arXiv subjects

A. V. Toporensky

Publications and source records attributed to A. V. Toporensky.

At least 19 recordsLinked to original sources

arXiv2026

Full set of scenarios of high energy collision in the Schwarzschild background and kinematic censorship

We consider collisions between particles moving freely in the Schwarzschild background. We suggest classification of scenarios that lead to unbounded energy output in the center of mass frame. Although this is forbidden in the exterior of a black hole, the phenomenon becomes possible with account of white hole region and mirror universe in the complete space-time diagram. Also, we scrutinize collisions in the vicinity of the bifurcation point and reveal the role of resting observers in the inner region beyond the horizon. In some scenarios $E_{c.m.}$ not only diverges but becomes seemingly infinite that is, as a matter of fact, impossible according to the principle of so-called kinematic censorship. We resolve a corresponding paradox and argue, why this principle remains valid.

gr-qc↗

arXiv2026

Generalized Lemaître time for rotating and charged black holes and its near-horizon properties

We consider the behavior of the analogue of the Lemaitre time when a particle approaches the horizon of a rotating black hole. For the Kerr metric, the aforementioned time coincides with the Doran or Natario time but we consider a more general class of metrics. We scrutiny relationship between (i) its finiteness or divergence, (ii) the forward-in-time condition, (iii) the sign of a generalized momentum/energy, (iv) the validity of the principle of kinematic censorship. The latter notion means impossibility to release in any event an energy which is literally infinite. As a consequence, we obtain a new explanation, why collisions of two particles inside the horizon do not lead to infinite energy in their center of mass frame. The same results are also obtained for the Reissner-Nordström metric

gr-qc↗

arXiv2026

High energy particle collisions under Cauchy horizon

We consider particle collision inside the inner horizon of the Reissner-Nordstrom metric in the so-called R region. We show that there exist scenario in which the enrgy in the center of mass frame grows unbounded. In contrast to the standard scenarios of high energy collisions in black hole background in the R region, fine tuning of particle parameters is not require. The effect found in this work can be considered as a massive particle counterpart of wave processes that contribute to instability of the inner black hole horizon.

physics.gen-ph↗

arXiv2025

Kinematic censorship and high energy particle collisions in the Schwarzschild background

We consider near-horizon collisions between two particles moving freely in the Schwarzschild metric in the region outside the horizon. One of them emerges from a white hole. We scrutiny when such a process can lead to the indefinitely large growth of the energy in the center of mass frame in the point of collision. We also trace how the kinematics of collision manifests itself in preserving the principle of kinematic censorship according to which the energy released in any event of collision cannot be literally infinite. According to this principle, the energy released in any event of collision, must remain finite although it can be made as large as one likes. Also, we find that particle decay near the singularity leads to unbounded release of energy independently of its initial value.

gr-qc↗

arXiv2025

The Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity

This paper brings a methodological character where we present a comprehensive formalism for constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). It was developed in series of our earlier works and, here, we unite it into a complete form. By employing the Noether method within a tensor formalism, conserved currents, superpotentials, and charges are constructed. These are shown to be covariant under coordinate transformations and local Lorentz rotations in TEGR, while in STEGR, they are covariant under coordinate transformations. The teleparallel (flat) connections in both theories are defined using the "turning off gravity" principle. Uniting such defined flat connections with tetrad in TEGR and metric in STEGR a new fruitful in applications notion "gauge" is introduced. The choice of various initial tetrads in TEGR or initial coordinates in STEGR leads to different gauges, what gives different conserved quantities. Finally, we discuss an appropriate choice of gauges from a possible set of them.

gr-qc↗

arXiv2025

Mass and angular momentum for the Kerr black hole in TEGR and STEGR

We study the energy-momentum characteristics of the rotating black hole - Kerr solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR). The previously constructed spacetime covariant and Lorentz invariant expressions for conserved Noether currents, superpotentials and charges are used. The Noether charges describe total energy, momentum or angular momentum of gravitating system depending on a choice of the displacement vector $ξ$. To define covariant and invariant conserved quantities both in TEGR and in STEGR on needs to use external fields which are flat teleparallel connections. To determine the non-dynamical connections in TEGR and STEGR we use the unified ``turning off'' gravity principle. Besides, to analyse the Noether conserved quantities in these theories, we use the concept of ``gauges''. The gauge changing can affect the Noether conserved quantities. We highlight two ways to turn off gravity - by $M \to 0$ and by $M \to 0 , ~ a \to 0$ which gives us different gauges in TEGR and STEGR. In both kind of gauges we get the expected values of black hole mass and angular momentum. Our attempts to find gauges which could lead to a correspondence to Einstein's equivalence principle for the Kerr solution where unsuccessful both in TEGR and STEGR. However, these exercises helped us to find a related gauge for the Schwarzschild solution in STEGR that is a novelty.

