Alberto Saa

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All published works

Action	Title	Year	Authors
+ PDF Chat	Finslerian structure of black holes	2025	Hengameh R. Dehkordi Mauricio Richartz Alberto Saa
+ PDF Chat	Stability of the spacetime of a magnetized compact object	2025	E. Ribeiro Lucas Formigari Marcos R. Ribeiro Élcio Abdalla Bertha Cuadros-Melgar C. Molina Amilcar R. de Queiroz Alberto Saa
+ PDF Chat	Stability of the spacetime of a magnetized compact object	2024	E. Ribeiro Lucas Formigari Marcos R. Ribeiro Élcio Abdalla Bertha Cuadros-Melgar C. Molina Amilcar R. de Queiroz Alberto Saa
+	Quasinormal modes and the analytical continuation of non-self-adjoint operators	2024	Martín G. Richarte J. C. Fabris Alberto Saa
+ PDF Chat	Quasinormal modes and the analytical continuation of non-self-adjoint operators	2024	M. G. Richarte J. C. Fabris Alberto Saa
+	The number of fundamental constants from a spacetime-based perspective	2023	George E. A. Matsas V. Pleitez Alberto Saa Daniel A. T. Vanzella
+ PDF Chat	A new derivation of the Hénon’s isochrone potentials	2022	Alberto Saa Roberto Venegeroles
+ PDF Chat	Isochrone spacetimes	2022	Alberto Saa Roberto Venegeroles
+	Isochrone spacetimes	2021	Alberto Saa Roberto Venegeroles
+	A simple derivation of the Henon's isochrone potentials	2021	Alberto Saa Roberto Venegeroles
+ PDF Chat	Quasinormal modes and self-adjoint extensions of the Schrödinger operator	2021	J. C. Fabris Martín G. Richarte Alberto Saa
+	Post-Newtonian Hamiltonian dynamics: applications to stationary spacetimes and statistical mechanics	2021	Ronaldo S. S. Vieira Javier Ramos-Caro Alberto Saa
+	Higher-dimensional Euclidean and non-Euclidean structures in planar circuit quantum electrodynamics	2021	Alberto Saa E. Miranda Francisco Rouxinol
+	Isochrone spacetimes	2021	Alberto Saa Roberto Venegeroles
+	A new derivation of the Henon's isochrone potentials	2021	Alberto Saa Roberto Venegeroles
+ PDF Chat	Accretion of perfect fluids onto a class of regular black holes	2020	Juliano C. S. Neves Alberto Saa
+ PDF Chat	Optimal global synchronization of partially forced Kuramoto oscillators	2019	Joyce Simão Clímaco Alberto Saa
+ PDF Chat	Dynamical properties of Bianchi-I spacetimes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity	2019	Saikat Chakraborty Kazuharu Bamba Alberto Saa
+ PDF Chat	Huygens’ envelope principle in Finsler spaces and analogue gravity	2019	Hengameh R. Dehkordi Alberto Saa
+ PDF Chat	Dynamical equivalence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity in Jordan and Einstein frames	2019	Saikat Chakraborty Sanchari Pal Alberto Saa
+ PDF Chat	Near-Horizon Modes and Self-adjoint Extensions of the Schrödinger Operator	2019	A. P. Balachandran Amilcar R. de Queiroz Alberto Saa
+	Efeito não-lineares de relatividade geral e matéria escura em galáxias.	2018	D. C. Rodrigues Alberto Saa Oliver F. Piattella J. C. Fabris
+ PDF Chat	Symmetries and synchronization in multilayer random networks	2018	Alberto Saa
+ PDF Chat	Stability aspects of relativistic thin magnetized disks	2017	Vanessa P. de Freitas Alberto Saa
+ PDF Chat	Vertical stability of circular orbits in relativistic razor-thin disks	2016	Ronaldo S. S. Vieira Javier Ramos-Caro Alberto Saa
