Integrable two-dimensional gravity model is proposed (with I. V. Volovich). Conformal block method for construction of global solutions in gravity is developed for arbitrary two-dimensional metrics admitting one Killing vector field. Geometric theory of defects (dislocations and disclinations) in elastic media is proposed (with I. V. Volovich). The media with defects is shown to correspond to Riemann–Cartan manifold. Torsion and curvature tensors are interpreted as the surface densities of Burgers and Frank vectors, respectively. Full classification of global solutions to vacuum Einstein equations with cosmological constant is given under the assumptions that four-dimensional space-time is a product of two surfaces and the metric has a block diagonal form (with T. Klosch and W. Kummer). The found pseudo-riemannian manifolds include solutions describing black holes, worm holes, cosmic strings, domain walls of curvature singularities.
Biography
Graduated from Faculty of Theoretical and Experimental Physics of Moscow State Engineering Physical Institute (department of Theoretical Nuclear Physics). Ph.D. obtained in 1985 at Steklov Mathematical Institute. D.Sci. degree obtained in 1995 at Steklov Mathematical Institute. Published more than 80 papers.
Main publications:
M. O. Katanaev, Geometrical methods in mathematical physics, Manuscript in Russian. Extended version of lectures delivered at the Academic Educational Center at Steklov Mathematical Institute during seven semesters, 2016 , xvi+1570 pp., arXiv: 1311.0733v3
M. O. Katanaev, “Geometric theory of defects”, Phys. Usp., 48:7 (2005), 675–701
M. O. Katanaev, “Effective action for scalar fields in two-dimensional gravity”, Ann. Physics, 296:1 (2002), 1–50 , arXiv: gr-qc/0101033
M. O. Katanaev, I. V. Volovich, “Theory of defects in solids and three-dimensional gravity”, Ann. Physics, 216:1 (1992), 1–28
M. O. Katanaev, I. V. Volovich, “String model with dynamical geometry and torsion”, Phys. Lett. B, 175:4 (1986), 413–416 , arXiv: hep-th/0209014
D. E. Afanasev, M. O. Katanaev, “Was there a Big Bang for the Universe with accelerated expansion?”, SQS'24 (Dubna, 29 July 2024 to 3 August 2024), Pisma v EChAYa, 2025, 1-8 (to appear)
2024
2.
M. O. Katanaev, “Reply to Comments on the article 'M O Katanaev, Complete separation of variables in the geodesic Hamilton–Jacobi equation in four dimensions, Physica Scripta (2023), 98, 104001' by V V Obukhov, K E Osetrin, and A V Shapovalov”, Phys. Scr., 99:6 (2024), 067001 , 2 pp.
3.
M. O. Katanaev, “Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions”, Theoret. and Math. Phys., 218:2 (2024), 264–275
2023
4.
M. O. Katanaev, “'t Hooft–Polyakov monopoles and a general spherically symmetric solution of the Bogomolny equations”, Modern Phys. Lett. A, 38:16-17 (2023), 2350082 , 8 pp. ;
5.
Mikhail O. Katanaev, Alexander V. Mark, “Combined Screw and Wedge Dislocations”, Universe, 9:12 (2023), 500 , 14 pp. ;
6.
M. O. Katanaev, “Complete separation of variables in the geodesic Hamilton–Jacobi equation in four dimensions”, Phys. Scr., 98:10 (2023), 104001 , 61 pp., arXiv: 2311.12907;
M. O. Katanaev, “On the existence of the global conformal gauge in string theory”, Eur. Phys. J. C, Part. Fields, 81 (2021), 581 , 10 pp., arXiv: 1912.08052;
11.
M. O. Katanaev, “Global conformal gauge in string theory”, Phys. Lett. B, 816 (2021), 136246 , 5 pp., arXiv: 2106.05839;
D. E. Afanasev, M. O. Katanaev, “Global properties of warped solutions in general relativity with an electromagnetic field and a cosmological constant. II”, Phys. Rev. D, 101:12 (2020), 124025 , 20 pp., arXiv: 2006.09209;
17.
D. E. Afanasev, M. O. Katanaev, “On global properties of warped solutions in General Relativity with an electromagnetic field and a cosmological constant”, Proc. of Sci., 376 (2020), 1–14;
18.
M. O. Katanaev, B. O. Volkov, “Point disclinations in the Chern–Simons geometric theory of defects”, Mod. Phys. Lett. B, 34:1 (2020), 2150012 , 14 pp. arXiv:1908.08473v1 [math-ph] ;
M. O. Katanaev, “Gauge Parameterization of the $n$-Field”, Proc. Steklov Inst. Math., 306 (2019), 127–134 , arXiv: physics/2001.08110
20.
