Horizon Fluctuations Research Articles

Black holes and random matrices

We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.

Teleporting entanglement during black hole evaporation

The unitary evaporation of a black hole (BH) in an initially pure state must lead to the eventual purification of the emitted radiation. It follows that the late radiation has to be entangled with the early radiation and, as a consequence, the entanglement among the Hawking pair partners has to decrease continuously from maximal to vanishing during the BH's life span. Starting from the basic premise that both the horizon radius and the center of mass of a finite-mass BH are fluctuating quantum mechanically, we show how this process is realized. First, it is shown that the horizon fluctuations induce a small amount of variance in the total linear momentum of each created pair. This is in contrast to the case of an infinitely massive BH, for which the total momentum of the produced pair vanishes exactly on account of momentum conservation. This variance leads to a random recoil of the BH during each emission and, as a result, the center of mass of the BH undergoes a quantum random walk. Consequently, the uncertainty in its momentum grows as the square root of the number of emissions. We then show that this uncertainty controls the amount of deviation from maximal entanglement of the produced pairs and that this deviation is determined by the ratio of the cumulative number of emitted particles to the initial BH entropy. Thus, the interplay between the horizon and center-of-mass fluctuations provides a mechanism for teleporting entanglement from the pair partners to the BH and the emitted radiation.

Horizon of quantum black holes in various dimensions

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general $(1+D)$-dimensional space-time, for $D>3$ and including the $D=1$ case. We find that the probability $P_{\rm BH}$ that such objects are (quantum) black holes behaves similarly to the probability in the $(3+1)$ framework for $D> 3$. In fact, for $D\ge 3$, the probability increases towards unity as the mass grows above the relevant $D$-dimensional Planck scale $m_D$. At fixed mass, however, $P_{\rm BH}$ decreases with increasing $D$, so that a particle with mass $m\simeq m_D$ has just about $10\%$ probability to be a black hole in $D=5$, and smaller for larger $D$. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for $D=1$, we find the probability is comparably larger for smaller masses, but $P_{\rm BH} < 0.5$, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass $m_D$ in $D>3$. For $D=1$ we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.

Accelerated detectors in Dirac vacuum: the effects of horizon fluctuations

We consider an Unruh–DeWitt detector interacting with a massless Dirac field. Assuming that the detector is moving along a hyperbolic trajectory, we modeled the effects of fluctuations of the event horizon using a Dirac equation with random coefficients. First, we develop the perturbation theory for the fermionic field in the presence of randomness. Furthermore, we evaluate corrections due to the randomness in the response function associated with different model detectors.

THERMAL RADIATION FROM A FLUCTUATING EVENT HORIZON

We consider a pointlike two-level system undergoing uniformly accelerated motion. We evaluate the transition probability rate of this system coupled to a massless scalar field near a fluctuating event horizon. Such horizon fluctuations are generated using random noise. We study the case of centered, stationary and Gaussian random processes. The transition probability of the two-level system is obtained from the positive-frequency Wightman function calculated to one-loop order in the noise averaging process. Our results show how this fluctuating-horizon model modifies the response function of the two-level system.

Quantum amplification effect in a horizon fluctuation

The appearance of a few unevenly- spaced bright flashes of light on top of Hawking radiation is the sign of the amplification effect in black hole horizon fluctuations. Previous studies on this problem suffer from the lack of considering all emitted photons in the theoretical spectroscopy of these fluctuations. In this paper, we include all of the physical transition weights and present a consistent intensity formula. This modifies a black hole radiation pattern.

Enhanced geometry fluctuations in Minkowski and black hole spacetimes

We will discuss selected physical effects of spacetime geometry fluctuations, especially the operational signatures of geometry fluctuations and their effects on black hole horizons. The operational signatures which we discuss involve the effects of the fluctuations on images, and include luminosity variations, spectral line broadening and angular blurring. Our main interest will be in black hole horizon fluctuations, especially horizon fluctuations which have been enhanced above the vacuum level by gravitons or matter in squeezed states. We investigate whether these fluctuations can alter the thermal character of a black hole. We find that this thermal character is remarkably robust, and that Hawking's original derivation using transplanckian modes does not seem to be sensitive even to enhanced horizon fluctuations.

Enhanced black hole horizon fluctuations

We discuss the possible role of quantum horizon fluctuations on black hole radiance, especially whether they can invalidate Hawking's analysis based upon transplanckian modes. We are particularly concerned with ``enhanced'' fluctuations produced by gravitons or matter fields in squeezed vacuum states sent into the black hole after the collapse process. This allows for the possibility of increasing the fluctuations well above the vacuum level. We find that these enhanced fluctuations could significantly alter stimulated emission, but have little effect upon the spontaneous emission. Thus the thermal character of the Hawking radiation is remarkably robust.

Quantum horizon fluctuations of an evaporating black hole

The quantum fluctuations of a black hole spacetime are studied within a low-energy effective field theory approach to quantum gravity. Our approach accounts for both intrinsic metric fluctuations and those induced by matter fields interacting with the gravitational field. Here we will concentrate on spherically symmetric fluctuations of the black hole horizon. Our results suggest that for a sufficiently massive evaporating black hole, fluctuations can accumulate over time and become significant well before reaching Planckian scales. In addition, we provide the sketch of a proof that the symmetrized two-point function of the stress-tensor operator smeared over a null hypersurface is actually divergent and discuss the implications for the analysis of horizon fluctuations. Finally, a natural way to probe quantum metric fluctuations near the horizon is briefly described.