+	Synchrony-optimized networks of Kuramoto oscillators with inertia	2016	Rafael S. Pinto Alberto Saa
+ PDF Chat	Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach	2015	Rafael S. Pinto Alberto Saa
+ PDF Chat	Doughnut-shaped soap bubbles	2015	Deison Préve Alberto Saa
+ PDF Chat	Explosive synchronization with partial degree-frequency correlation	2015	Rafael S. Pinto Alberto Saa
+ PDF Chat	Chaos in the Kepler Problem with Quadrupole Perturbations	2015	Gabriela Iunes Depetri Alberto Saa
+	Synchrony-optimized power grids	2014	Rafael S. Pinto Alberto Saa
+	Regular rotating black holes and the weak energy condition	2014	Juliano C. S. Neves Alberto Saa
+ PDF Chat	Chaotic oscillations in singularly perturbed FitzHugh–Nagumo systems	2013	Peterson T.C. Barbosa Alberto Saa
+ PDF Chat	Superradiance without event horizons in general relativity	2013	Maurício Richartz Alberto Saa
+ PDF Chat	Modeling the ATP Production in Mitochondria	2013	Alberto Saa Kellen Manoela Siqueira
+ PDF Chat	No asymptotically highly damped quasinormal modes without horizons?	2013	Cecilia Chirenti Alberto Saa Jozef Skákala
+	Pesin’s Relation for Weakly Chaotic One-Dimensional Systems	2013	Alberto Saa Roberto Venegeroles
+ PDF Chat	Quasinormal modes for the scattering on a naked Reissner-Nordström singularity	2012	Cecilia Chirenti Alberto Saa Jozef Skákala
+ PDF Chat	Quantum singularities in Hořava-Lifshitz cosmology	2012	João Paulo M. Pitelli Alberto Saa
+	Bilhares : aspectos clássicos e quânticos	2012	Renato de Sá Teles Alberto Saa
+ PDF Chat	Double-null formulation of the general Vaidya metric	2012	Cecilia Chirenti Alberto Saa
+ PDF Chat	Pesin-type relation for subexponential instability	2012	Alberto Saa Roberto Venegeroles
+ PDF Chat	Lyapunov statistics and mixing rates for intermittent systems	2011	Carlos J. A. Pires Alberto Saa Roberto Venegeroles
+ PDF Chat	Challenging the weak cosmic censorship conjecture with charged quantum particles	2011	Maurício Richartz Alberto Saa
+ PDF Chat	Quasinormal modes for the charged Vaidya metric	2011	Cecilia Chirenti Alberto Saa
+ PDF Chat	Searching for curvature pion radiation from protons in strongly magnetized pulsars	2011	Douglas Fregolente Alberto Saa
+ PDF Chat	Nonstationary regime for quasinormal modes of the charged Vaidya metric	2011	Cecilia Chirenti Alberto Saa
+ PDF Chat	Alternative numerical computation of one-sided Lévy and Mittag-Leffler distributions	2011	Alberto Saa Roberto Venegeroles
+ PDF Chat	Destroying a near-extremal Kerr-Newman black hole	2011	Alberto Saa Raphael Santarelli
+ PDF Chat	Local electromagnetic duality and gauge invariance	2011	Alberto Saa
+	Massive particle production from accelerated sources in high magnetic fields	2011	Douglas Fregolente Alberto Saa
+	Massive particle production from accelerated sources in high magnetic fields	2011	Douglas Fregolente Alberto Saa
+	Massive particle production from accelerated sources in high magnetic fields	2011	Douglas Fregolente Alberto Saa
+ PDF Chat	Ergodic transitions in continuous-time random walks	2010	Alberto Saa Roberto Venegeroles
+ PDF Chat	Relativistic Weierstrass random walks	2010	Alberto Saa Roberto Venegeroles
+	Relativistic Weierstrass Random Walks.	2010	Alberto Saa Roberto Venegeroles
