Emergent horizon,Hawking radiation and chaos in the collapsed polymer model of a black hole

We have proposed that the interior of a macroscopic Schwarzschild black hole (BH) consists of highly excited, long, closed, interacting strings and, as such, can be modeled as a collapsed polymer. It was previously shown that the scaling relations of the collapsed‐polymer model agree with those of the BH. The current paper further substantiates this proposal with an investigation into some of its dynamical consequences. In particular, we show that the model predicts, without relying on gravitational effects, an emergent horizon. We further show that the horizon fluctuates quantum mechanically as it should and that the strength of the fluctuations is inversely proportional to the BH entropy. It is then demonstrated that the emission of Hawking radiation is realized microscopically by the quantum‐induced escape of small pieces of string, with the rate of escape and the energy per emitted piece both parametrically matching the Hawking temperature. We also show, using standard methods from statistical mechanics and chaos theory, how our model accounts for some other known properties of BHs. These include the accepted results for the scrambling time and the viscosity‐to‐entropy ratio, which in our model apply not only at the horizon but throughout the BH interior.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Entropy of the rotating and charged black string to all orders in the Planck length

<正>By using the entanglement entropy method,this paper calculates the statistical entropy of the Bose and Fermi fields in thin films,and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string.Here,the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string.Taking into account the effect of the generalized uncertainty principle on quantum state density,it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model.These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect.The ultraviolet cut-off in the brick-wall model is not reasonable.The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon.From the viewpoint of quantum statistical mechanics,the correction value of Bekenstein-Hawking entropy is obtained.This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.     

Spontaneous and induced decay of metastable strings and domain walls

We consider decay of metastable topological configurations such as strings and domain walls. The transition from a state with higher energy density to a state with lower one proceeds through quantum tunneling or through thermally catalyzed quantum tunneling (at sufficiently small temperatures). The transition rate is calculated at zero temperature including the preexponential factor and also at a finite low temperature. The thermal enhancement factor is closely related to the probability (effective length) of destruction of the string (the domain wall) in collisions of the Goldstone bosons, corresponding to transverse waves on the string (wall). We derive a general formula which allows to find the probability (effective length) of a string (wall) breakup by a collision of arbitrary number of the bosons. We find that the destruction of a string only takes place in collisions of even number of the bosons, while the destruction of the wall can occur in a collision of any number of particles. We explicitly calculate the energy dependence of such processes in two-particle collisions for arbitrary relation between the energy and the largest infrared scale (the size of a critical gap).     

Point-like structure and off-shell dual strings

We argue that in a consistent off-shell dual formalism the amplitude for the emission of a scalar off-shell state by a string consists of two components. One of these contains the particle poles in the off-shell leg and the other is intimately related to the insertion of a point-like energy density on the string. As a result, the amplitude for a string to emit a zero momentum scalar state into the vacuum (which may be relevant for spontaneous symmetry breaking) is described by the amplitude for a finite fraction of the energy in the string to collapse to a spatial point at some time (this fraction and its space-time position being integrated over). The off-shell amplitudes have an elegant formulation in terms of a set of “confined modes” which can be assigned quark flavour quantum numbers to reproduce the Chan-Paton scheme.We suggest the dual model be modified by allowing for the coupling of scalar closed strings to the vacuum and the resulting effect on the space-time structure of dual Green functions is described.We find that even the emission of a single zero-momentum closed string modifies the elastic amplitude in a significant manner, leading to a power-behaved fixed-angle cross section in contrast to the usual exponential decrease of the dual model. This arises from point-like scattering between energy densities accumulating in the colliding strings. The relationship between the fixed angle and Regge limits is discussed. The fixed angle behaviour is found to be the asymptotic limit in momentum transfer of a fixed pole that arises in the Regge limit.     

Stable charged cosmic strings

We study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electroweak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple trough in the Higgs vacuum expectation value of radius ≈10(-18) m. The vacuum remains stable in our model, because neutral strings are not energetically favored.     

