de Sitter black holes. The result shows that the tunnelling rate is related to the change of Bekenstein-Hawking entropy and the exact radiant spectrum is no longer precisely thermal after considering the black hole background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation and electric charge conservation are…
We use the black hole entropy function to study the effect of Born-Infeld terms on the entropy of extremal black holes in heterotic string theory in four dimensions. We find that after adding a set of higher curvature terms to the effective action, attractor mechanism works and Born-Infeld terms contribute to the stretching of near horizon geometry. In the alpha'--> 0 limit, the solutions of attractor equations for moduli fields and the resulting entropy, are in conformity with the ones for standard two charge black holes.
We calculate corrections to the Bekenstein-Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing $k$ by $-k$. Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild-de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.
For general finite temperature different from the Hawking one there appears a well known conical singularity in the Euclidean classical solution of gravitational equations. The method of regularizing the cone by regular surface is used to determine the curvature tensors for such a metrics. This allows one to calculate the one-loop matter effective action and the corresponding one-loop quantum corrections to the entropy in the framework of the path integral approach of Gibbons and Hawking. The two-dimensional and four-dimensional cases are considered. The entropy of the Rindler space is shown t…
We revisit the computation of logarithmic corrections to black holes with N equal or greater than 2 supersymmetry. We employ an on-shell method that takes advantage of the symmetries in the AdS(2) x S**2 near horizon geometry. For bulk modes interactions are incorporated through the spectrum of chiral primaries that we derive afresh. The spectrum of boundary states is computed explicitly by analyzing gauge variations. Elementary heat kernels in 4D and 2D then give the logarithmic corrections to the black hole entropy. Our computation represents a streamlined and simplified derivation that agre…
We find R^4 correction to the non-extremal D1D5P solution of the supergravity by exactly solving the differential equations of motion and by using the entropy function formalism. In both cases, we find the same correction to the supergravity solution. We then calculate the correction to the entropy using the free energy method and the entropy function formalism. The results are the same.
We reviewed the field redefinition approach of Seeley-DeWitt expansion for the determination of Seeley-DeWitt coefficients from arXiv:1505.01156. We apply this approach to compute the first three Seeley-DeWitt coefficients for \say{non-minimal} $\mathcal{N}=1$ Einstein-Maxwell supergravity in four dimensions. Finally, we use the third coefficient for the computation of the logarithmic corrections to the Bekenstein-Hawking entropy of non-extremal black holes following arXiv:1205.0971. We determine the logarithmic corrections for non-extremal Kerr-Newman, Kerr, Reissner-Nordström and Schwarzschi…
We study the entropy of non-supersymmetric extremal black holes which exhibit attractor mechanism by making use of the entropy function. This method, being simple, can be used to calculate corrections to the entropy due to higher order corrections to the action. In particular we apply this method for five dimensional non-supersymmetric extremal black hole which carries two magnetic charges and find the R^2 corrections to the entropy. Using the behavior of the action evaluated for the extremal black hole near the horizon, we also present a simple expression for C-function corrected by higher or…
We compute the statistical entropy of the three charge (D1-D5-p) five dimensional black hole to sub-leading order in a large charge expansion. We find an agreement with the macroscopic calculation of the Wald entropy in R^2 corrected supergravity theory. The two calculations have a overlapping regime of validity which is not the Cardy regime. We use this result to clarify the 4d-5d lift for black holes on Taub-NUT space. In particular, we compute sub-leading corrections to the formula S^{4d} = S^{5d}. In the microscopic analysis, this correction arises from excitations bound to the Taub-NUT sp…
We use the formalism of geodesic Witten diagrams to study the holographic realization of the conformal block expansion for entanglement entropy of two disjoint intervals. The agreement between the Ryu-Takayanagi formula and the identity block contribution has a dual realization as the product of bulk to boundary propagators. Quantum bulk corrections instead arise from stripped higher order diagrams and back-reaction effects; these are also mapped to the structure for $G_N^0$ terms found in \cite{Faulkner:2013ana}, with the former identified as the bulk entanglement entropy across the Ryu-Takay…