+ PDF Chat	Accretion of nonminimally coupled scalar fields into black holes	2009	Manuela G. Rodrigues Alberto Saa
+ PDF Chat	Anisotropic singularities in modified gravity models	2009	Michele Ferraz Figueiró Alberto Saa
+ PDF Chat	Can quantum mechanics fool the cosmic censor?	2009	George E. A. Matsas Maurício Richartz Alberto Saa A. R. R. da Silva Daniel A. T. Vanzella
+ PDF Chat	Relativistic Invariance of Lyapunov Exponents in Bounded and Unbounded Systems	2009	Adilson E. Motter Alberto Saa
+	Inflação vetorial : uma introdução	2009	André Luís Delvas Fróes Alberto Saa
+ PDF Chat	Gravitational wave recoil in Robinson-Trautman spacetimes	2008	Rodrigo Panosso Macedo Alberto Saa
+ PDF Chat	Overspinning a nearly extreme black hole and the weak cosmic censorship conjecture	2008	Maurício Richartz Alberto Saa
+ PDF Chat	Lifetime and decay of unstable particles in strong gravitational fields	2008	Douglas Fregolente Alberto Saa
+ PDF Chat	Non-Gaussian features of chaotic Hamiltonian transport	2008	Roberto Venegeroles Alberto Saa
+ PDF Chat	Quasinormal mode characterization of evaporating mini black holes	2007	Élcio Abdalla Cecilia Chirenti Alberto Saa
+ PDF Chat	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-dimensional Vaidya metric with a cosmological constant in double-null coordinates	2007	Alberto Saa
+ PDF Chat	A third-order curvature invariant in static spacetimes	2007	Alberto Saa
+ PDF Chat	Homogeneous cosmologies and the Maupertuis-Jacobi principle	2007	Luciana A. Elias Alberto Saa
+	The number of dimensional fundamental constants	2007	George E. A. Matsas V. Pleitez Alberto Saa Daniel A. T. Vanzella
+	Non-Minimally Coupled Cosmology as Geodesic Motion	2007	Luciana A. Elias Alberto Saa
+	Quasinormal modes for the Vaidya metric	2006	Élcio Abdalla Cecilia Chirenti Alberto Saa
+ PDF Chat	Extracellular polymeric bacterial coverages as minimal area surfaces	2006	Alberto Saa O. Teschke
+ PDF Chat	The radiation of a uniformly accelerated charge is beyond the horizon: A simple derivation	2006	Camila de Almeida Alberto Saa
+ PDF Chat	Phase space solutions in scalar-tensor cosmological models	2005	J. C. C. de Souza Alberto Saa
+ PDF Chat	Volume elements and torsion	2005	Ricardo A. Mosna Alberto Saa
+	Phase space solutions in scalar-tensor cosmological models	2005	J. C. C. de Souza Alberto Saa
+ PDF Chat	QUANTUM EFFECTS AND SUPERQUINTESSENCE IN THE NEW AGE OF PRECISION COSMOLOGY	2004	E. Gunzig Alberto Saa
+	Nonminimal coupling, exponential potentials and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>w</mml:mi><mml:mo><</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:math>regime of dark energy	2004	F. C. Carvalho Alberto Saa
+ PDF Chat	Semianalytical approach for the Vaidya metric in double-null coordinates	2004	Fernando Girotto Alberto Saa
+ PDF Chat	On the viability of local criteria for chaos	2004	Alberto Saa
+ PDF Chat	Field propagation in de Sitter black holes	2004	C. Molina Davi Giugno Élcio Abdalla Alberto Saa
+ PDF Chat	Conformal Quantum Effects and the Anisotropic Singularities of Scalar-Tensor Theories of Gravity	2004	E. Gunzig Alberto Saa