physics.gen-ph↗

arXiv2024

The equivalence principle for a plane gravitational wave in torsion based and non-metricity based teleparallel equivalents of general relativity

We study the energy-momentum characteristics of the plane ``+''-polarised gravitational wave solution of general relativity in the Teleparallel Equivalent of General Relativity (TEGR) and the Symmetric Teleparallel Equivalent of General Relativity (STEGR) using the previously constructed Noether currents. The current components describe locally measured by observer energy-momentum if the displacement vector $ξ$ is equal to the observer's 4-velocity. To determine the non-dynamical connection in these theories we use the unified ``turning of'' gravity principle. For a constructive analysis of the values of Noether currents and superpotentials in TEGR and STEGR, we use the concept of ``gauges''. The gauge changing can affect the Noether current values. We study under what conditions the Noether current for the freely falling observer is zero. When they are established, zero result can be interpreted as a correspondence to the equivalence principle, and it is a novelty for gravitational waves in TEGR and STEGR. We highlight two important cases with positive and zero energy, which reproduce the results of previous works with a different approach to determine gravitational energy-momentum in TEGR, and give their interpretation.

gr-qc↗

arXiv2023

Conserved quantities in STEGR and applications

We derive conservation laws in Symmetric Teleparallel Equivalent of General Relativity (STEGR) with direct application of Noether's theorem. This approach allows us to construct covariant conserved currents, corresponding superpotentials and invariant charges. A necessary component of our constructions is the concept of "turning off" gravity, introduced in the framework of STEGR to define the flat and torsionless connection. By calculating currents, one can obtain local characteristics of gravitational field like energy density. Surface integration of superpotentials gives charges which correspond to global quantities of the system like mass, momentum, etc. To test our results for the obtained currents and superpotentials, we calculate the energy density measured by freely falling observer in the simple solutions (Friedman universe, Schwartzchild black hole) and total mass of the Schwartzchild black hole. We find ambiguities in obtaining the connection, which explicitly affect the values of conserved quantities, and discuss possible solutions to this problem.

gr-qc↗

arXiv2023

On particle dynamics near the singularity inside the Schwarzschild black hole and T-spheres

The problem of the speed of the objects inside the Schwarzschild black hole is considered. The general result is that the value of the relative speed of the objects following their non-zero angular momentum trajectories, both of geodesic and non-geodesic character, when approaching the ultimate singularity, tends to the value of speed of light. There is only one exception when both objects move in the same plane and have parallel angular momenta. This outcome appears to have a deeper sense: it reflects the anisotropic character of the dynamics of interior of this particular black hole. The result in question means that near the singularity, collisions of two particles lead to an indefinitely large energy in the center of mass frame. Aforementioned properties have their counterpart in the phenomenon of an indefinitely large blueshift near the singularity. Thus the angular momentum of a particle turns out to be an important feature that affects the final behavior of particle near the singularity. Motivated by this fact, we generalize the Lema\^ıtre frame under the horizon in such a way that reference particles themselves have nonzero angular momentum. Our results apply not only to the Schwarzschild singularity but also to other space-like ones for which the scale factor $g\rightarrow \infty $. We also analyze another type of singulairites for which the circumference radius vanishes but $g$ remains finite.

gr-qc↗

arXiv2022

How to delay death and look further into the future if you fall into a black hole

In this note, we present a pedagogical illustration of peculiar properties of motion in the vicinity and inside black holes. We discuss how a momentary impulse can modify the lifetime of an object radially falling into a Schwarzschild black hole down to singularity. The well known upper limit for a proper time spent within a horizon, in fact, requires an infinitely powerful kick. We calculate the proper time interval (perceived as personal lifetime of a falling observer) till the contact with the singularity, as well as the time interval in the Lemaître frame (which reflects how far into the future of the outer world a falling observer can look), for different values of the kick received by the falling body. We discuss the ideal strategy to increase both time intervals by the engine with a finite power. This example is suitable for university seminars for undergraduate students specializing in General Relativity and related astrophysical subjects.

