Adam Cieślik | Jagiellonian University in Krakow (original) (raw)

Papers by Adam Cieślik

arXiv (Cornell University), May 12, 2023

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime... more We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parameterized explicitly by constants of motion-the energy, the angular momentum, and the Carter constant-and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial and polar type. This uniformity has been achieved by applying a little-known result due to Biermann and Weierstrass, regarding solutions of a certain class of ordinary differential equations. Different from other expressions in terms of Weierstrass functions, our solution is explicitly real for all types of geodesics. In particular, for the first time the so-called transit orbits are now expressed by explicitly real Weierstrass functions.

Physical review, Jul 9, 2020

We investigate stationary spherically symmetric accretion of the relativistic Vlasov gas on Reiss... more We investigate stationary spherically symmetric accretion of the relativistic Vlasov gas on Reissner-Nordström black holes. The model is based on a recent analysis done by Rioseco and Sarbach for the Schwarzschild spacetime. Both models share many common features: The gas characterized by the Maxwell-Jüttner distribution at infinity is no longer in thermal equilibrium in the vicinity of the black hole. The radial pressure at the black-hole horizon can be even an order of magnitude smaller than the tangential pressure. Quantitative characteristics of the Reissner-Nordström model depend on the charge parameter. For black holes with fixed asymptotic mass, the mass accretion rate decreases with the increasing black-hole charge. The ratio of the tangential pressure to the radial pressure at the horizon also decreases with the increasing charge. On the other hand, the particle density at the horizon (normalized by its asymptotic value) grows with the black-hole charge parameter.

Classical and Quantum Gravity, Oct 18, 2022

The theory of Schwarzschild geodesics is revisited. Basing on a result by Weierstrass and Bierman... more The theory of Schwarzschild geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, timelike and null trajectories in terms of Weierstrass elliptic functions. Quite remarkably, a single formula works for an entire geodesic trajectory, even if it passes through turning points. Using this formula, we derive expressions for the proper and coordinate time along the geodesic.

Physical review, Sep 16, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

arXiv (Cornell University), Mar 23, 2022

arXiv (Cornell University), Aug 8, 2022

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occ... more We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic boundary conditions: at infinity the gas obeys the Maxwell-Jüttner distribution, restricted to the equatorial plane (both in positions and momenta). In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The rest-mass and energy accretion rates, normalized by the black hole mass and appropriate asymptotic surface densities of the gas, increase with increasing asymptotic temperature. The accretion slows down the rotation of the black hole.

Acta Physica Polonica, 2023

Physical Review D

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime... more We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parametrized explicitly by constants of motion-the energy, the angular momentum, and the Carter constant-and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial and polar type. This uniformity has been achieved by applying a little-known result due to Biermann and Weierstrass, regarding solutions of a certain class of ordinary differential equations. Different from other expressions in terms of Weierstrass functions, our solution is explicitly real for all types of geodesics. In particular, for the first time the so-called transit orbits are now expressed by explicitly real Weierstrass functions.

Acta Physica Polonica B Proceedings Supplement

Physical Review D

Classical and Quantum Gravity, 2022

Physical Review D, 2022

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occ... more We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic boundary conditions: at infinity the gas obeys the Maxwell-Jüttner distribution, restricted to the equatorial plane (both in positions and momenta). In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The rest-mass and energy-accretion rates, normalized by the black hole mass and appropriate asymptotic surface densities of the gas, increase with increasing asymptotic temperature. The accretion slows down the rotation of the black hole.

Celem pracy jest zbadanie czy efektywna czasoprzestrzeń dobrze reprezentuje właściwości pełnej cz... more Celem pracy jest zbadanie czy efektywna czasoprzestrzeń dobrze reprezentuje właściwości pełnej czasoprzestrzeni. W związku z tym przebadano ruch masywnych cząstek próbnych w obu czasoprzestrzeniach. Rozważane czasoprzestrzenie poddano analizie analitycznej oraz za pomocą programu Mathematica 11 wygenerowano wykresy linii geodezyjnych dla cząstek próbnych, co pozwoliło ocenić różnice jakościowe między obiema czasoprzestrzeniami. Ruch cząstek próbnych w obu czasoprzestrzeniach różni się, jednak badając metrykę efektywną uzyskano dobry obraz pełnej metryki zwłaszcza w obszarze, gdzie niejednorodności są małe. Praca pokazuje, że badanie pełnej czasoprzestrzeni jest bardziej złożone od badania czasoprzestrzeni efektywnej.The purpose of this research is to examine whether effective space-time represents the properties of full space-time. Therefore, the movement of massive test particles in both time-spaces were examined. Considered space-times were subjected to analytical analysis and usi...

The theory of Schwarzschild timelike geodesics is revisited. Basing on a result by Weierstrass an... more The theory of Schwarzschild timelike geodesics is revisited. Basing on a result by Weierstrass and Biermann, we derive a formula describing all non radial, time-like trajectories in terms of Weierstrass elliptic functions. Quite remarkably, a single formula works for an entire geodesic trajectory, even if it passes through turning points. Using this formula, we derive expressions for the proper and coordinate time along the geodesic.

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2020

Physical Review D, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2020

arXiv (Cornell University), May 12, 2023

Physical review, Jul 9, 2020

Classical and Quantum Gravity, Oct 18, 2022

Physical review, Sep 16, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

arXiv (Cornell University), Mar 23, 2022

arXiv (Cornell University), Aug 8, 2022

Acta Physica Polonica, 2023

Physical Review D

We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime... more We derive novel analytical solutions describing timelike and null geodesics in the Kerr spacetime. The solutions are parametrized explicitly by constants of motion-the energy, the angular momentum, and the Carter constant-and initial coordinates. A single set of formulas is valid for all null and timelike geodesics, irrespectively of their radial and polar type. This uniformity has been achieved by applying a little-known result due to Biermann and Weierstrass, regarding solutions of a certain class of ordinary differential equations. Different from other expressions in terms of Weierstrass functions, our solution is explicitly real for all types of geodesics. In particular, for the first time the so-called transit orbits are now expressed by explicitly real Weierstrass functions.

Acta Physica Polonica B Proceedings Supplement

Physical Review D

Classical and Quantum Gravity, 2022

Physical Review D, 2022

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occ... more We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic boundary conditions: at infinity the gas obeys the Maxwell-Jüttner distribution, restricted to the equatorial plane (both in positions and momenta). In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The rest-mass and energy-accretion rates, normalized by the black hole mass and appropriate asymptotic surface densities of the gas, increase with increasing asymptotic temperature. The accretion slows down the rotation of the black hole.

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2020

Physical Review D, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2019

We propose a covariant definition of standing gravitational waves in general relativity.

Physical Review D, 2020

The theory of Schwarzschild geodesics is revisited. Using a theorem due to Weierstrass and Bierma... more The theory of Schwarzschild geodesics is revisited. Using a theorem due to Weierstrass and Biermann, we derive concise formulas describing all timelike and null trajectories in terms of Weierstrass elliptic functions. The formulation given in this note uses an analogue of the so-called Mino time.

ArXiv, 2022