arXiv subjects

Pavel Krtouš

Publications and source records attributed to Pavel Krtouš.

14 recordsLinked to original sources

arXiv2026

Models of a point particle in a three-dimensional AdS universe

In 2+1-dimensional gravity, a conical deficit is commonly interpreted as a point-like particle. A distributional description of such a source is problematic since the Einstein equations are non- linear. Moreover, the total mass of the spacetime with nontrivial asymptotics is obfuscated by the infinite amount of background energy in the distant regions. In this work, we support the standard claim that the mass of a point particle is given by the angular deficit of the asymptotic geometry. We approximate the singular matter source by a sufficiently regular energy distribution, and we study the limit of negligible size for such a distribution while keeping the asymptotic geometry intact. Comparing spacetimes with equal asymptotics ensures that we correctly identify and remove the cosmological matter. We find that the angular deficit of the resulting conical spacetime is given by a limit of the local mass of the object, where the local mass is a natural concept of additive mass in 2+1 gravity. Surprisingly, the limiting mass is different from the BTZ mass parameter, although both masses are closely related.

gr-qc↗

arXiv2026

Conical singularity in spacetimes with NUT is observer-dependent

We discuss the issue of defining and measuring conical deficits (conicity) in spacetimes with the torsion singularity such as the Misner string in Taub--NUT spacetime. We propose a geometric definition that generalizes the standard notion of conicity to stationary axially symmetric spacetimes with torsion singularity, where the conical deficit becomes observer-dependent -- it depends on the choice of a timelike Killing vector. This implies the existence of observers who perceive no conical singularity along the symmetry axis. As a result, in any spacetime with a non-vanishing NUT parameter, there are observers for whom the conicity has the same value on both semi-axes. This challenges the usual interpretation of conicity differences as indicators of string/rod-induced acceleration along the axis. We illustrate our definition across the full Plebański--Demiański class, including the recently identified accelerated Taub--NUT solution. Our attempts in determining a canonical observer lead to even less desirable definitions of conicity.

gr-qc↗

arXiv2025

Conformal Einstein equation and symplectic flux with a positive cosmological constant

We analyze the conformal Einstein equation with a positive cosmological constant to extract fall-off conditions of the gravitational fields. The fall-off conditions are consistent with a finite, non-trivial presymplectic current on the future boundary of de Sitter. Hence our result allows a non-zero gravitational flux across the boundary of the de Sitter. We present an explicit gauge-free computation to show that the Gibbons-Hawking boundary term, counterterm in the action, and fall-off condition of gravitational field in conformal Einstein equation are crucial to reproduce the finite symplectic flux.

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arXiv2025

Point particles on the string in a three-dimensional AdS universe

BTZ spacetime is a long-known locally AdS solution to the Einstein equations in 1 timelike and 2 spacelike dimensions. Its static variant is interpreted as a black hole whose mass is related to the period of the angular coordinate. This solution can be parametrically continued into one without horizons but with a conical deficit in the center. Such a solution is interpreted as a spacetime with a massive particle. It has been shown that this particle can be in static equilibrium with a cosmic string passing through the spacetime to infinity. In this work, we explore the interaction of point particles with strings, such as a bound system of two particles connected by a string of finite length. We identify additive local mass in the static spacetimes and apply it to the case of particles and strings. Finally, using the cut and glue method, we construct the system of two particles oscillating on the string, which goes out of the scope of static systems.

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arXiv2025

On a lower-dimensional Killing vector origin of irreducible Killing tensors

Considering a spacetime foliated by co-dimension-2 hypersurfaces, we find the conditions under which lower-dimensional symmetries of a base space can be lifted up to irreducible Killing tensors of the full spacetime. In this construction, the key ingredient for irreducibility is the non-commutativity of the underlying Killing vectors. It gives rise to a tower of growing rank Killing tensors determined by the structure constants of the corresponding Lie algebra. A canonical example of a metric with such emergent non-trivial hidden symmetries in all dimensions is provided by rotating (off-shell) generalized Lense-Thirring spacetimes, where the irreducible Killing tensors arise from the underlying spherical symmetry of the base space. A physical on-shell realization of this construction in four dimensions is embodied by a rotating black hole in the Einstein-Maxwell-Dilaton-Axion theory. Further examples of equal spinning Myers-Perry spacetimes and spacetimes built on planar and Taub-NUT base metrics are also discussed.

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arXiv2022

Higher-dimensional black holes with multiple equal rotations

We study a limit of the Kerr-(A)dS spacetime in a general dimension where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts - the first part has the form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire spacetime, but only for the directions not subject to the limit, and the second part can be interpreted as the Kähler metrics. However, this separation is not integrable, thus it does not lead to a product of independent manifolds. We also reconstruct the original number of explicit and hidden symmetries associated with Killing vectors and Killing tensors. Therefore, the resulting spacetime represents a special subcase of the generalized Kerr-NUT-(A)dS metric that retains the full Killing tower of symmetries. In $D=6$, we present evidence of an enhanced symmetry structure after the limit. Namely, we find additional Killing vectors and show that one of the Killing tensors becomes reducible as it can be decomposed into Killing vectors.

