arXiv subjects

Alexander Kamenshchik

Publications and source records attributed to Alexander Kamenshchik.

At least 19 recordsLinked to original sources

arXiv2026

IR finite correlation functions in de Sitter space, a smooth massless limit, and an autonomous equation

We explore two-point and four-point correlation functions of a massive scalar field on the flat de Sitter background in the long-wavelength approximation. By employing the Yang-Feldman-type equation, we compute the two-point correlation function up to $λ^3$ order and the four-point correlation function up to $λ^2$ order. In contrast to the standard theory of a massive scalar field based on the de Sitter-invariant vacuum, we develop a vacuum-independent reasoning that may not possess de Sitter invariance but results in a smooth massless limit of the correlation function's infrared part. Our elaboration allows us to calculate correlation functions of a free massive scalar field and to proceed with quantum corrections, relying only on the known infrared part of the two-point correlation function of a free massless one. Remarkably, the two-point correlation function of a free massive scalar field coincides with that of the Ornstein-Uhlenbeck stochastic process and has a clear physical interpretation. We compare our results with those obtained using the Schwinger-Keldysh diagrammatic technique, Starobinsky's stochastic approach, and the Hartree-Fock approximation. At last, we construct a renormalization group-inspired autonomous equation for the two-point correlation function. Integrating its approximate version, one obtains the non-analytic expression with respect to a self-interaction coupling constant $λ$. That solution reproduces the correct perturbative series up to the two-loop level. In the late-time limit, it almost coincides with the result of Starobinsky's stochastic approach over the whole interval of a new dimensionless parameter $0 \leq \tfrac{π^2 m^4}{3λH^4} < \infty$.

hep-th↗

arXiv2026

On gravitational collapse and integrable singularities

Schwarzschild black holes are expected to emerge as the end states of the classical gravitational collapse from non-singular configurations. After integrable curvature singularities appear, the interior geometry can be modelled to exhibit a transition, called ``Minkowski breaking'', when the inner horizon disappears, before all matter collapses into the central singularity. This picture implies a quantum framework to describe the final stages of the gravitational collapse, and here we will provide more insights from the semiclassical approximation for the energy-momentum tensor and the Madelung approximation for collapsing matter. In particular, we will show that the quantum potential in the Raychaudhuri equation starts to strongly oppose the collapse towards the Schwarzschild singularity precisely after the Minkowski breaking.

gr-qc↗

arXiv2026

Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation

We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic theory reasonably well. Second, we apply the technique of autonomous equations to the Borel-Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger-Dyson-type differential equations.

hep-th↗

arXiv2026

Two-time physics, Carroll symmetry and Jordan algebras

We describe Carroll particles with nonzero energy (i.e., particles that remain at rest) within the framework of two-time (2T) physics developed by Bars and collaborators. In a spacetime with one additional time and one additional space dimension, one can gauge the phase-space symmetry that exchanges generalized coordinates with their conjugate momenta, thereby unifying the description of apparently different one-time systems. We develop both classical and quantum descriptions of the Carroll particle arising from 2T physics, and explore links between the extended phase space of 2T physics and Freudenthal triple systems constructed over a semisimple cubic Jordan algebra (the Lorentzian spin factor).

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arXiv2026

Two Times for Freudenthal

We investigate the algebraic structure of the two-time physics introduced some time ago by I. Bars and his co-authors, clarifying its relations with quadratic and cubic Jordan algebras, as well as with reduced Freudenthal triple systems (FTS) based on them. In particular, the `extended' phase space introduced by Bars can be endowed with the structure of a reduced FTS constructed over a semi-simple cubic Jordan algebra (named Lorentzian spin factor), characterized by a primitive, invariant symmetric tensor of rank $4$. The $Sp(2,\mathbb{R})$-gauge fixing procedure typical of two-time physics yields algebraic-differential constraints on the quartic polynomial associated to such a tensor, implying that only two (isomorphic) nilpotent orbits of the non-transitive action of the automorphism group of the Lorentzian spin factor are spanned by the conjugated variables which coordinatize the `extended' phase space. We illustrate our results in relativistic, manifestly Lorentz-covariant physical systems, as well as in non-relativistic systems (such as the non-relativistic massive particle, the hydrogen atom, and the Carroll particle with non-vanishing energy).

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arXiv2026

On Schwarzschild black hole singularity formation

We examine whether the Schwarzschild black hole can emerge as the continuous end state of gravitational collapse from a non-singular configuration. Employing a time dependent extension of the regular Schwarzschild metric, we track the evolution of the geometry during collapse and find that the process cannot remain continuous. The metric function develops a discontinuity at the origin, marking a breakdown of spacetime smoothness, an effect identified as ``Minkowski breaking.'' Before the Schwarzschild point source can form at $r=0$, curvature singularities appear and the Cauchy horizon disappears. These results strongly suggest that spacetime may not evolve smoothly toward the Schwarzschild geometry. Instead, the formation of a Schwarzschild black hole appears to entail a discrete change in the structure of spacetime, pointing to the need for a noncontinuous, possibly quantized, framework to describe the emergence or regularization of gravitational singularities.

gr-qc↗

arXiv2025

From the Fokker-Planck equation to perturbative QFT's results in de Sitter space

A technique to build perturbative series for the spectator field's correlation functions in de Sitter space through the Fokker-Planck equation is proposed. We derive from the first-order differential equation the iterative integral relation for equal- and multi-time correlation functions. With an appropriate integration, the obtained two-point and four-point correlation functions are in agreement with quantum field theory's ones.

hep-th↗

arXiv2025

Regular Schwarzschild black holes and cosmological models

We study regular Schwarzschild black holes in General Relativity as an alternative to the singular counterpart. We analyze two types of solutions which are completely parameterised by the ADM mass alone. We find that both families of regular solutions contain a de Sitter condensate at the core and admit (quasi) extremal black hole configurations in which the two horizons are arbitrarily close. Cosmological models based on these regular configurations are also analyzed, finding that they describe non-trivial Kantowski-Sachs universes free of singularities.

