ПРОГНОЗ ОБЛАСТЕЙ СЖАТИЯ И РАСТЯЖЕНИЯ В ГЕОЛОГИЧЕСКИХ СТРУКТУРАХ С ИСПОЛЬЗОВАНИЕМ ДАННЫХ ТОЛЬКО О СКОРОСТЯХ ПРОДОЛЬНЫХ ВОЛН В ГЕОЛОГИЧЕСКОЙ СРЕДЕ

The article presents accurate solutions for the problem for two elastic half‐spaces with an arbitrary curvilinear interface. Our study shows that dilatation solutions (Poisson integrals) are dependent on neither an overall compression modulus nor the Poisson ratio, and depend only on the velocity of longitudinal waves. These specific solutions can be supplemented by general solutions for an incompressible elastic medium, and the boundary conditions of the rigid contact for the sum of the solutions can thus be satisfied. Relatively simple calculations make it possible to determine the divergence of the displacement field and reduce the entire problem solving process to a study of Poisson equations with a known divergence. Furthermore, predictions of volumetric compression or extension are important for geological investigations, since the zones characterized by reduced pressure rates may act as fluid attractors.Приведены точные решения упругой задачи для двух полупространств, разделенных произвольной криволинейной поверхностью. Показано, что частные решения для дилатации (интегралы Пуассона) не зависят ни от модуля всестороннего сжатия, ни от коэффициента Пуассона, а зависят только от скорости продольных волн. Эти частные решения могут быть дополнены общими решениями для несжимаемой упругой среды, и тем самым будут выполнены граничные условия жесткого контакта для суммы означенных решений. Возникает возможность сравнительно простыми вычислениями определить дивергенцию поля перемещений и свести всю задачу к исследованию уравнений типа Пуассона при известной дивергенции. Кроме того, сам прогноз объемного сжатия или растяжения имеет важное геологическое значение, так как зоны пониженного давления могут быть аттракторами флюидов

Perturbative instabilities in Horava gravity

We investigate the scalar and tensor perturbations in Horava gravity, with and without detailed balance, around a flat background. Once both types of perturbations are taken into account, it is revealed that the theory is plagued by ghost-like scalar instabilities in the range of parameters which would render it power-counting renormalizable, that cannot be overcome by simple tricks such as analytic continuation. Implementing a consistent flow between the UV and IR limits seems thus more challenging than initially presumed, regardless of whether the theory approaches General Relativity at low energies or not. Even in the phenomenologically viable parameter space, the tensor sector leads to additional potential problems, such as fine-tunings and super-luminal propagation.Comment: 21 pages, version published at Class. Quant. Gra

The Generalized Second Law implies a Quantum Singularity Theorem

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose's original singularity theorem, it implies that spacetime is null geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann--Robertson--Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. An introductory section describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.) A proof of the coarse-grained ordinary second law is given.Comment: 46 pages, 8 figures. v2: discussion of global hyperbolicity revised (4.1, 5.2), more comments on AdS. v3: major revisions including change of title. v4: similar to published version, but with corrections to plan of paper (1) and definition of global hyperbolicity (3.2). v5: fixed proof of Thm. 1, changed wording of Thm. 3 & proof of Thm. 4, revised Sec. 5.2, new footnote

Perturbations of Self-Accelerated Universe

We discuss small perturbations on the self-accelerated solution of the DGP model, and argue that claims of instability of the solution that are based on linearized calculations are unwarranted because of the following: (1) Small perturbations of an empty self-accelerated background can be quantized consistently without yielding ghosts. (2) Conformal sources, such as radiation, do not give rise to instabilities either. (3) A typical non-conformal source could introduce ghosts in the linearized approximation and become unstable, however, it also invalidates the approximation itself. Such a source creates a halo of variable curvature that locally dominates over the self-accelerated background and extends over a domain in which the linearization breaks down. Perturbations that are valid outside the halo may not continue inside, as it is suggested by some non-perturbative solutions. (4) In the Euclidean continuation of the theory, with arbitrary sources, we derive certain constraints imposed by the second order equations on first order perturbations, thus restricting the linearized solutions that could be continued into the full nonlinear theory. Naive linearized solutions fail to satisfy the above constraints. (5) Finally, we clarify in detail subtleties associated with the boundary conditions and analytic properties of the Green's functions.Comment: 39 LaTex page

Supergravity based inflation models: a review

In this review, we discuss inflation models based on supergravity. After explaining the difficulties in realizing inflation in the context of supergravity, we show how to evade such difficulties. Depending on types of inflation, we give concrete examples, particularly paying attention to chaotic inflation because the ongoing experiments like Planck might detect the tensor perturbations in near future. We also discuss inflation models in Jordan frame supergravity, motivated by Higgs inflation.Comment: 30 pages, invited review for Classical and Quantum Gravity, published versio

PREDICTION OF COMPRESSION AND EXTENSION ZONES IN GEOLOGICAL STRUCTURES BASED ONLY ON THE VELOCITIES OF LONGITUDINAL WAVES IN THE GEOLOGICAL MEDIUM

The article presents accurate solutions for the problem for two elastic half‐spaces with an arbitrary curvilinear interface. Our study shows that dilatation solutions (Poisson integrals) are dependent on neither an overall compression modulus nor the Poisson ratio, and depend only on the velocity of longitudinal waves. These specific solutions can be supplemented by general solutions for an incompressible elastic medium, and the boundary conditions of the rigid contact for the sum of the solutions can thus be satisfied. Relatively simple calculations make it possible to determine the divergence of the displacement field and reduce the entire problem solving process to a study of Poisson equations with a known divergence. Furthermore, predictions of volumetric compression or extension are important for geological investigations, since the zones characterized by reduced pressure rates may act as fluid attractors