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arXiv2020

Self-force on a static particle near a black hole

We study the self-force acting on a static charged point-like particle near a Schwarzschild black hole. We obtain the point-like particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object nearby. The massive object is modeled by a black hole or a naked singularity. In this fully interacting system the massive object is supported above the black hole by a strut. Such a strut has a non-zero tension which corresponds to the external force compensating the gravitational force and the electromagnetic self-force acting on the massive object. We discuss details of the limiting procedure leading to the point-like particle situation. As a result, we obtain the standard gravitational force in the static frame of the Schwarzschild spacetime and the electromagnetic self-force. The electromagnetic-self force differs slightly from the classical results in a domain near the horizon. The difference is due to taking into account an influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of the gravitational self-force, are not uniquely defined and they depend on details of the limiting procedure.

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arXiv2020

Thermodynamics of two black holes

We study a system of two charged non-rotating black holes separated by a strut. Using the exact solution of the Einstein-Maxwell equations, which describes this system, we construct a consistent form of the first law of thermodynamics. We derive thermodynamic parameters related to the strut in an explicit form. The intensive thermodynamical quantity associated with the strut is its tension. We call the corresponding extensive quantity the thermodynamical length and we provide an explicit expression and interpretation for it.

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arXiv2019

Duality and $μ$-separability of Maxwell equations in Kerr-NUT-(A)dS spacetime

We study properties of a recently proposed new ansatz for separation of variables in the Maxwell equations in four dimensional Kerr-NUT-(A)dS spacetime. We demonstrate that a dual field, which is also a solution of the source-free Maxwell equations, can be presented in a similar form. This result implies that the corresponding separated equations possess a discrete symmetry under a special transform of the separation parameters.

hep-th↗

arXiv2018

Separation of Maxwell equations in Kerr-NUT-(A)dS spacetimes

In this paper we explicitly demonstrate separability of the Maxwell equations in a wide class of higher-dimensional metrics which include the Kerr-NUT-(A)dS solution as a special case. Namely, we prove such separability for the most general metric admitting the principal tensor (a non-degenerate closed conformal Killing-Yano 2-form). To this purpose we use a special ansatz for the electromagnetic potential, which we represent as a product of a (rank 2) polarization tensor with the gradient of a potential function, generalizing the ansatz recently proposed by Lunin. We show that for a special choice of the polarization tensor written in terms of the principal tensor, both the Lorenz gauge condition and the Maxwell equations reduce to a composition of mutually commuting operators acting on the potential function. A solution to both these equations can be written in terms of an eigenfunction of these commuting operators. When incorporating a multiplicative separability ansatz, it turns out that the eigenvalue equations reduce to a set of separated ordinary differential equations with the eigenvalues playing a role of separability constants. The remaining ambiguity in the separated equations is related to an identification of D-2 polarizations of the electromagnetic field. We thus obtained a sufficiently rich set of solutions for the Maxwell equations in these spacetimes.

hep-th↗

arXiv2018

Massive Vector Fields in Rotating Black-Hole Spacetimes: Separability and Quasinormal Modes

We demonstrate the separability of the massive vector (Proca) field equation in general Kerr-NUT-(A)dS black hole spacetimes in any number of dimensions, filling a long-standing gap in the literature. The obtained separated equations are studied in more detail for the four-dimensional Kerr geometry and the corresponding quasinormal modes are calculated. Two of the three independent polarizations of the Proca field are shown to emerge from the separation ansatz and the results are found in a perfect agreement with those of the recent numerical study where the full coupled partial differential equations were tackled without using the separability property.

hep-th↗

arXiv2018

Separation of variables in Maxwell equations in Plebanski-Demianski spacetime

A new method for separating variables in Maxwell's equations in four- and higher-dimensional Kerr-(A)dS spacetimes proposed recently by Lunin is generalized to any off-shell metric that admits a principal Killing-Yano tensor. The key observation is that Lunin's ansatz for the vector potential can be formulated in a covariant form - in terms of the principal tensor. In particular, focusing on the four-dimensional case we demonstrate separability of Maxwell's equations in the Kerr-NUT-(A)dS and the Plebanski-Demianski family of spacetimes. The new method of separation of variables is quite different from the standard approach based on the Newman-Penrose formalism.

hep-th↗

arXiv2016

The gyraton solutions on generalized Melvin universe with cosmological constant

We present and analyze new exact gyraton solutions of algebraic type II on generalized Melvin universe of type D which admit non-vanishing cosmological constant $Λ$. We show that it generalizes both, gyraton solutions on Melvin and on direct product spacetimes. When we set $Λ= 0$ we get solutions on Melvin spacetime and for $Σ= 1$ we obtain solutions on direct product spacetimes. We demonstrate that the solutions are member of the Kundt family of spacetimes as its subcases. We show that the Einstein equations reduce to a set of equations on the transverse 2-space. We also discuss the polynomial scalar invariants which are non-constant in general but constant for sub-solutions on direct product spacetimes.

gr-qc↗

arXiv1995

Particle Interpretations and Green Functions for a Free Scalar Field

The formalism of Ashtekar and Magnon \cite{AshtekarMagnon:1975} for the definition of particles in quantum field theory in curved spacetime is further developed. The relation between basic objects of this formalism (e.g., the complex structure) and different Green functions is found. It allows one to derive composition laws for Green functions. The relation of two definitions of particles is reformulated in the formalism and the base-independent Bogoljubov transformation is expressed using quantities which are derivable directly from the ``in-out'' Green function.

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