Military Aspects of Countering Hybrid Aggression: Ukrainian Experiences

Ukraine became the object of military aggression by Russia, which became the realization of the final phase of hybrid aggression. This aggression has been carried out without stopping all the time since the independence of Ukraine. Economic blackmail, gas wars, the Budapest memorandum, internal destabilization, the 5th column and Russian citizens in the Ukrainian government, the Russian church in Ukraine, the distribution of pro-Russian content in the information field of Ukraine etc. All of these events were elements of Russian "soft power" against Ukraine which created favorable conditions for the final blow by the so-called 2nd army of the world

Renormalized stress-energy tensor near the horizon of a slowly evolving, rotating black hole

The renormalized expectation value of the stress-energy tensor〈Tμν〉^ren of a quantum field in an arbitrary quantum state near the future horizon of a rotating (Kerr) black hole is derived in two very different ways: One derivation (restricted for simplicity to a massless scalar field) makes use of traditional techniques of quantum field theory in curved spacetime, augmented by a variant of the "η formalism" for handling superradiant modes. The other derivation (valid for any quantum field) uses the equivalence principle to infer, from〈Tμν〉^ren in flat spacetime, what must be〈Tμν〉^ren near the hole’s horizon. The two derivations give the same result—a result in accord with a previous conjecture by Zurek and Thorne: 〈Tμν〉^ren, in any quantum state, is equal to that, 〈Tμν〉^ZAMO, which zero-angular-momentum observers (ZAMO’s) would compute from their own physical measurements near the horizon, plus a vacuum-polarization contribution Tμνvac pol , which is the negative of the stress-energy of a rigidly rotating thermal reservoir with angular velocity equal to that of the horizon ΩH, and (red-shifted) temperature equal to that of the Hawking temperature TH. A discussion of the conditions of validity for equivalence-principle arguments reveals that curvature-coupling effects (of which the equivalence principle is unaware) should produce fractional corrections of order α^2≡(surface gravity of hole)^2×(distance to horizon)^2 to Tμνvac pol; and since gravitational blue-shifts cause the largest components of Tμνvac pol in the proper reference frame of the ZAMO’s to be of O(α-2), curvature-coupling effects in Tμνvac pol and thence in 〈Tμν〉^ren are of O(α^0) in the ZAMO frame. It is shown, by a quantum-field-theory derivation of the density matrix, that in the Hartle-Hawking vacuum the near-horizon ZAMO’s see a thermal reservoir with angular velocity ΩH and temperature TH whose thermal stress-energy 〈Tμν〉^ZAMO gets renormalized away by Tμνvac pol, annulling the O(α^-2) and O(α^-1) pieces of 〈Tμν〉^ren, and leaving only the O(α^0) vacuum-polarization, curvature-coupling contributions. This translates into 〈Tll〉^ren=〈Tlφ〉^ren=0 on the future horizon in the Hartle-Hawking vacuum, where l and φ denote components on the horizon generator lμ and on the generator of rotations ∂/∂φ. In quantum states representing a black hole in the real Universe (with both evaporation and accretion occurring), the fluxes of red-shifted energy and angular momentum across the future horizon, per unit solid angle sinθ dθ dφ, are shown to equal the corresponding accretion fluxes into the hole’s atmosphere from the external universe minus the fluxes evaporated by the hole. As a consequence, the hole’s horizon evolves in accord with standard expectations. As an aside it is shown that the Hartle-Hawking vacuum state ‖H〉 is singular at and outside the velocity-of-light surface scrSL, i.e., at sufficiently large radii that the rest frame of its thermal reservoir is moving at or faster than the speed of light. Its renormalized stress-energy tensor is divergent there, and its Hadamard function does not have the correct behavior. To make ‖H〉 be well behaved (and have the properties described above), one must prevent its rotating thermal reservoir from reaching out to scrSL, e.g., by placing a perfectly reflecting mirror around the hole just inside scrSL

