Please use this identifier to cite or link to this item: http://ena.lp.edu.ua:8080/handle/ntb/46128
Title: On the null one-way solution to Maxwell equations in the Kerr space-time
Other Titles: Про однонапрямлений ізотропний розв’язок рівнянь Максвелла у просторі Керра
Authors: Пелих, В.
Тайстра, Ю.
Pelykh, V.
Taistra, Y.
Affiliation: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
Національний університет “Львівська політехніка”
Pidstryhach Institute for Applied Problems for Mechanics and Mathematics
Lviv Polytechnic National University
Bibliographic description (Ukraine): Pelykh V. On the null one-way solution to Maxwell equations in the Kerr space-time / V. Pelykh, Y. Taistra // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 2. — P. 201–206.
Bibliographic description (International): Pelykh V. On the null one-way solution to Maxwell equations in the Kerr space-time / V. Pelykh, Y. Taistra // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2018. — Vol 5. — No 2. — P. 201–206.
Is part of: Mathematical Modeling and Computing, 2 (5), 2018
Issue: 2
Issue Date: 26-Feb-2018
Publisher: Lviv Politechnic Publishing House
Place of the edition/event: Львів
Lviv
UDC: 537.876
517.927.2
517.955
Keywords: алгебраїчно спеціальне поле
рівняння Максвелла
простір-час Керра
algebraically special field
Maxwell equations
Kerr space-time
Number of pages: 6
Page range: 201-206
Start page: 201
End page: 206
Abstract: Розглянуто рівняння Максвелла з умовою однонапрямленого ізотропного поля в просторі Керра. Для кожного ЗДР, отриманого після застосування методу відокремлення змінних, накладено деякі граничні умови. Це приводить до обмеженості константи відокремлення ω та до фіксованості азимутального числа m значеннями ±1. Розглянута задача показує фізичну застосовність особливих розв’язків і становить інтерес для астрофізики.
We consider Maxwell equations with the null one-way condition in the Kerr space-time. For each ODE equation, which is obtained by using the method of separable variables, we impose some boundary conditions. This is resulting in the boundedness of the separation constant ω and in fixing the azimuthal number m by the values ±1. The problem considered demonstrates physical applicability of singular solutions and presents an interest for astrophysics.
URI: http://ena.lp.edu.ua:8080/handle/ntb/46128
Copyright owner: CMM IAPMM NASU
© 2018 Lviv Polytechnic National University
References (Ukraine): 1. Teukolsky S. A. Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations. The Astrophysical Journal. 185, 635–647 (1973).
2. Fiziev P. P. Classes of exact solutions to the Teukolsky master equation. Classical and Quantum Gravity. 27 (13), 135001 (2010).
3. Borissov R. S., Fiziev P. P. Exact solutions of Teukolsky master equation with continious spectrum. Bulg. J. Phys. 37, 065–089 (2010); arXiv:0903.3617v3 [gr-qc] (2010).
4. Pelykh V. O., Taistra Y. V. A Class of General Solutions of the Maxwell Equations in the Kerr Space-Time. J. Math. Sci. 229 (2), 162–173 (2018).
5. Torres del Castillo G. P. 3-D spinors, spin-weighted functions and their applications. Vol. 20 of Progress in mathematical physics. New York, Springer Science+Business Media, LLC (2003).
6. Visser M. The Kerr spacetime: A Brief introduction. In Kerr Fest: Black Holes in Astrophysics, General Relativity and Quantum Gravity Christchurch. New Zealand (2004), (2007).
7. O’Neill B. The geometry of Kerr black holes. Wellesley, Massachusetts, Reprint of the A. K. Peters (1995).
8. Pelykh V. O., Taistra Y. V. Null one-way fields in the Kerr spacetime. Ukr. Journ. of Phys. 62 (11), 1007–1013 (2017).
9. Penrose R., Rindler W. Spinors and space-time. Two-spinor calculus and relativistic fields. Vol. 1. Cambridge University Press (1984).