+ PDF Chat	A NOTE ON DUALITIES IN EINSTEIN'S GRAVITY IN THE PRESENCE OF A NON-MINIMALLY COUPLED SCALAR FIELD	2003	L. Raul Abramo L. Brenig E. Gunzig Alberto Saa
+ PDF Chat	Singularities of gravity in the presence of nonminimally coupled scalar fields	2003	L. Raul Abramo L. Brenig E. Gunzig Alberto Saa
+	Field propagation in the Schwarzschild-de Sitter black hole	2003	C. Molina Élcio Abdalla Alberto Saa
+	Stability properties and asymptotics for N non-minimally coupled scalar fields cosmology	2003	L. Brenig Ana Elisa Bastos Figueiredo E. Gunzig T. M. Rocha Filho Alberto Saa
+	Dynamical study of the singularities of gravity in the presence of non-minimally coupled scalar fields	2003	L. Raul Abramo L. Brenig E. Gunzig Alberto Saa
+	Superinflation and quintessence in the presence of an extra field	2002	Ana Elisa Bastos Figueiredo T. M. Rocha Filho E. Gunzig L. Brenig Alberto Saa
+ PDF Chat	Superinflation, quintessence, and nonsingular cosmologies	2001	E. Gunzig Alberto Saa L. Brenig Valerio Faraoni T. M. Rocha Filho Ana Elisa Bastos Figueiredo
+ PDF Chat	Chaos around the superposition of a monopole and a thick disk	2000	Alberto Saa
+	Superinflation, quintessence, and the avoidance of the initial singularity	2000	Alberto Saa E. Gunzig L. Brenig Valerio Faraoni T. M. Rocha Filho Ana Elisa Bastos Figueiredo
+ PDF Chat	Chaos around the superposition of a black-hole and a thin disk	1999	Alberto Saa Roberto Venegeroles
+ PDF Chat	NONEXISTENCE THEOREMS FOR TRAVERSABLE WORMHOLES	1999	Alberto Saa
+ PDF Chat	Comment on “Theorem for Nonrotating Singularity-Free Universes”	1998	Alberto Saa
+ PDF Chat	THE GRAVITATIONAL VAVILOV–CHERENKOV EFFECT	1998	Alberto Saa Marcelo Schiffer
+ PDF Chat	Bound states due to an accelerated mirror	1997	Alberto Saa Marcelo Schiffer
+ PDF Chat	Propagating Torsion from First Principles	1997	Alberto Saa
+ PDF Chat	Quantum dynamics of non-relativistic particles and isometric embeddings	1997	Alberto Saa
+ PDF Chat	Searching for nonminimally coupled scalar hairs	1996	Alberto Saa
+ PDF Chat	Self-organized criticality and the lattice topology	1996	Alberto Saa
+ PDF Chat	New no-scalar-hair theorem for black holes	1996	Alberto Saa
+ PDF Chat	Canonical quantization of the relativistic particle in static spacetimes	1996	Alberto Saa
+ PDF Chat	A geometrical action for dilaton gravity	1995	Alberto Saa
+ PDF Chat	Volume-forms and minimal action principles in affine manifolds	1995	Alberto Saa
+	Is minimal coupling procedure compatible with minimal action principle? 1	1994	Alberto Saa
+ PDF Chat	GAUGE FIELDS ON RIEMANN-CARTAN SPACE-TIMES	1994	Alberto Saa
+	Is minimal coupling procedure compatible with minimal action principle?	1994	Alberto Saa
+ PDF Chat	Quantization of a spinning particle with anomalous magnetic moment	1993	Д. М. Гитман Alberto Saa
+ PDF Chat	Strings in background fields and Einstein-Cartan theory of gravity	1993	Alberto Saa
+ PDF Chat	PSEUDOCLASSICAL MODEL OF SPINNING PARTICLE WITH ANOMALOUS MAGNETIC MOMENTUM	1993	Д. М. Гитман Alberto Saa
+	Einstein-Cartan theory of gravity revisited	1993	Alberto Saa
+	Pressure in thermal scalar field theory to three-loop order	1992	J. Frenkel Alberto Saa J. C. Taylor

Common Coauthors

Coauthor	Papers Together
Roberto Venegeroles	15
Edgard Gunzig	9
L. Brenig	7
Cecilia Chirenti	7
Élcio Abdalla	6
