Quantum Black Holes Research Articles

Information Conservation in a Noncommutative Quantum Black Hole Based on Canonical Typicality**Supported by the National Natural Science Foundation of China under Grant No. 11647060, Shaanxi Youth Outstanding Talent Support Plan, and the Fundamental Research Funds of Xianyang Normal University under Grant Nos. 15XSYK034 and XSYGG201802

A method for calculating the radiation spectrum of an arbitrary black holes was recently proposed by Ma et al., [Europhys. Lett. 122 (2018) 30001] in which a non-thermal spectrum of a black hole can be obtained from its entropy using an approach based on canonical typicality. The non-thermal spectrum of a black hole enables a nonzero correlation between the black hole and its radiation, which can ensure that information is conserved during black hole evaporation. In this paper, by using the Kantowski-Sachs metric and Feynman-Hibbs procedure, the entropy of a noncommutative quantum black hole is calculated based on the Wheeler-DeWitt equation. Then, the radiation spectrum of the noncommutative quantum black hole is studied based on canonical typicality method. At last, the correlation between the radiation spectra is calculated. It is shown that the noncommutative effect increases the correlation among radiation and the information remains conserved for noncommutative quantum black holes.

Thermal interpretation of Schwinger effect in near-extremal RN black hole

We propose a thermal interpretation of the Schwinger effect for charged spinless scalars and spin-1/2 fermions in an extremal and near-extremal Reissner–Nordström (RN) black hole. The emission of charges has the distribution with an effective temperature determined by the Davies–Unruh temperature for accelerating charges by the electric field and the scalar curvature of [Formula: see text] from the near-horizon geometry [Formula: see text]. We find a charge bound for the extremal micro-black hole to remain stable against the Schwinger emission in analogy with the Breitenlohner–Freedman bound for the [Formula: see text] space. In the in–out formalism, we find the one-loop QED effective action consistent with the vacuum persistence and interpret the vacuum persistence as the leading Schwinger effect and the effect of a charged vacuum of the Coulomb field.

Quantum black hole entropy from 4d supersymmetric Cardy formula

We study supersymmetric index of 4d $SU(N)$ $\mathcal{N}=4$ super Yang-Mills theory on $S^1 \times M_3$. We compute asymptotic behavior of the index in the limit of shrinking $S^1$ for arbitrary $N$ by a refinement of supersymmetric Cardy formula. The asymptotic behavior for the superconformal index case ($M_3 =S^3$) at large $N$ agrees with the Bekenstein-Hawking entropy of rotating electrically charged BPS black hole in $AdS_5$ via a Legendre transformation as recently shown in literature. We also find that the agreement formally persists for finite $N$ if we slightly modify the AdS/CFT dictionary between Newton constant and $N$. This implies an existence of non-renormalization property of the quantum black hole entropy. We also study the cases with other gauge groups and additional matters, and the orbifold $\mathcal{N}=4$ super Yang-Mills theory. It turns out that the entropies of all the CFT examples in this paper are given by $2\pi \sqrt{Q_1 Q_2 +Q_1 Q_3 +Q_2 Q_3 -2c(J_1 +J_2 )} $ with charges $Q_{1,2,3}$, angular momenta $J_{1,2}$ and central charge $c$. The results for other $M_3$ make predictions to the gravity side.

Fluctuation-dissipation and correlation-propagation relations in (1 + 3)D moving detector-quantum field systems

The fluctuation-dissipation relations (FDR) are powerful relations which can capture the essence of the interplay between a system and its environment. Challenging problems of this nature which FDRs aid in our understanding include the backreaction of quantum field processes like particle creation on the spacetime dynamics in early universe cosmology or quantum black holes. The less familiar, yet equally important correlation-propagation relations (CPR) relate the correlations of stochastic forces on different detectors to the retarded and advanced parts of the radiation propagated in the field. Here, we analyze a system of N uniformly-accelerated Unruh-DeWitt detectors whose internal degrees of freedom (idf) are minimally coupled to a real, massless, scalar field in 4D Minkowski space, extending prior work in 2D with derivative coupling. Using the influence functional formalism, we derive the stochastic equations describing the nonequilibrium dynamics of the idfs. We show after the detector-field dynamics has reached equilibration the existence of the FDR and the CPR for the detectors, which combine to form a generalized fluctuation-dissipation matrix relation. We show explicitly the energy flows between the constituents of the system of detectors and between the system and the quantum field environment. This power balance anchors the generalized FDR. We anticipate this matrix relation to provide a useful guardrail in expounding some basic issues in relativistic quantum information, such as ensuring the self-consistency of the energy balance and tracking the quantum information transfer in the detector-field system.