D. E. Afanasev, M. O. Katanaev, “Global properties of warped solutions in general relativity with an electromagnetic field and a cosmological constant”, Phys. Rev. D, 100:2 (2019), 024052 , 16 pp., arXiv: 1904.04648
Matematicheskaya fizika i prilozheniya, Sbornik statei. K 95-letiyu so dnya rozhdeniya akademika Vasiliya Sergeevicha Vladimirova, Trudy MIAN, 306, ed. I. V. Volovich, M. O. Katanaev, MIAN, M., 2019 , 352 pp.
2018
22.
M. O. Katanaev, “Chern–Simons Action and Disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133
23.
M. O. Katanaev, Lekts. Kursy NOC, 29, 2018, 3–364
24.
M. O. Katanaev, “Description of Disclinations and Dislocations by the Chern–Simons Action for $SO(3)$-Connection”, Phys. Part. Nucl., 49:5 (2018), 890–893
25.
Kompleksnyi analiz, matematicheskaya fizika i prilozheniya, Sbornik statei, Trudy MIAN, 301, ed. A. I. Aptekarev, M. O. Katanaev, S. P. Suetin, MAIK «Nauka/Interperiodika», M., 2018 , 335 pp.
2017
26.
M. O. Katanaev, “Cosmological models with homogeneous and isotropic spatial sections”, Theoret. and Math. Phys., 191:2 (2017), 661–668
27.
M. O. Katanaev, “Chern–Simons term in the geometric theory of defects”, Phys. Rev. D, 96 (2017), 84054 , 8 pp., arXiv: math-ph/1705.07888
M. O. Katanaev, “Mathematical foundations of general relativity. Part 1”, Mathematical foundations of general relativity. Part 1, Lekts. Kursy NOC, 28, Steklov Math. Institute of RAS, Moscow, 2017, 3–312
2018
29.
M. O. Katanaev, “Normal coordinates in affine geometry”, Lobachevskii Journal of Mathematics, 39:3 (2018), 464–476
2016
30.
M. O. Katanaev, Geometrical methods in mathematical physics, Manuscript in Russian. Extended version of lectures delivered at the Academic Educational Center at Steklov Mathematical Institute during seven semesters, 2016 , xvi+1570 pp., arXiv: 1311.0733v3
31.
M. O. Katanaev, “Rotational elastic waves in a cylindrical waveguide with wedge dislocation”, J. Phys. A, 49:8 (2016), 85202 , 8 pp., arXiv: cond-mat/1502.07935
M. O. Katanaev, “Killing vector fields and a homogeneous isotropic universe”, Phys. Usp., 59:7 (2016), 689–700 , arXiv: gr-qc/1610.05628
2015
33.
M. O. Katanaev, Geometrical methods in mathematical physics. Applications in quantum mechanics. Part 2, Lekts. Kursy NOC, 26, Steklov Math. Institute of RAS, Moscow, 2015 , 186 pp.
34.
M. O. Katanaev, Geometrical methods in mathematical physics. Applications in quantum mechanics. Part 1, Lekts. Kursy NOC, 25, Steklov Math. Institute of RAS, Moscow, 2015 , 176 pp.
35.
M. O. Katanaev, “Rotational elastic waves in double wall tube”, Phys. Lett. A, 379:24–25 (2015), 1544–1548 , arXiv: 1503.01759
M. O. Katanaev, I. G. Mannanov, “Wedge dislocations, three-dimensional gravity, and the Riemann–Hilbert problem”, Phys. Part. Nucl., 43 (2012), 639–643
41.
M. O. Katanaev, I. G. Mannanov, “Wedge dislocations and three-dimensional gravity”, p-Adic Numb. Ultramet. Anal. Appl., 4:1 (2012), 5–19
M. O. Katanaev, “Simple proof of the adiabatic theorem”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 1(22) (2011), 99–107
43.
M. O. Katanaev, “Adiabatic theorem for finite dimensional quantum mechanical systems”, Russian Phys. J., 2011, no. 3, 342–353 , arXiv: 0909.0370
44.
M. O. Katanaev, “On geometric interpretation of the Aharonov–Bohm effect”, Russian Phys. J., 54:5 (2011), 507–514
2012
45.
M. O. Katanaev, “On geometric interpretation of the Berry phase”, Russian Phys. J., 54:10 (2012), 1082–1092 , arXiv: 1212.1782
2010
46.