10. KinnersleyW. Type D vacuum metrics. J. Math. Phys. 10, 1195–1203 (1969).
11. Stewart J. M. Advanced general relativity. Cambridge University Press (1991).
12. O’Donnell P. Introduction to 2-Spinors in General Relativity. World Scientific (2003).
13. Pelykh V. O., Taistra Y. V. Solution with Separable Variables for Null One-way Maxwell Field in Kerr Space-time. Acta Phys. Polon. Supp. 10, 387–390 (2017).
14. Starobinskii A. A., Churilov S. M. Amplification of electromagnetic and gravitational waves scattered by a rotating “black hole”. Zh. Eksp. Teor. Fiz. 65, 3–11 (1973).
15. Chandrasekhar S. The mathematical theory of black holes. New York, Oxford Univ. Press (1983).
16. Pelykh V., Taistra Y. A class of exact solutions of Maxwell equations in Kerr space-time and their physical manifestations. In The third Zeldovich meeting SNAUPS-2018, 23–27 April 2018, Minsk, Belarus. Institute of Physics NAS of Belarus (2018).
17. Gnedin N. I., Dymnikova I. G. Rotation of the plane of polarization of a photon in space-time of the D type according to the Petrov classification. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki. 94, 26–31 (1988), (in Russian).
References (International): 1. Teukolsky S. A. Perturbations of a rotating black hole. I. Fundamental equations for gravitational, electromagnetic, and neutrino-field perturbations. The Astrophysical Journal. 185, 635–647 (1973).
2. Fiziev P. P. Classes of exact solutions to the Teukolsky master equation. Classical and Quantum Gravity. 27 (13), 135001 (2010).
3. Borissov R. S., Fiziev P. P. Exact solutions of Teukolsky master equation with continious spectrum. Bulg. J. Phys. 37, 065–089 (2010); arXiv:0903.3617v3 [gr-qc] (2010).
4. Pelykh V. O., Taistra Y. V. A Class of General Solutions of the Maxwell Equations in the Kerr Space-Time. J. Math. Sci. 229 (2), 162–173 (2018).
5. Torres del Castillo G. P. 3-D spinors, spin-weighted functions and their applications. Vol. 20 of Progress in mathematical physics. New York, Springer Science+Business Media, LLC (2003).
6. Visser M. The Kerr spacetime: A Brief introduction. In Kerr Fest: Black Holes in Astrophysics, General Relativity and Quantum Gravity Christchurch. New Zealand (2004), (2007).
7. O’Neill B. The geometry of Kerr black holes. Wellesley, Massachusetts, Reprint of the A. K. Peters (1995).
8. Pelykh V. O., Taistra Y. V. Null one-way fields in the Kerr spacetime. Ukr. Journ. of Phys. 62 (11), 1007–1013 (2017).
9. Penrose R., Rindler W. Spinors and space-time. Two-spinor calculus and relativistic fields. Vol. 1. Cambridge University Press (1984).
10. KinnersleyW. Type D vacuum metrics. J. Math. Phys. 10, 1195–1203 (1969).
11. Stewart J. M. Advanced general relativity. Cambridge University Press (1991).
12. O’Donnell P. Introduction to 2-Spinors in General Relativity. World Scientific (2003).
13. Pelykh V. O., Taistra Y. V. Solution with Separable Variables for Null One-way Maxwell Field in Kerr Space-time. Acta Phys. Polon. Supp. 10, 387–390 (2017).
14. Starobinskii A. A., Churilov S. M. Amplification of electromagnetic and gravitational waves scattered by a rotating "black hole". Zh. Eksp. Teor. Fiz. 65, 3–11 (1973).
15. Chandrasekhar S. The mathematical theory of black holes. New York, Oxford Univ. Press (1983).
16. Pelykh V., Taistra Y. A class of exact solutions of Maxwell equations in Kerr space-time and their physical manifestations. In The third Zeldovich meeting SNAUPS-2018, 23–27 April 2018, Minsk, Belarus. Institute of Physics NAS of Belarus (2018).
17. Gnedin N. I., Dymnikova I. G. Rotation of the plane of polarization of a photon in space-time of the D type according to the Petrov classification. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki. 94, 26–31 (1988), (in Russian).
Content type: Article
Appears in Collections:Mathematical Modeling And Computing. – 2018. – Vol. 5, No. 2



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