Perturbing microscopic black holes inspired by noncommutativity

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel–Kramers–Brillouin (WKB) approximation we show that the widely used WKB method does not converge in the critical cases where instabilities show up at the third order. By employing the inverted potential method, we demonstrate that the instabilities are an artifact of the WKB method. Finally, we discuss the usefulness of the asymptotic iteration method to find the QNMs.

Out-of-time-ordered correlators and quantum walks.

Out-of-time-ordered correlators (OTOCs) have recently attracted significant attention, finding applications in disparate areas, from the physics of many-body systems to quantum black holes, with an exponential growth of the OTOCs indicating quantum chaos. Here we consider OTOCs in the context of coined discrete quantum walks, a well-studied model of quantization of classical random walks with applications to quantum algorithms. Three separate cases of operators, variously localized in the coin and walker spaces, are discussed in this context and it is found that the approximated behavior of the OTOC is well described by simple algebraic functions in all three cases with different timescales of growth. The quadratic increase of OTOCs signals the absence of quantum chaos in these simplest forms of quantum walks.

Fast scrambling on sparse graphs

Given a quantum many-body system with few-body interactions, how rapidly can quantum information be hidden during time evolution? The fast-scrambling conjecture is that the time to thoroughly mix information among N degrees of freedom grows at least logarithmically in N. We derive this inequality for generic quantum systems at infinite temperature, bounding the scrambling time by a finite decay time of local quantum correlations at late times. Using Lieb-Robinson bounds, generalized Sachdev-Ye-Kitaev models, and random unitary circuits, we propose that a logarithmic scrambling time can be achieved in most quantum systems with sparse connectivity. These models also elucidate how quantum chaos is not universally related to scrambling: We construct random few-body circuits with infinite Lyapunov exponent but logarithmic scrambling time. We discuss analogies between quantum models on graphs and quantum black holes and suggest methods to experimentally study scrambling with as many as 100 sparsely connected quantum degrees of freedom.

Extended quantum portrait of MGD black holes and information entropy

The extended minimal geometric deformation (EMGD) is employed on the fluid membrane paradigm, to describe compact stellar objects as Bose–Einstein condensates (BEC) consisting of gravitons. The black hole quantum portrait, besides deriving a preciser phenomenological bound for the fluid brane tension, is then scrutinized from the point of view of the configurational entropy. It yields a range for the critical density of the EMGD BEC, whose configurational entropy has global minima suggesting the configurational stability of the EMGD BEC.

Weak-field limit and regular solutions in polynomial higher-derivative gravities

In the present work we show that, in the linear regime, gravity theories with more than four derivatives can have remarkable regularity properties if compared to their fourth-order counterpart. To this end, we derive the expressions for the metric potentials associated to a pointlike mass in a general higher-order gravity model in the Newtonian limit. It is shown that any polynomial model with at least six derivatives in both spin-2 and spin-0 sectors has regular curvature invariants. We also discuss the dynamical problem of the collapse of a small mass, considered as a spherical superposition of nonspinning gyratons. Similarly to the static case, for models with more than four derivatives the Kretschmann invariant is regular during the collapse of a thick null shell. We also verify the existence of the mass gap for the formation of mini black holes even if complex and/or degenerate poles are allowed, generalizing previous considerations on the subject and covering the case of Lee–Wick gravity. These interesting regularity properties of sixth- and higher-derivative models at the linear level reinforce the question of whether there can be nonsingular black holes in the full nonlinear model.

Gravitational axial perturbations and quasinormal modes of loop quantum black holes

Loop quantum gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole’s singularity. The detection of gravitational waves, on the other hand, has opened the way to new perspectives in the investigation of the spacetime structure. In this work, by the use of a WKB method introduced by Schutz and Will (Astrophys J 291:L33, 1985), and after improved by Iyer and Will (Phys Rev D 35:3621, 1987), we study the gravitational wave spectrum emitted by loop quantum black holes, which correspond to a quantized version of the Schwarzschild spacetime by LQG techniques. From the results obtained, loop quantum black holes have been shown stable under axial gravitational perturbations.