M. O. Katanaev, “Global solutions in gravity. Euclidean signature”, Fundamental interactions, eds. D. Grumiller, A. Rebhan, D. Vassilevich, World Sci. Publ., Hackensack, NJ, 2010, 249–266 , arXiv: 0808.1559
47.
G. de Berredo-Peixoto, M. O. Katanaev, E. Konstantinova, I. Shapiro, “Schrodinger equation in the space with cylindrical geometric defect and possible application to multi-wall nanotubes”, Nuovo Cimento, B125 (2010), 915–931 , arXiv: 1010.2913
48.
M. O. Katanaev, “Torsion and Burgers vector of a tube dislocation”, 10th Hellenic School and Workshops on Elementary Particle Physics and Gravity (Corfu, Greece, 8–12 Sep 2010), PoS CNCFG, 2010, 022 , 7 pp.
2009
49.
G. de Berredo-Peixoto, M. O. Katanaev, “Tube dislocations in gravity”, J. Math. Phys., 50 (2009), 042501 , 23 pp., arXiv: 0810.0243
M. O. Katanaev, “Akusticheskie fonony v gidrodinamike i metrika Shvartsshilda”, Problemy sovremennoi teoreticheskoi fiziki, K 60-letiyu I. L. Bukhbindera, Tomskii gos. pedagogicheskii un-t, 2008, 208–215
2007
51.
G. de Berredo-Peixoto, M. O. Katanaev, “Inside the BTZ black hole”, Phys. Rev. D, 75:2 (2007), 024004 , 13 pp., arXiv: gr-qc/0611143
M. O. Katanaev, “Polynomial Hamiltonian form of general relativity”, Theoret. and Math. Phys., 148:3 (2006), 1264–1294
2005
54.
M. O. Katanaev, “Geometric theory of defects”, Phys. Usp., 48:7 (2005), 675–701
55.
M. O. Katanaev, “Introduction to the geometric theory of defects”, Proceedings of 3rd Summer School in Modern Mathematical Physics (Zlatibor, Serbia and Montenegro, 20–31 Aug 2004), eds. B. Dragovich, IFTP, Belgrade, 2005, 65–73
2004
56.
M. O. Katanaev, “One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model”, Theoret. and Math. Phys., 138:2 (2004), 163–176
2003
57.
M. O. Katanaev, “Wedge Dislocation in the Geometric Theory of Defects”, Theoret. and Math. Phys., 135:2 (2003), 733–744
2002
58.
M. O. Katanaev, “Effective action for scalar fields in two-dimensional gravity”, Ann. Physics, 296:1 (2002), 1–50 , arXiv: gr-qc/0101033
M. O. Katanaev, “Global solutions in gravity”, Constrained dynamics and quantum gravity (Villasimius, 1999), Nuclear Phys. B Proc. Suppl., 88, 2000, 233–236 , arXiv: gr-qc/9912039
M. O. Katanaev, “Global Solutions in Gravity. Lorentzian Signature”, Proc. Steklov Inst. Math., 228 (2000), 158–183
1999
61.
M. O. Katanaev, Klösch, W. Kummer, “Global properties of warped solutions in general relativity”, Ann. Physics, 276:2 (1999), 191–222 , arXiv: gr-qc/9807079
M. O. Katanaev, I. V. Volovich, “Scattering on dislocations and cosmic strings in the geometric theory of defects”, Ann. Physics, 271:2 (1999), 203–232 , arXiv: gr-qc/9801081
M. O. Katanaev, W. Kummer, H. Liebl, “On the completeness of the black hole singularity in 2D dilaton theories”, Nuclear Phys. B, 486:1-2 (1997), 353–370 , arXiv: gr-qc/9602040
M. O. Katanaev, W. Kummer, H. Liebl, “Geometric interpretation and classification of global solutions in generalized dilaton gravity”, Phys. Rev. D (3), 53:10 (1996), 5609–5618 , arXiv: gr-qc/9511009
M. O. Katanaev, “Canonical quantization of the string with dynamical geometry and anomaly free nontrivial string in two dimensions”, Nuclear Phys. B, 416:2 (1994), 563–605 , arXiv: hep-th/0101168
M. O. Katanaev, “Dynamical torsion and the problem of the indefinite metric in the general theory of relativity”, Soviet J. Nuclear Phys., 43:3 (1986), 490–491
82.
