The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas

We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.

Introduction to Turbulent Transport of Particles, Temperature and Magnetic Fields

Turbulence and the associated turbulent transport of scalar and vector fields is a classical physics problem that has dazzled scientists for over a century, yet many fundamental questions remain. Igor Rogachevskii, in this concise book, systematically applies various analytical methods to the turbulent transfer of temperature, particles and magnetic field. Introducing key concepts in turbulent transport including essential physics principles and statistical tools, this interdisciplinary book is suitable for a range of readers such as theoretical physicists, astrophysicists, geophysicists, plasma physicists, and researchers in fluid mechanics and related topics in engineering. With an overview to various analytical methods such as mean-field approach, dimensional analysis, multi-scale approach, quasi-linear approach, spectral tau approach, path-integral approach and analysis based on budget equations, it is also an accessible reference tool for advanced graduates, PhD students and researchers.

Komar integrals for theories of higher order in the Riemann curvature and black-hole chemistry

We construct Komar-type integrals for theories of gravity of higher order in the Riemann curvature coupled to simple kinds of matter (scalar and vector fields) and we use them to compute Smarr formulae for black-hole solutions in those theories. The equivalence between f (R) and Brans-Dicke theories is used to argue that the dimensionful parameters that appear in scalar potentials must be interpreted as thermodynamical variables (pressures) and we give a general expression for their conjugate potentials (volumes).

Separation of variables in the WZW models

We consider dynamics of scalar and vector fields on gravitational backgrounds of the Wess-Zumino-Witten models. For SO(4) and its cosets, we demonstrate full separation of variables for all fields and find a close analogy with a similar separation of vector equations in the backgrounds of the Myers-Perry black holes. For SO(5) and higher groups separation of variables is found only in some subsectors.

Classifying pole-skipping points

We clarify general mathematical and physical properties of pole-skipping points. For this purpose, we analyse scalar and vector fields in hyperbolic space. This setup is chosen because it is simple enough to allow us to obtain analytical expressions for the Green’s function and check everything explicitly, while it contains all the essential features of pole-skipping points. We classify pole-skipping points in three types (type-I, II, III). Type-I and Type-II are distinguished by the (limiting) behavior of the Green’s function near the pole-skipping points. Type-III can arise at non-integer iω values, which is due to a specific UV condition, contrary to the types I and II, which are related to a non-unique near horizon boundary condition. We also clarify the relation between the pole-skipping structure of the Green’s function and the near horizon analysis. We point out that there are subtle cases where the near horizon analysis alone may not be able to capture the existence and properties of the pole-skipping points.

Field theory in normal conical coordinates

In the scientific literature, the field theory is most fully covered in the cylindrical and spherical coordinate systems. This is explained by the fact that the mathematical apparatus of these systems is most well studied. When the source of field has a more complex structure than a point or a straight line, there is a need for new approaches to their study. The goal of this research is to adapt the field theory related to curvilinear coordinates in order to represent it in the normal conical coordinates. In addition, an important part of the research is the development of a geometrical modeling apparatus for scalar and vector field level surfaces using computer graphics. The paper shows the dependences of normal conical coordinates on rectangular Cartesian coordinates, Lame coefficients. The differential characteristics of the scalar and vector fields in normal conical coordinates are obtained: Laplacian of scalar and vector fields, divergence, rotation of the vector field. The example case shows the features of the application of the mathematical apparatus of geometrical field modeling in normal conical coordinates. For the first time, expressions for the characteristics of the scalar and vector fields in normal conical coordinates are obtained. Methods for geometrical modeling of fields using computer graphics have been developed to provide illustration in their study.

Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in d-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.