Testing quantum black holes with gravitational waves

We argue that near-future detections of gravitational waves from merging black hole binaries can test a long-standing proposal, originally due to Bekenstein and Mukhanov, that the areas of black hole horizons are quantized in integer multiples of the Planck area times an dimensionless constant . This condition quantizes the frequency of radiation that can be absorbed or emitted by a black hole. If this quantization applies to the ‘ring down’ gravitational radiation emitted immediately after a black hole merger, a single measurement consistent with the predictions of classical general relativity would rule out most or all (depending on the spin of the hole) of the extant proposals in the literature for the value of . A measurement of two such events for final black holes with substantially different spins would rule out the proposal for any . If the modification of general relativity is confined to the near-horizon region within the hole’s light ring and does not affect the initial ring down signal, a detection of ‘echoes’ with characteristic properties could still confirm the proposal.

Quasi stable black holes and their implications

We had already derived the criteria for thermal stability of charged rotating quantum black holes, for horizon areas that are large relative to the Planck area. We also had extended it for black holes with arbitrary number of hairs in arbitrary dimensional spacetime. We found that most of the criteria for thermal stability are satisfied even by some unstable black holes, although they do not satisfy all the criteria. These black holes are called ‘Quasi Stable’ black holes. We have already calculated thermal fluctuations and correlations among hairs of a stable quantum black hole. In this paper, we extend this work for quasi stable quantum black holes. We get the interesting result that quasi stable black holes have finite fluctuations and correlations for some of its hairs, although the black hole will ultimately radiate away due to Hawking radiation. We have also shown that quasi stable black holes may decay in a slower rate in comparision to unstable black holes.

Prediction of declining solar activity trends during solar cycles 25 and 26 and indication of other solar minimum

In this work we present a case that Microscopic Black Holes (MBH) of mass $10^{16}\ kg$ to $3 \cdot 10^{19}\ kg$ experience acceleration as they move within stellar material at low velocities. The accelerating forces are caused by the fact that a MBH moving through stellar material leaves a trail of hot rarified gas. The rarified gas behind a MBH exerts lower gravitational force on the MBH than the dense gas in front of it. The accelerating forces exceed the gravitational drag forces when MBH moves at Mach number $\mathcal{M}<\mathcal{M}_0$. The equilibrium Mach number $\mathcal{M}_0$ depends on MBH mass and stellar material characteristics. Our calculations open the possibility of MBH orbiting within stars including Sun at Mach number $\mathcal{M}_0$. At the end of this work we list some unresolved problems which result from our calculations.

Q-deformed Einstein equations from entropic force

In this study, we investigate the influences of fermionic q-deformation on the Einstein equations by taking into account of Verlinde’s entropic gravity approach and Strominger’s proposal on quantum black holes. According to Verlinde’s proposal, gravity is interpreted as an entropic force. Moreover, Strominger’s suggestion claims that extremal black holes obey deformed statistics instead of the standard Bose or Fermi statistics. Inspired by Verlinde’s and Strominger’s suggestions, we represent some thermostatistical functions of VPJC-type q-deformed fermion gas model for the high-temperature limit. Applying the Verlinde’s entropic gravity approach to the q-deformed entropy function, q-deformed Einstein equations with the effective cosmological constant are derived. The results obtained in this work are compared with the related works in the literature.

A UV complete picture of black hole conforming to low energy effective field theory

In this paper, we propose a UV complete, quantum improved picture of a black hole geometry that conforms to the IR gravity of effective field theory. Our work builds on identifying an effective space-distributed notion of black hole fluid in quantum improved regular Einstein gravity and its theoretical correspondence with a cosmology inspired power law fluctuation of matter. Hence, we make use of phenomenological asymptotic scales of matter fluctuation in static space to consequently derive a UV complete line-element of black hole space–time. In this appraisal, it gets explicit how principle of causality is preserved even while there is an effective spread of black hole fluid across horizon(s). Gravity changes from its conventional classical geometry-state to a quantum masked profile across a hypersurface of characteristic radius [Formula: see text]. We make analyses that probe the newly proposed quantum improved gravity in the contexts of regularity of Einstein fields, complete predictability of Hawking radiation process, and first law of black hole thermodynamics. It emerges that quantum black hole geometry self-regulates a regular timelike core that is abide by every quantum theoretical constraint while being flat around its center.

Quantum information or entanglement transfer between subsystems

The size of quantum information -- or entanglement -- transfer rates between subsystems is a generic question in problems ranging from decoherence in quantum computation and sensing, to quantum underpinnings of thermodynamics, to the behavior of quantum black holes. We investigate such rates for given couplings between subsystems, for sufficiently random subsystem evolution, and find evidence for a conjectured relation of these rates to the size of the couplings. This provides a direct connection between entanglement transfer and the microphysical couplings responsible for it.