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arXiv2024

Again About Singularity Crossing In Gravitation And Cosmology

We discuss the problem of singularity crossing in isotropic and anisotropic universes. We study at which conditions singularities can disappear in quantum cosmology and how quantum particles behave in the vicinity of singularities. Some attempts to develop general approach to the connection between the field reparametrization and the elimination of singularities is presented as well.

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arXiv2024

Cosmology from Schwarzschild black hole revisited

We study cosmological models based on the interior of the revisited Schwarzschild black hole recently reported in [Phys.~Rev.~D{\bf 109} (2024) 104032]. We find that these solutions describe a non-trivial Kantowski-Sachs universe, for which we provide an explicit analytical example with all the details and describe some general features of the singularity.

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arXiv2024

Regular Friedmann Universes and Matter Transformations

We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born-Infeld-type fields. Remarkably, for the minimally coupled scalar field and the tachyon field, the regularity of the cosmological evolution, or in other words, the existence of bounce, implies the necessity of the transition between scalar fields with standard kinetic terms to those with phantom ones. In both cases, the potentials in the vicinity of the point of the transition have a non-analyticity of the cusp form that is characterized by the same exponent and is equal to 2/3. If, in the tachyon models evolution, the pressure changes its sign, then another transformation of the Born-Infeld-type field occurs: the tachyon transforms into a pseudotachyon, and vice versa. We also undertake an analysis of the stability of the cosmological evolution in our models; we rely on the study of the speed of sound squared.

gr-qc↗

arXiv2024

From black hole mimickers to black holes

We present a simple analytical model for studying the collapse of an ultracompact stellar object (regular black hole mimicker with infinite redshift surface) to form a (integrable) black hole, in the framework of General Relativity. Both initial and final configurations have the same ADM mass, so that the transition represents an internal redistribution of matter without emission of energy. The model, despite being quite idealized, can be viewed as a good starting point to investigate near-horizon quantum physics

gr-qc↗

arXiv2023

Looking for Carroll particles in two time spacetime

We make an attempt to describe Carroll particles with a non-vanishing value of energy (i.e. the Carroll particles which always stay in rest) in the framework of two time physics, developed in the series of papers by I. Bars and his co-authors. In the spacetime with one additional time dimension and one additional space dimension one can localize the symmetry which exists between generalized coordinate and their conjugate momenta. Such a localization implies the introduction of the gauge fields, which in turn implies the appearance of some first-class constraints. Choosing different gauge-fixing conditions and solving the constraints one obtain different time parameters, Hamiltonians, and generally, physical systems in the standard one time spacetime. In this way such systems as non-relativistic particle, relativistic particles, hydrogen atoms and harmonic oscillators were described as dual systems in the framework of the two time physics. Here, we find a set of gauge fixing conditions which provides as with such a parametrization of the phase space variables in the two time world which gives the description of Carroll particle in the one time world. Besides, we construct the quantum theory of such a particle using an unexpected correspondence between our parametrization and that obtained by Bars for the hydrogen atom in 1999.

hep-th↗

arXiv2023

Bianchi-I cosmologies, magnetic fields and singularities

We study the effects of a spatially homogenous magnetic field in Bianchi-I cosmological models. The cases of a pure magnetic field and two models with additional dust and a massless scalar field (stiff matter) are also considered. At the beginning of the cosmological evolution,i.e., in the neighborhood of the singularity, the universe is described by one of Kasner's solutions, and asymptotically by another Kasner solution when the volume of the universe tends to infinity. The transition law between these two Kasner regimes is established, and shown to coincide with the analogous law for the empty Bianchi-II universe. The universe filled with dust and a magnetic field undergoes the process of isotropization, while the presence of a massless scalar field induces a modification of the relations between Kasner indices in the two asymptotic regimes. In all of these cases, we analyze the approach to the singularity in some detail and comment on the issue of the possible singularity crossing.

gr-qc↗

arXiv2023

Newman-Janis algorithm's application to regular black hole models

We examine the Newman-Janis algorithm's application to an exact regular static solution sustained by a minimally coupled scalar field with a non-standard kinetic term. Although coordinate complexification leads to a regular Kerr-like black hole, we are facing discrepancies in Einstein's equations in a fairly small domain, for which the regularizing parameter is responsible. Outside this most intriguing region, the geometry is nothing but the standard Kerr spacetime.

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arXiv2022

Background independence and field redefinitions in quantum gravity

It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in configuration space. We show that any path-integral approach to quantum gravity leads to a tension between these properties, such that they cannot hold simultaneously.

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arXiv2022

Covariant singularities: a brief review

The Hawking-Penrose theorem is not covariant under field redefinitions. Should the invariance under such transformations be a true principle in Nature, spacetime singularities become dubious objects. We here review the concept of covariant singularities, that is, singularities that are invariant under both spacetime diffeomorphisms and field redefinitions.

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arXiv2021

Absence of covariant singularities in pure gravity

The assumptions of the Hawking-Penrose singularity theorem are not covariant under field redefinitions. Thus we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with any other fields. We show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.

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