Geometric Horizon Research Articles

Geometric horizons in binary black hole mergers

We numerically study the algebraic properties of the Weyl tensor through the merger of two non-spinning black holes (BHs). We are particularly interested in the conjecture that for such a vacuum spacetime, which is zeroth-order algebraically general, a geometric horizon (GH), on which the spacetime is algebraically special and which is identified by the vanishing of a complex scalar invariant (), characterizes a smooth foliation independent surface (horizon) associated with the BH. In the first simulation we investigate the level-0 sets of (since ) in the head-on collision of two unequal mass BHs. In the second simulation we shall investigate the level-ɛ sets of through a quasi-circular merger of two non-spinning, equal mass BHs. The numerical results, as displayed in the figures presented, provide evidence that a (unique) smooth GH can be identified throughout all stages of the binary BH merger.

Geometric surfaces: An invariant characterization of spherically symmetric black hole horizons and wormhole throats

We consider a spherically symmetric line element which admits either a black hole geometry or a wormhole geometry and show that in both cases the apparent horizon or the wormhole throat is partially characterized by the zero set of a single curvature invariant. The detection of the apparent horizon by this invariant is consistent with the geometric horizon detection conjectures and implies that it is a geometric horizon of the black hole, while the detection of the wormhole throat presents a conceptual problem for the conjectures. To distinguish between these surfaces, we determine a set of curvature invariants that fully characterize the apparent horizon and wormhole throat. Motivated by this result, we introduce the concept of a geometric surface as a generalization of a geometric horizon and extend the geometric horizon detection conjectures to geometric surfaces. As an application, we employ curvature invariants to characterize three important surfaces of the line element introduced by Simpson, Martin-Moruno, and Visser, which describes transitions between regular Vaidya black holes, traversable wormholes, and black bounces.

Persistence in black hole lattice cosmological models

Dynamical solutions for an evolving multiple network of black holes near a cosmological bounce dominated by a scalar field are investigated. In particular, we consider the class of black hole lattice models in a hyperspherical cosmology, and we focus on the special case of eight regularly-spaced black holes with equal masses when the model parameter κ > 1. We first derive exact time evolving solutions of instantaneously-static models, by utilizing perturbative solutions of the constraint equations that can then be used to develop exact 4D dynamical solutions of the Einstein field equations. We use the notion of a geometric horizon, which can be characterized by curvature invariants, to determine the black hole horizon. We explicitly compute the invariants for the exact dynamical models obtained. As an application, we discuss whether black holes can persist in such a Universe that collapses and then subsequently bounces into a new expansionary phase. We find evidence that in the physical models under investigation (and particularly for κ > 1) the individual black holes do not merge before nor at the bounce, so that consequently black holes can indeed persist through the bounce.

Geometric horizons in the Kastor-Traschen multi-black-hole solutions

We investigate the existence of invariantly defined quasi-local hypersurfaces in the Kastor-Traschen solution containing $N$ charge-equal-to-mass black holes. These hypersurfaces are characterized by the vanishing of particular curvature invariants, known as Cartan invariants, which are generated using the frame approach. The Cartan invariants of interest describe the expansion of the outgoing and ingoing null vectors belonging to the invariant null frame arising from the Cartan-Karlhede algorithm. We show that the evolution of the hypersurfaces surrounding the black holes depends on an upper-bound on the total mass for the case of two and three equal mass black holes. We discuss the results in the context of the geometric horizon conjectures.

Identification of black hole horizons using scalar curvature invariants

We introduce the concept of a geometric horizon, which is a surface distinguished by the vanishing of certain curvature invariants which characterize its special algebraic character. We motivate its use for the detection of the event horizon of a stationary black hole by providing a set of appropriate scalar polynomial curvature invariants that vanish on this surface. We extend this result by proving that a non-expanding horizon, which generalizes a Killing horizon, coincides with the geometric horizon. Finally, we consider the imploding spherically symmetric metrics and show that the geometric horizon identifies a unique quasi-local surface corresponding to the unique spherically symmetric marginally trapped tube, implying that the spherically symmetric dynamical black holes admit a geometric horizon. Based on these results, we propose a suite of conjectures concerning the application of geometric horizons to more general dynamical black hole scenarios.