Decoding infrared imprints of quantum origins of black holes

We analyze the emission spectrum of a (fundamentally quantum) black hole in the Kerr–Newman family by assuming a discretization of black hole geometry and the holographic entropy–area relation. We demonstrate that, given the above structure of black hole entropy, a macroscopic black hole always has non-continuously separated mass states and therefore they descend down in discrete manner. We evaluate the step size of the discrete spectrum, which vanishes in the extremal limit, leading to a continuum spectrum as expected from thermal nature of black holes. This further reveals an interesting relation, in each class, between the dynamic and kinematic length scales for all black holes belonging to the Kerr–Newman family, pointing towards a possible universal character across the class, dependent only on black hole mass. Further, we have presented the computation of maximum number of emitted quanta from the black hole as well as an estimation of its lifetime. We also argue the independence of these features from the presence of additional spacetime dimensions.

Does Compton–Schwarzschild duality in higher dimensions exclude TeV quantum gravity?

In three spatial dimensions, the Compton wavelength [Formula: see text]) and Schwarzschild radius [Formula: see text]) are dual under the transformation [Formula: see text], where [Formula: see text] is the Planck mass. This suggests that there could be a fundamental link — termed the Black Hole Uncertainty Principle or Compton–Schwarzschild correspondence — between elementary particles with [Formula: see text] and black holes in the [Formula: see text] regime. In the presence of [Formula: see text] extra dimensions, compactified on some scale [Formula: see text] exceeding the Planck length [Formula: see text], one expects [Formula: see text] for [Formula: see text], which breaks this duality. However, it may be restored in some circumstances because the effective Compton wavelength of a particle depends on the form of the [Formula: see text]-dimensional wave function. If this is spherically symmetric, then one still has [Formula: see text], as in the [Formula: see text]-dimensional case. The effective Planck length is then increased and the Planck mass reduced, allowing the possibility of TeV quantum gravity and black hole production at the LHC. However, if the wave function of a particle is asymmetric and has a scale [Formula: see text] in the extra dimensions, then [Formula: see text], so that the duality between [Formula: see text] and [Formula: see text] is preserved. In this case, the effective Planck length is increased even more but the Planck mass is unchanged, so that TeV quantum gravity is precluded and black holes cannot be generated in collider experiments. Nevertheless, the extra dimensions could still have consequences for the detectability of black hole evaporations and the enhancement of pair-production at accelerators on scales below [Formula: see text]. Though phenomenologically general for higher-dimensional theories, our results are shown to be consistent with string theory via the minimum positional uncertainty derived from [Formula: see text]-particle scattering amplitudes.

Schwarzschild-de Sitter black hole in canonical quantization

We solve Wheeler-De Witt (WDW) metric probability wave equation on the apparent horizon hypersurface of the Schwarzschild de Sitter (SdS) black hole. To do so we choose radial dependent mass function M(r) for its internal regions in the presence of a dynamical massless quantum matter scalar field ψ(r) and calculate canonical supper hamiltonian constraint on t-constant hypersurface near the horizon r = M(r). In this case M(r) become geometrical degrees of freedom while ψ(r) is matter degrees of freedom of the apparent horizon. However our solution is obtained versus the quantum harmonic oscillator which defined against the well known hermit polynomials. In the latter case we obtain quantized mass of the SdS quantum black hole as in which Λ is the cosmological constant and n = 0,1, 2, ⋯ are quantum numbers of the hermit polynomials. This shows that a quantized SdS in its ground state has a nonzero value for the mass . Thus one can infer that the latter result satisfies Penrose hypotheses for cosmic censorship where a causal singularity may be covered by a horizon surface.

Mimicking black hole event horizons in atomic and solid-state systems

Holographic quantum matter exhibits an intriguing connection between quantum black holes and more conventional (albeit strongly interacting) quantum many-body systems. This connection is manifested in the study of their thermodynamics,statistical mechanics and many-body quantum chaos. After explaining some of those connections and their significance, we focus on the most promising example to date of holographic quantum matter, the family of Sachdev-Ye-Kitaev (SYK) models. Those are simple quantum mechanical models that are thought to realize, holographically, quantum black holes. We review and assess various proposals for experimental realizations of the SYK models. Such experimental realization offers the exciting prospect of accessing black hole physics, and thus addressing many mysterious questions in quantum gravity, in tabletop experiments.