Douglas Fregolente	5
C. Molina	4
Rafael S. Pinto	4
T. M. Rocha Filho	4
Ana Elisa Bastos Figueiredo	4
Maurício Richartz	4
J. C. Fabris	3
Amilcar R. de Queiroz	3
George E. A. Matsas	3
L. Raul Abramo	3
Daniel A. T. Vanzella	3
V. Pleitez	2
Saikat Chakraborty	2
J. C. C. de Souza	2
Javier Ramos-Caro	2
Jozef Skákala	2
Luciana A. Elias	2
Martín G. Richarte	2
Valerio Faraoni	2
Ronaldo S. S. Vieira	2
Bertha Cuadros-Melgar	2
Marcelo Schiffer	2
Juliano C. S. Neves	2
Lucas Formigari	2
Marcos R. Ribeiro	2
Д. М. Гитман	2
Camila de Almeida	1
Michele Ferraz Figueiró	1
Peterson T.C. Barbosa	1
E. Ribeiro	1
J. Frenkel	1
Vanessa P. de Freitas	1
Renato de Sá Teles	1
J. C. Fabris	1
E. Ribeiro	1
M. G. Richarte	1
Joyce Simão Clímaco	1
Manuela G. Rodrigues	1
D. C. Rodrigues	1
André Luís Delvas Fróes	1
Kellen Manoela Siqueira	1
Carlos J. A. Pires	1
Kazuharu Bamba	1
Oliver F. Piattella	1
A. P. Balachandran	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Superinflation, quintessence, and nonsingular cosmologies	2001	E. Gunzig Alberto Saa L. Brenig Valerio Faraoni T. M. Rocha Filho Ana Elisa Bastos Figueiredo	6
+ PDF Chat	GAUGE FIELDS ON RIEMANN-CARTAN SPACE-TIMES	1994	Alberto Saa	6
+ PDF Chat	Semianalytical approach for the Vaidya metric in double-null coordinates	2004	Fernando Girotto Alberto Saa	6
+ PDF Chat	Singularities of gravity in the presence of nonminimally coupled scalar fields	2003	L. Raul Abramo L. Brenig E. Gunzig Alberto Saa	5
+ PDF Chat	Quasinormal modes of black holes: From astrophysics to string theory	2011	R. A. Konoplya A. Zhidenko	5
+	Quasinormal modes for the Vaidya metric	2006	Élcio Abdalla Cecilia Chirenti Alberto Saa	5
+ PDF Chat	Measurements of Ω and Λ from 42 High‐Redshift Supernovae	1999	S. Perlmutter G. Aldering G. Goldhaber R. A. Knop P. Nugent P. G. Castro Susana E. Deustua S. Fabbro A. Goobar D. E. Groom	5
+	An Introduction to Infinite Ergodic Theory	1997	Jon Aaronson	5
+	An introduction to infinite ergodic theory	1997	Jon Aaronson	5
+	Synchronization in complex networks	2008	Àlex Arenas Albert Dı́az-Guilera Jürgen Kurths Yamir Moreno Changsong Zhou	5
+ PDF Chat	Pesin-Type Identity for Intermittent Dynamics with a Zero Lyaponov Exponent	2009	Nickolay Korabel Eli Barkai	4
+ PDF Chat	Quasinormal modes of black holes and black branes	2009	Emanuele Berti Vítor Cardoso Andrei O. Starinets	4
+ PDF Chat	Spontaneous synchrony in power-grid networks	2013	Adilson E. Motter Seth A. Myers Marian Anghel Takashi Nishikawa	4
+ PDF Chat	Quasinormal modes in pure de Sitter spacetimes	2004	Daping Du Bin Wang Ru-Keng Su	4
+	Resonant relaxation in stellar systems	1996	K. P. Rauch Scott Tremaine	4
+ PDF Chat	Weak Cosmic Censorship: As Strong as Ever	2008	Shahar Hod	4
+ PDF Chat	Overspinning a Nearly Extreme Charged Black Hole via a Quantum Tunneling Process	2007	George E. A. Matsas André R. R. da Silva	4
+ PDF Chat	Overspinning a nearly extreme black hole and the weak cosmic censorship conjecture	2008	Maurício Richartz Alberto Saa	4
+ PDF Chat	The cosmological constant and dark energy	2003	P. J. E. Peebles Bharat Ratra	4
+	Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant	1998	Adam G. Riess A. V. Filippenko P. Challis A. Clocchiatti Alan H. Diercks P. Garnavich Ron Gilliland Craig J. Hogan Saurabh W. Jha R. Kirshner	4