Fading characteristics of maritime propagation channel for beyond geometrical horizon communications in C-band

The design of a maritime communication system requires the understanding of the wireless propagation channel above the sea. For broadband communication systems, a carrier frequency in the C-band is of interest because of allocatable spectrum. Therefore, the German Aerospace Center performed a long-distance channel measurement campaign at 5.2 GHz on the North sea to investigate large and small-scale fading characteristics. The results show that our measurement data conforms with the ITU-R and the Bullington’s path loss model to predict the power loss caused by diffraction over the Earth’s surface. Further, the first tap of the channel impulse response experiences Rician fading due to superposition of a strong line-of-sight (LoS) path and multipath components originating from the sea surface and ship body. We found that the fading of the second tap follows a Rician distribution, but with a much smaller K-factor compared to the first tap. The K-factor showed a dependence on the distance between the transmitter and receiver. Particularly, the K-factor of the first tap decreases significantly when the distance between the transmitter and receiver is larger than the clearance distance of the first Fresnel zone. Therefore, we propose a distance-dependent K-factor model for the first and the second tap.

On a duration problem with unbounded geometrical horizon

We consider a full information duration problem with random, unbounded horizon. We choose the object and hold it as long as it will be relatively best or second best object. We show that the problem of stopping on two first order statistics reduces to the problem on stopping only on the relatively best object. We derive the optimal strategy and the value of the problem. The similarities between duration problem and the best or second best choice problem are revealed.

C-Pro: A coastal projector monitoring system using terrestrial photogrammetry with a geometric horizon constraint

This paper describes a methodological protocol to project a terrestrial photograph of a coastal area – or whatever indicator is contained on it – in a georeferenced plane taking advantage of the terrestrial horizon as a geometric key. This feature, which appears in many beach photos, helps in camera repositioning and as a constraint in collinearity adjustment. This procedure is implemented in a tool called Coastal Projector (C-Pro) that is based on Matlab and adapts its methodology in accordance with the input data and the available parameters of the acquisition system. The method is tested in three coastal areas to assess the influence that the horizon constraint presents in the results. The proposed methodology increases the reliability and efficient use of existing recreational cameras (with non-optimal requirements, unknown image calibration, and at elevations lower than 7m) to provide quantitative coastal data.

Primordial cosmic fluctuations for variable gravity

The observability of primordial cosmic fluctuations does not require a geometric horizon H−1, which is exceeded temporarily by the wavelength of fluctuations. The primordial information can be protected against later thermal washout even if all relevant wavelengths remain smaller than H−1. This is demonstrated by formulating the equations governing the cosmic fluctuations in a form that is manifestly invariant under conformal field transformations of the metric. Beyond the field equations this holds for the defining equation for the correlation function, as expressed by the inverse of the second functional derivative of the quantum effective action. An observable almost scale invariant spectrum does not need an expanding geometry. For a variable Planck mass it can even arise in flat Minkowski space.

Highly Accurate Attitude Estimation via Horizon Detection

Attitude pitch and roll angle estimation from visual information is necessary for GPS-free navigation of airborne vehicles. We propose a highly accurate method to estimate the attitude by horizon detection in fisheye images. A Canny edge detector and a probabilistic Hough voting scheme are used to compute an approximate attitude and the corresponding horizon line in the image. Horizon edge pixels are extracted in a band close to the approximate horizon line. The attitude estimates are refined through registration of the extracted edge pixels with the geometrical horizon from a digital elevation map DEM, in our case the SRTM3 database, extracted at a given approximate position. The proposed method has been evaluated using 1629 images from a flight trial with flight altitudes up to 600i¾?m in an area with ground elevations ranging from sea level up to 500i¾?m. Compared with the ground truth from a filtered inertial measurement unit IMU/GPS solution, the standard deviation for the pitch and roll angle errors obtained with 30 Mpixel images are 0.04i¾? and 0.05i¾?, respectively, with mean errors smaller than 0.02i¾?. To achieve the high-accuracy attitude estimates, the ray refraction in the earth's atmosphere has been taken into account. The attitude errors obtained on real images are less or equal to those achieved on synthetic images for previous methods with DEM refinement, and the errors are about one order of magnitude smaller than for any previous vision-based method without DEM refinement.

