Related papers: Second-order perturbation theory: the problem of i…
In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to…
The second order perturbations in Friedmann-Robertson-Walker universe filled with a perfect fluid are completely formulated in the gauge invariant manner without any gauge fixing. All components of the Einstein equations are derived…
Previously, we attempted to over-spin Kerr-Taub-NUT black holes with test fields satisfying the null energy condition. We derived that a non-generic over-spinning could be achieved with strict restrictions on the test field modes and the…
Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
To fully exploit the capabilities of next-generation gravitational wave detectors, we need to significantly improve the accuracy of our models of gravitational-wave-emitting systems. This paper focuses on one way of doing so: by taking…
An analytical solution of the perturbed equations is obtained, which exists in all ergodic models of collisionless spherical stellar systems with a single length parameter. This solution corresponds to variations of this parameter, i.e.,…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
We extend the general framework of perturbative quantum field theory developped for the pure Yang-Mills model to gravity. First we present a variant of the elimination procedure of the anomalies in the second order of perturbation theory.…
We propose and construct a two-parameter perturbative expansion around a Friedmann-Lema\^{i}tre-Robertson-Walker geometry that can be used to model high-order gravitational effects in the presence of non-linear structure. This framework…
Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…
The sinh-Gordon model on a half-line with integrable boundary conditions is considered in low order perturbation theory developed in affine Toda field theory. The quantum corrections to the classical reflection factor of the model are…
Recently a novel perturbative continuum limit for quantum gravity has been proposed and demonstrated to work at first order. Every interaction monomial $\sigma$ is dressed with a coefficient function $f^\sigma_\Lambda(\varphi)$ of the…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
Cosmological perturbation theory is a key tool to study the universe. The linear or first order theory is well understood, however, developing and applying the theory beyond linear order is at the cutting edge of current research in…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
We critically examine the magnitude of theoretical uncertainties in perturbative calculations of first-order phase transitions, using the Standard Model effective field theory as our guide. In the usual daisy-resummed approach, we find…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…