Entanglement entropy,black holes and holography

We observe that the entanglement entropy resulting from tracing over a subregion of an initially pure state can grow faster than the surface area of the subregion (indeed, proportional to the volume), in contrast to examples studied previously. The pure states with this property have long-range correlations between interior and exterior modes and are constructed by purification of the desired density matrix. We show that imposing a no-gravitational-collapse condition on the pure state is sufficient to exclude faster than area law entropy scaling. This observation leads to an interpretation of holography as an upper bound on the realizable entropy (entanglement or von Neumann) of a region, rather than on the dimension of its Hilbert space.     

The Role of Magnetic Field in Anisotropic String Cosmological Model

In this paper we consider a spatially homogenous and anisotropic Bianchi type-V space-time model to investigate the effects of a magnetic field in string cosmology. We assume that the string’s direction and magnetic field are along x-axis. The field equations are solved by using the equation of state for a cloud of strings and variable magnetic permeability. We derive exact solutions for three types of strings: (i) Nambu strings, (ii) string model where the sum of energy density and string tension density is zero and (iii) Takabayasi strings. We examine the behaviour of scale factors and other physical parameters with and without magnetic field and it is found that the magnetic field effects the dynamics of the universe at early time. During late time the universe becomes isotropic even in the presence of magnetic field. The universe expands with decelerated rate during early stages of the evolution of the universe but it goes to marginal inflation at late times.     

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.     

Topological entanglement entropy

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.     

Quantum Limits on the Entropy of Bandlimited Radiation

Physical limits on the amount of information carried by bandlimited waveforms radiated in one and three dimensions are considered. It is shown that the entropy of radiation can achieve the Bekenstein bound using a “burst” of energy, whose density vanishes as the radiating system expands. In comparison, black body radiation of infinite bandwidth achieves the same entropy scaling, that is proportional to the volume of the space, but requires an energy density that remains constant as the system expands. Rather than following the standard statistical physics approach of counting the number of eigenstates of the Hamiltonian of the quantum wave field, our derivation first considers an optimal subspace approximation, and then determines the number of bits that are required to represent any waveform in the space spanned by this representation with a minimum quantized energy error. This favors a geometric interpretation where the complexity of state counting is replaced by the one of determining the minimum cardinality covering of the signal space by high-dimensional balls, or boxes, whose size is lower bounded by quantum constraints. All derivations are given for both deterministic and stochastic settings.     

Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody

We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.     

Bekenstein-Hawking Cosmological Entropy and Correction Term Corresponding Cosmological Horizon of Rotating and Charged Black String

Utilizing the quantum statistical method and applying the new state density equation motivated by generalized uncertainty principle in quantum gravitaty, we avoid the difficulty in solving wave equation and directly calculate the partition function ofbosonic and fermionic field on the background of rotating and charged black string. Then near the cosmological horizon, entropies of bosonic and fermionic field are calculated on the background of black string. When constant λ introduced ingeneralized uncertainty principle takes a proper value, we derive Bekenstein-Hawking entropy and the correction value corresponding cosmological horizon on the background of rotating and charged black string. Because we use the new state density equation, in our calculation there are not divergent term and small massapproximation in the original brick-wall method. From the view of quantum statistic mechanics, the correction value to Bekenstein-Hawking entropy of the black string is derived. It makes people deeply understand the correction value to the entropyof the black string cosmological horizon in non-spherical coordinate spacetime.     

String Scattering from Decaying Branes

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szegö, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.     

Black hole greybody factors and absorption of scalars by effective strings

We compute the greybody factors for classical black holes in a domain where two kinds of charges and their anticharges are excited by the extra energy over extremality. We compare the result to the greybody factors expected from an effective string mode] which was earlier shown to give the correct entropy. In the regime where the left- and right-moving temperatures are much smaller than the square root of the effective string tension, we find a non-trivial greybody factor which agrees with the effective string mode]. However, if the temperatures are comparable with the square root of the effective string tension, the greybody factors agree only at the leading order in energy. Nevertheless, there are several interesting relations between the two results, suggesting that a modification of the effective string mode] might lead to better agreement.     

Universality of black hole quantum computing

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model‐independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft‐enough in order not to offset the basic properties of the system. We derive model‐independent bounds on some crucial time‐scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time‐scales are of the order of the black hole half‐life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life‐time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life‐time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro‐state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.