physics.pop-ph↗

arXiv2022

Regular frames for spherically symmetric black holes revisited

We consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up to now, several standard frames of such a kind are known. It was shown in literature before, how some of them can be united in one picture as different limits of a general scheme. However, some types of frames (the Kruskal-Szekeres and Lema\^ıtre ones) and transformations to them from the original one remained completely disjoint. We show that the Kruskal-Szekeres and Lema\^ıtre frames stem from the same root. Overall, our approach in some sense completes the procedure and gives the most general scheme. We relate the parameter of transformation $e_{0}$ to the specific energy of fiducial observers and show that in the limit $% e_{0}\rightarrow 0$ a homogeneous metric under the horizon can be obtained by a smooth limiting transition.

gr-qc↗

arXiv2021

On Conserved Quantities for the Schwarzschild Black Hole in Teleparallel Gravity

We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $ξ$ and we consider two different options where $ξ$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained generalised freely falling frame with an arbitrary initial velocity. We also demonstrate how to determine the inertial spin connection for various tetrads used in our calculations, and find a certain ambiguity in the "switching off" gravity method where different tetrads can share the same inertial spin connection.

gr-qc↗

arXiv2020

On strategies of motion under the black hole horizon

In this methodological paper we consider two problems an astronaut faces with under the black hole horizon in the Schwarzschild metric. 1) How to maximize the survival proper time. 2) How to make a visible part of the outer Universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the "river model". Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point 1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point 2) requires maximizing the peculiar velocity of the observer. Both goals 1) and 2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology, and its application for the problems studied in the present paper can be used in advanced general relativity courses.

gr-qc↗

arXiv2019

Zero-momentum trajectories inside a black hole and high energy particle collisions

We consider properties of the trajectory with the zero momentum inside a spherically symmetric black hole. We work mostly in the Painlevé% -Gullstrand frame and use the concept of the "river model of black hole". This consept allows us to decompose (in a "cosmological manner") the geodesic motion of a test particle into a "flow" of the frame and a peculiar motion with respect to this frame. After this decomposition the application of standard formulae of special relativity for kinematic processes becomes possible. The present paper expands the notion of peculiar velocities to the region under the horzion and exploits it for the description of two physical processess - high energy collisions and redshift. Using this approach we (i) present a novel description of particle collisions occuring near black hole horizons inside the event horizon. In particular, we show that the trajectory under discussion is relevant for ultra-high energy collisions. (ii) In the framework of the river model, we derive a simple formula (both outside and inside the horizon) for the redshift in the case of radial motion. It represents the product of two factors. One of them is responsible for pure gravitational part whereas the other one gives the Doppler shift due to peculiar motion with respect to the "flow".

gr-qc↗

arXiv2017

On stable exponential cosmological solutions in the EGB model with a $Λ$-term in dimensions D = 5,6,7,8

A $D$-dimensional Einstein-Gauss-Bonnet (EGB) flat cosmological model with a cosmological term $Λ$ is considered. We focus on solutions with exponential dependence of scale factor on time. Using previously developed general analysis of stability of such solutions done by V.D.Ivashchuk (2016) we apply the criterion from that paper to all known exponential solutions up to dimensionality 7+1. We show that this criterion which guarantees stability of solution under consideration is fulfilled for all combination of coupling constant of the theory except for some discrete set.

gr-qc↗

arXiv2015

Cosmological redshift, recession velocities and acceleration measures in FRW cosmologies

In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker one is the most known example of them. We describe how different quantities behave in this frame. Special attention is paid to potentially observable parameters. We discuss different variants for choosing measures of velocity and acceleration representing the Hubble flow, and present illustrative calculations of apparent acceleration in flat $ΛCDM$ model for various epochs. We generalize description of the "tethered" galaxies problem for different velocity measures and equations of state, and illustrate time behavior of velocities and redshifts in the $ΛCDM$ model.

gr-qc↗

arXiv2013

The Hubble flow: an observer's perspective

In this methodological note we discuss some details and peculiarities of the cosmic expansion as viewed by a realistic observer. We show that the velocity $v_Θ$ related to a change (measured by observer's clock) of the angular distance, plays an important role in formation of a meaningful observed picture of the expansion of the universe. Usage of this velocity and the angular distance (in addition to the standard approach --- proper distance and corresponding velocity) allows to present the cosmic expansion in a more illustrative manner. These parameters play a key role in visualization of the expansion.

physics.pop-ph↗

arXiv2012

On stability of power-law solution in multidimensional Gauss-Bonnet cosmology

We consider dynamics of a flat anisotropic multidimensional cosmological model in Gauss-Bonnet gravity in the presence of a homogeneous magnetic field. In particular, we find conditions under which the known power-law vacuum solution can be an attractor for the case with non-zero magnetic field. We also describe a particular class of numerical solution in $(5+1)$-dimensional case which does not approach the power-law regime.

gr-qc↗