I. V. Volovich, M. O. Katanaev, “Scalar fields and dynamical torsion in Kaluza–Klein theories”, Theoret. and Math. Phys., 66:1 (1986), 53–60
1985
83.
M. O. Katanayev, I. V. Volovich, “Higgs fields in Kaluza-Klein theory with dynamical torsion”, Phys. Lett. B, 156:5-6 (1985), 327–330
Spherically symmetric ‘t Hooft-Polyakov monopoles M. O. Katanaev International Conference "Selected Topics in Mathematical Physics" Dedicated to 75-th Anniversary of I. V. Volovich September 27, 2021 15:55
14.
Global conformal gauge in string theory M. O. Katanaev Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS March 25, 2021 11:00
Closing I. Ya. Aref'eva, M. O. Katanaev 3rd French Russian Conference on Random Geometry and Physics: Sachdev–Ye–Kitaev Model and Related Topics June 7, 2019 12:10
Geometric theory of defects M. O. Katanaev 8th International Conference on Mathematical Modeling. July 4–July 8, 2017, Yakutsk, Russia July 5, 2017 15:15
On homogeneous and isotropic universe M. Katanaev "Beyond the Concordance Model II". Cape Town, South Africa, 28 November–2 December 2016 November 28, 2016 16:15
On homogeneous and isotropic universe M. O. Katanaev International conference "6th Russian-Armenian Workshop on Mathematical Analysis, Mathematical Physics and Analytical Mechanics" September 14, 2016 12:55
On homogeneous and isotropic universe M. O. Katanaev The third Russian-Chinese conference on complex analysis, algebra, algebraic geometry and mathematical physics May 12, 2016 15:50
On homogeneous and isotropic Universe M. O. Katanaev Семинар, посвящённый памяти академика А. А. Логунова и 100-летию общей теории относительности. ФГБУ ИФВЭ НИЦ КИ, Протвино, Россия, 19 ноября 2015 г. November 19, 2015 15:30
71.
Geometric theory of defects M. O. Katanaev 27th Indian-Summer School on Graphene – the Bridge between Low- and High-Energy Physics. September 14–18, 2015, Prague, Czech Republic September 17, 2015 11:30
72.
Geometric theory of defects M. O. Katanaev Fifth school-conference on algebraic geometry and complex analysis for
young russian mathematicians August 22, 2015 14:40
On homogeneous and isotropic universe M. O. Katanaev 28th Texas Symposium on Relativistic Astrophysics. Geneva, Switzerland, December 13–18, 2015 December 14, 2014 16:35
86.
Geometric theory of defects and gravity M. O. Katanaev International Conference on "New Trends in Field Theory", 01–05 November 2014, BHU, Varanasi, India November 3, 2014
87.
Point massive particle in General Relativity M. O. Katanaev International conference MIAN-Institute of mathematics of China Academy of Science on Complex Analysis and Mathematical Physics October 15, 2014 10:00
Passage through the Einstein–Rosen bridge M. O. Katanaev International Conference «Quantum Field Theory and Gravity (QFTG’14)». Tomsk, Russia, July 28–August 3, 2014 July 29, 2014 12:30
91.
Passage through the Einstein–Rosen bridge M. O. Katanaev 15th Russian Gravitational Conference – International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-15) and the International School on Gravitation and Cosmology (GRACOS-2014). Kazan, Russia, June 30–July 5, 2014 July 1, 2014
92.
On homogeneous and isotropic Universe M. O. Katanaev ICGAC-12, XIIth International Conference on Gravitation, Astrophysics and Cosmology. June 28–July 5, 2015, PFUR, Moscow, Russia June 30, 2014 16:45
93.
Проход по мосту Эйнштейна–Розена M. O. Katanaev Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS February 13, 2014 11:00
94.
Point massive particle in General Relativity M. O. Katanaev 19th International Symposium on Particles, Strings and Cosmology (PASCOS 2013). 20–26 November 2013, Taipei, Taiwan November 20, 2013 13:30
Point massive particle in General Relativity M. O. Katanaev ICIS 2013 - Les Rencontres du Vietnam: Hot Topics in General Relativity and Gravitation. July 28–August 03, 2013, Quy Nhon, Vietnam July 30, 2013 10:50
97.
Point massive particle in General Relativity M. O. Katanaev 29th International Workshop on High Energy Physics: New Results and Actual Problems in Particle Physics, Astrophysics and Cosmology (IHEP 2013). 26–28 June 2013, Protvino, Russia June 28, 2013 10:30
Point massive particle in General Relativity M. O. Katanaev International conference on "New Trends in Field Theories". Banaras Hindu Univercity, Varanasi, India, November 23–26, 2012 November 26, 2012
101.