Noise kernel and the stress energy bitensor of quantum fields in hot flat space and the Schwarzschild black hole under the Gaussian approximation

We continue our investigation of the properties of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D 63, 104001 (2001)] by working out explicit examples by means of the modified point-separation scheme and the Gaussian approximation for the Green functions in the manner of Bekenstein, Parker, and Page [J. D. Bekenstein and L. Parker, Phys. Rev. D 23, 2850 (1981); D. N. Page, ibid. 25, 1499 (1982)]. In the first part we consider the class of optical spacetimes. As a first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical-Schwarzschild spacetime we obtain after this procedure a finite expression for the noise kernel at the horizon. In the second part we consider the noise kernel for a scalar field in the Schwarzschild black hole. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation back reaction. Much of the work in this part is to determine how the divergent piece conformally transforms under the point-separation scheme. For the Schwarzschild metric we find that the fluctuations of the stress tensor of the Hawking flux in the far field region checks with the analytic results given by Campos and Hu earlier [A. Campos and B. L. Hu, Phys. Rev. D 58, 125021 (1998); Int. J. Theor. Phys. 38, 1253 (1999)]. We also verify Page's result for the stress tensor, which, though used often, still lacks a rigorous proof, since in his original work the direct use of the conformal transformation was circumvented. We find that the noise kernel at the Schwarzschild horizon is finite. This dispels speculations in some recent papers that the black hole fluctuations diverge at the horizon. However, as already manifest in the optical case, the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel evaluated there. We check this using the trace anomaly expression and identify the failure as occurring at the fourth covariant derivative order.

Wave propagation in stochastic spacetimes: Localization, amplification, and particle creation

Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves occurs in a Robertson-Walker universe with time-independent metric stochasticity, while time-dependent metric stochasticity induces exponential instability in the particle production rate. For the Schwarzschild metric, time-independent randomness can decrease the total luminosity of Hawking radiation due to multiple scattering of waves outside the black hole and gives rise to event horizon fluctuations and thus fluctuations in the Hawking temperature.

Cosmological and black hole horizon fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Light cone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the $\ensuremath{\delta}$ function on the classical light cone with a Gaussian function, the width of which is a measure of the scale of the light cone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.

Fourier spectra of three-dimensional data

view Abstract Citations (78) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Fourier Spectra of Three-dimensional Data Baumgart, David J. ; Fry, J. N. Abstract We evaluate the power spectrum, bispectrum, and tentatively the trispectrum, i.e., the two-, three-, and four-point galaxy correlation functions in Fourier transform space, for data from the CfA catalog and from the Perseus-Pisces redshift compilation of Giovanelli & Haynes. We work in the transform domain to avoid many systematic problems that afflict direct evaluations of correlation functions; this enables us to extend our knowledge of galaxy clustering to scales of order 100h^-1^ Mpc. At these large scales, the observed power spectrum ought to reflect directly the initial conditions. Our observed power spectrum agrees well with cold dark matter. The best fit gives {OMEGA}h = 0.34 +/- 0.10, while the inferred amplitude of scale-invariant horizon fluctuations is ɛ~(2-4) x 10^-5^. The observed bispectrum obeys the so-called hierarchical pattern, with a reduced threepoint amplitude that is consistent with gravitational instability in perturbation theory starting from Gaussian initial conditions. The trispectrum is only marginally detected, but is again consistent with the hierarchical pattern; the reduced four-point amplitude is determined only to be of order unity. These results constitute perhaps the first direct observational suggestion that gravitational instability in the perturbative regime indeed operates on large scales. Publication: The Astrophysical Journal Pub Date: July 1991 DOI: 10.1086/170166 Bibcode: 1991ApJ...375...25B Keywords: Fourier Transformation; Galactic Clusters; Galactic Structure; Power Spectra; Three Dimensional Models; Astronomical Catalogs; Computational Astrophysics; Numerical Analysis; Perturbation Theory; Astrophysics; GALAXIES: CLUSTERING; NUMERICAL METHODS full text sources ADS |

Strings from Gravity

The quantum properties of black holes are compared with those of elementary and composite particles. As argued before by this author, it is desirable to search for a theory of black holes in which quantum mechanical "information" is not drained away by the horizon, but such a theory requires a drastically new approach in formulating general coordinate transformations with horizons in a quantum theory. It is subsequently shown that a closed string with string tension T = 1/8πG reproduces in a remarkable way the horizon fluctuations so that a new geometric interpretation of strings is suggested.

XXX. Fluctuations in the intensity of radio waves from galactic sources

Summary It has been shown previously that the fluctuations in the intensity of radio energy from the galactic sources have a local terrestrial origin. This paper describes further observations of the two most intense sources, in the constellations of Cygnus and Cassiopeia, taken over a wide range of angles of elevation. At high angles of elevation the radio fluctuations are shown to be correlated with the occurrence of “spread” ionospheric echoes from the F region. When the sources are low on the northern horizon fluctuations are always observed; these are probably introduced by the passage of radio waves through the continuously disturbed ionospheric regions at high magnetic latitudes. Spaced receiver observations taken over base lines of 0·1, 4 and 11 km. enable the scale of the radio energy diffraction pattern across the ground to be determined.