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

AbstractWe consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higher-derivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the ‘Einstein’ and ‘Galileon’ frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.

Characterizing the Amount and Speed of Discounting Procedures

This paper introduces the concepts of amount and speed of a discounting procedure in order to generate well-characterized families of procedures for use in social project evaluation. Exponential discounting sequesters the concepts of amount and speed into a single parameter that needs to be disaggregated in order to characterize nonconstant rate procedures. The inverse of the present value of a unit stream of benefits provides a natural measure of the amount a procedure discounts the future. We propose geometrical and time horizon based measures of how rapidly a discounting procedure acquires its ultimate present value, and we prove these to be the same. This provides an unambiguous measure of the speed of discounting, a measure whose values lie between 0 (slow) and 2 (fast). Exponential discounting has a speed of 1. A commonly proposed approach to aggregating individual discounting procedures into a social one for project evaluation averages the individual discount functions. We point to serious shortcoming with this approach and propose an alternative for which the amount and time horizon of the social procedure are the averages of the amounts and time horizons of the individual procedures. We further show that the social procedure will in general be slower than the average of the speeds of the individual procedures. For potential applications in social project evaluation we characterize three families of two-parameter discounting procedures – hyperbolic, gamma, and Weibull – in terms of their discount functions, their discount rate functions, their amounts, their speeds and their time horizons. (The appendix characterizes additional families, including the quasi-hyperbolic one.) A one parameter version of hyperbolic discounting, d(t) = (1+rt)-2, has amount r and speed 0, and this procedure is our candidate for use in social project evaluation, although additional empirical work will be needed to fully justify a one-parameter simplification of more general procedures.

Detection of potential fractures and small faults using seismic attributes

Often it is difficult to map subtle faults and other trace-to-trace discontinuities hidden in 3D seismic data. They may appear as minor changes in the seismic waveform that are not easily correlated using conventional interpretation of seismic cross-sections. To map these changes we have investigated and computed several different seismic attributes sensitive to the existence of small faults and fractures in our target reservoir, the Late Permian Unayzah sandstone of central Saudi Arabia. In addition to the traditional geometric horizon attributes such as dip and azimuth, we found that both coherence and spectral decomposition were useful in imaging seismic discontinuities.

‘Faster than light’ photons in gravitational fields — Causality, anomalies and horizons

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a ‘horizon theorem’ which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation. These results are consequences of an effective action which in QED is valid only for low frequency photons. Their relevance to signal propagation and causality, which are controlled by high frequency propagation, is dependent on the dispersive properties of the modified propagation. This will be discussed elsewhere. A comparison is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.

Simplified calculation of coverage area for MF AM broadcast stations

It is shown that the coverage area of medium- and high-frequency stations using ground-wave propagation beyond the horizon, especially MF AM stations, can be calculated by a simplified method. Recent field measurements have shown that the cumbersome FCC and CCIR calculations for estimating service area can be simplified to allow calculations with a PC, or even a programmable pocket calculator. The ground-wave electrical field intensity calculations are simplified by the introduction of a shadow or diffraction factor in the Norton planar earth expression. This factor permits the ground E field to be calculated well beyond the geometric and radio horizon, where E-field values are close to the atmospheric noise level. The approach permits engineers or technicians to calculate their own E=field curves for any frequency and any kind of soil.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On Directions from which Cosmic Rays may Reach Earth Satellites