Точечная массивная частица в общей теории относительности M. O. Katanaev International Conference-Session of the Section of Nuclear Physics of the Physical Sciences Division of RAS "Physics of Fundamental Interactions". National Research Nuclear University MEPhI, November 12–16, 2012 November 16, 2012 15:45
Клиновые дислокации и трехмерная гравитация M. O. Katanaev International conference "Fourth Russian-Armenian workshop on mathematical physics, complex analysis and related topics" September 15, 2012 11:20
Multivalued fields for defects in spacetime and gravity M. O. Katanaev, H. Kleinert Thirteen Marcel Grossmann Meeting – MG13 – on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field theories", 1–7 July, 2012, Stockholm July 3, 2012
Geometric theory of defects and gravity M. O. Katanaev Sixth Aegean Summer Workshop "Quantum Gravity and Quantum Cosmology". 12–17 September, 2011. Naxos island, Greece September 13, 2011 17:30
111.
Tube dislocations in gravity M. O. Katanaev International Workshop on Astrophysics and Cosmology for Matter and Antimatter", 5–9 September, 2011, San Marino September 5, 2011 18:00
Geometric theory of defects M. O. Katanaev The 11th international scientific Baikal Summer School on Physics of Elementary Particles and Astrophysics. 3–10 of July 2011, Bolshie Koty, Russia July 9, 2011 17:00
114.
Tube dislocations in gravity M. O. Katanaev Petrov 2010 anniversary symposium on General Relativity and Gravitation. Kazan, Russia, November 1–6, 2010 November 5, 2010 11:30
Tube dislocations in gravity M. O. Katanaev International Scientific Conference "Mathematical Physics 6th Meeting: Summer School and Conference on Modern Mathematical Physics", 14–23 September 2010, Belgrade, Serbia September 16, 2010 15:30
117.
Tube dislocations in gravity M. O. Katanaev Satellite Workshop on Noncommutative Field Theory and Gravity, September 8–12, 2010, Corfu, Greece September 11, 2010 16:00
118.
Tube dislocations in gravity M. Katanaev International conference "Quantum field theory and gravity". 5–10 July 2010, Tomsk July 8, 2010 15:00
119.
Tubular dislocations in gravity M. O. Katanaev International Conference "Modern Problems of Gravitation, Cosmology and Relativistic Astrophysics". June 28–July 3, 2010, PFUR, Moscow, Russia June 29, 2010 12:50
Global Solutions in Gravity M. O. Katanaev Joint Focus Program on Frontiers of Black Hole Physics. Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Korea, December 6–17, 2010
126.
Geometric Theory of Defects M. O. Katanaev Joint Focus Program on Frontiers of Black Hole Physics. Asia Pacific Center for Theoretical Physics (APCTP), Pohang, Korea, December 6–17, 2010
Point massive particle in General Relativity M. O. Katanaev 20th International Conference on General Relativity and Gravitation and 10th Amaldi Conference on Gravitational Waves (Amaldi10). 7–13 July 2013, Warsaw, Poland
Геометрическая теория дефектов M. O. Katanaev International conference "Fifth Russian-Armenian Workshop on Mathematical Physics, Complex Analysis and Related Topics"
Books in Math-Net.Ru
Mathematical physics and applications, Collected papers. In commemoration of the 95th anniversary of Academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 306, ed. I. V. Volovich, M. O. Katanaev, 2019, 352 с. http://mi.mathnet.ru/book1763
M. O. Katanaev, Mathematical foundations of general relativity. Part 2, Lekts. Kursy NOC, 29, 2018, 366 с. http://mi.mathnet.ru/book1729
Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, ed. A. I. Aptekarev, M. O. Katanaev, S. P. Suetin, 2018, 335 с. http://mi.mathnet.ru/book1696
M. O. Katanaev, Mathematical foundations of general relativity. Part 1, Lekts. Kursy NOC, 28, 2017, 312 с. http://mi.mathnet.ru/book1699
M. O. Katanaev, Geometrical methods in mathematical physics. Applications in quantum mechanics. Part 1, Lekts. Kursy NOC, 25, 2015, 176 с. http://mi.mathnet.ru/book1603
M. O. Katanaev, Geometrical methods in mathematical physics. Applications in quantum mechanics. Part 2, Lekts. Kursy NOC, 26, 2015, 186 с. http://mi.mathnet.ru/book1604
2025
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