Effects of mode degeneracy in the LIGO Livingston Observatory recycling cavity

We analyze the electromagnetic fields in a Pound-Drever-Hall locked, marginally unstable, Fabry-Perot cavity as a function of small changes in the cavity length during resonance. More specifically, we compare the results of a detailed numerical model with the behavior of the recycling cavity of the Laser Interferometer Gravitational-wave Observatory (LIGO) detector that is located in Livingston, Louisiana. In the interferometer's normal mode of operation, the recycling cavity is stabilized by inducing a thermal lens in the cavity mirrors with an external CO2 laser. During the study described here, this thermal compensation system was not operating, causing the cavity to be marginally optically unstable and cavity modes to become degenerate. In contrast to stable optical cavities, the modal content of the resonating beam in the uncompensated recycling cavity is significantly altered by very small cavity length changes. This modifies the error signals used to control the cavity length in such a way that the zero crossing point is no longer the point of maximum power in the cavity nor is it the point where the input beam mode in the cavity is maximized.Comment: Eight pages in two-column format. Six color figures. To be published JOSA

Regression of Environmental Noise in LIGO Data

We address the problem of noise regression in the output of gravitational-wave (GW) interferometers, using data from the physical environmental monitors (PEM). The objective of the regression analysis is to predict environmental noise in the gravitational-wave channel from the PEM measurements. One of the most promising regression method is based on the construction of Wiener-Kolmogorov filters. Using this method, the seismic noise cancellation from the LIGO GW channel has already been performed. In the presented approach the Wiener-Kolmogorov method has been extended, incorporating banks of Wiener filters in the time-frequency domain, multi-channel analysis and regulation schemes, which greatly enhance the versatility of the regression analysis. Also we presents the first results on regression of the bi-coherent noise in the LIGO data

Laser Interferometers as Dark Matter Detectors

While the global cosmological and local galactic abundance of dark matter is well established, its identity, physical size, and composition remain a mystery. In this paper, we analyze an important question of dark matter detectability through its gravitational interaction, using current and next generation gravitational-wave observatories to look for macroscopic (kilogram-scale or larger) objects. Keeping the size of the dark matter objects to be smaller than the physical dimensions of the detectors, and keeping their mass as a free parameter, we derive the expected event rates. For favorable choice of mass, we find that dark matter interactions could be detected in space-based detectors such as LISA at a rate of one per ten years. We then assume the existence of an additional Yukawa force between dark matter and regular matter. By choosing the range of the force to be comparable to the size of the detectors, we derive the levels of sensitivity to such a new force, which exceeds the sensitivity of other probes in a wide range of parameters. For sufficiently large Yukawa coupling strength, the rate of dark matter events can then exceed 10 per year for both ground- and space-based detectors. Thus, gravitational-wave observatories can make an important contribution to a global effort of searching for nongravitational interactions of dark matter

In-situ characterization of the thermal state of resonant optical interferometers via tracking of their higher-order mode resonances

Thermal lensing in resonant optical interferometers such as those used for gravitational wave detection is a concern due to the negative impact on control signals and instrument sensitivity. In this paper we describe a method for monitoring the thermal state of such interferometers by probing the higher-order spatial mode resonances of the cavities within them. We demonstrate the use of this technique to measure changes in the Advanced LIGO input mode cleaner cavity geometry as a function of input power, and subsequently infer the optical absorption at the mirror surfaces at the level of 1 ppm per mirror. We also demonstrate the generation of a useful error signal for thermal state of the Advanced LIGO power recycling cavity by continuously tracking the first order spatial mode resonance frequency. Such an error signal could be used as an input to thermal compensation systems to maintain the interferometer cavity geometries in the presence of transients in circulating light power levels, thereby maintaining optimal sensitivity and maximizing the duty-cycle of the detectors

Global feed-forward vibration isolation in a km scale interferometer

Using a network of seismometers and sets of optimal filters, we implemented a feed-forward control technique to minimize the seismic contribution to multiple interferometric degrees of freedom of the Laser Interferometer Gravitational-wave Observatory interferometers. The filters are constructed by using the Levinson–Durbin recursion relation to approximate the optimal Wiener filter. By reducing the RMS of the interferometer feedback signals below ~10 Hz, we have improved the stability and duty cycle of the joint network of gravitational wave detectors. By suppressing the large control forces and mirror motions, we have dramatically reduced the rate of non-Gaussian transients in the gravitational wave signal stream

Proof of the Generalized Second Law for Quasistationary Semiclassical Black Holes

A simple direct explicit proof of the generalized second law of black hole thermodynamics is given for a quasistationary semiclassical black hole.Comment: 12 pages, LaTeX, report Alberta-Thy-10-93 (revision of paper in response to Phys. Rev. Lett. referees' comments, which suffered a series of long delays