It is easy to feel, on an intuitive basis, that primary cosmic rays of at least some energy range will be able to reach a satellite in earth-orbit from all directions above the local geometric horizon and from essentially no directions below the horizon. This argument suggests that directional cosmic ray detectors on board satellites may safely assume that the only particles received from earthward directions must be splash or albedo particles from the atmosphere, and that any equipment liable to possible radiation damage should be preferentially located on the earthward side of the satellite. In actual fact primary cosmic rays can have quite sharply curved trajectories in the magnetosphere, thereby enabling some particles to gain access to a satellite from a range of directions below the local geometric horizon. The present work presents recent quantitative results on this matter.

New light on Novaya Zemlya polar mirage

While seeking a Northeast Passage to the Orient, the explorer Willem Barents and his crew were stranded for the winter at Novaya Zemlya (76°12'N). During the perpetual night of their arctic winter, one noontime in January 1597 the explorers were astonished to see the Sun appear two weeks sooner than expected at that latitude. At the time, the Sun's actual position was still about 5° below the geometrical horizon.

Marine boundary layer refractive effects in the infrared

Abstract : An experiment was conducted to determine whether ducting phenomena (gradients in refractivity) occur close to the ocean surface at infrared wavelengths. A CO2 laser beam (10.6 microns) was transmitted and received over an 8.5 km path in San Diego Bay. For the cases investigated (sea warmer than the air), the results of the study indicate that for air temperature gradients less than 1 C/meter, the distance to the infrared horizon was only 60% of the normal geometrical horizon.

Continuity and Local Evolution in the Neolithic of South China: A Non-Nuclear Approach [and Comments and Reply

The Neolithic of South China (and of the Far East generally) has traditionally been reconstructed on nuclear-diffusionist models; chronologies and local culture sequences in South China have been related to the rise of agriculture and Neolithic technology in North China, and their subsequent spread into the South, often seen to have resulted from a movement of peoples out of the "nuclear area." Recent data now suggest a generally contemporaneous though largely autonomous development of agriculture, pottery, polished stone tools, and boat transport within South China, beginning in the Pleistocene-Holocene transition and marked by technological continuity with gradually crystallizing local "Bacsonian" subcultures after ca. 8000 B.C. The Middle Neolithic "Lungshanoid" and "Yueh" horizons of the Yangtze Delta and southern coast, respectively, are suggested to have emerged (possibly with a significant stimulus from the changing land-sea configuration in the early Holocene) by the 6th or 5th millennium B.C. and themselves provided the substrata from which the Geometric horizon of Southeast China evolved in the late 3d-early 2d millennium B.C. In the absence of compelling evidence to the contrary, an assumed local evolution and parallel development over the wide region constitutes the most appropiate theoretical model with which to frame the data, and leads generally to more productive lines of investigation (e.g., man-land relationships, prior cultural-technological history, potential within the cultures themselves for innovation) than do other a priori models. The assumption of a locally evolving cultural system has proved highly useful and predictively successful in its application to Neolithic development in the Yellow River Basin of North China, the Red River Basin and contiguous zones in North Vietnam, Japan, and certain key sites in South China. With the now known or strongly suspected antiquity of a number of culture traits (rice, painted pottery, rectangular adze) wide-spread over South China and beyond, and the futility in attempting to pinpoint their precise point of origin, it is suggested that such a framework will eventually find wide application over the mainland of East Asia.

Distance Off by Vertical Sextant Angle

The note by J. W. Crosbie prompts the writer to the following comments. Lecky's Tables2 do not cover vertical angles below the geometrical horizon (zenith distance =90°), or, indeed, angles of less than 10’ above it. Crosbie's method, also, does not cater for angles below the geometrical horizon, though it could be adapted to do so. His extraordinary evolutions with the traverse tables, undertaken to avoid solving a quadratic equation by orthodox methods, are fascinating. Surely, a slide rule, with which the equation could be solved in a few seconds, is available in today's chartroom.