+ PDF Chat	Explosive synchronization with partial degree-frequency correlation	2015	Rafael S. Pinto Alberto Saa	4
+ PDF Chat	The geometry of isochrone orbits: from Archimedes’ parabolae to Kepler’s third law	2020	Paul Ramond Jérôme Perez	4
+ PDF Chat	Chaos around the superposition of a black-hole and a thin disk	1999	Alberto Saa Roberto Venegeroles	4
+	On the stability of gravity in the presence of a non-minimally coupled scalar field	2002	L. Raul Abramo L. Brenig E. Gunzig	4
+ PDF Chat	Stochastic Gravity: Theory and Applications	2004	B. L. Hu Enric Verdaguer	4
+ PDF Chat	<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>-dimensional Vaidya metric with a cosmological constant in double-null coordinates	2007	Alberto Saa	4
+ PDF Chat	Quantization of systems with time-dependent constraints. Example of a relativistic particle in a plane wave	1993	S. P. Gavrilov Д. М. Гитман	3
+ PDF Chat	On the Vaidya limit of the Tolman model	1994	Charles Hellaby	3
+	Return of the quantum cosmic censor	2008	Shahar Hod	3
+ PDF Chat	Wave tails in time-dependent backgrounds	2002	Shahar Hod	3
+	Exterior solution for a charged radiating sphere in general relativity (stars)	1974	K. D. Krori J. Barua	3
+ PDF Chat	The many faces of superradiance	1998	Jacob D. Bekenstein Marcelo Schiffer	3
+ PDF Chat	Radiative falloff in Schwarzschild–de Sitter spacetime	1999	P. R. Brady Chris M. Chambers William G. Laarakkers Eric Poisson	3
+ PDF Chat	Separation of trajectories and its relation to entropy for intermittent systems with a zero Lyapunov exponent	2010	Nickolay Korabel Eli Barkai	3
+ PDF Chat	Physical equivalence between nonlinear gravity theories and a general-relativistic self-gravitating scalar field	1994	Guido Magnano Leszek M. Sokołowski	3
+ PDF Chat	Analysis of a power grid using a Kuramoto-like model	2008	Г. Филатрелла Arne Hejde Nielsen Niels Falsig Pedersen	3
+ PDF Chat	Quasinormal modes in a time-dependent black hole background	2005	Cheng-Gang Shao Bin Wang Élcio Abdalla Ru-Keng Su	3
+	Foundations of Differential Geometry	1963	Shôshichi Kobayashi Katsumi Nomizu	3
+ PDF Chat	Optimal Synchronization of Complex Networks	2014	Per Sebastian Skardal Dane Taylor Jie Sun	3
+ PDF Chat	Synchrony-optimized networks of non-identical Kuramoto oscillators	2007	Markus Brede	3
+ PDF Chat	Telling tails in the presence of a cosmological constant	1997	P. R. Brady Chris M. Chambers William Krivan Pablo Laguna	3
+ PDF Chat	Lyapunov statistics and mixing rates for intermittent systems	2011	Carlos J. A. Pires Alberto Saa Roberto Venegeroles	3
+	Cosmological Imprint of an Energy Component with General Equation of State	1998	R. R. Caldwell R. Dave Paul J. Steinhardt	3
+ PDF Chat	Gravitational collapse of type II fluid in higher dimensional space-times	2002	Sushant G. Ghosh Naresh Dadhich	3
+	Tracking extended quintessence	2000	Carlo Baccigalupi S. Matarrese F. Perrotta	3
+ PDF Chat	Model reduction for networks of coupled oscillators	2015	Georg A. Gottwald	3
+ PDF Chat	A geometrical action for dilaton gravity	1995	Alberto Saa	3
+ PDF Chat	Overcharging a black hole and cosmic censorship	1999	Veronika E. Hubeny	3
+ PDF Chat	Nonstationary regime for quasinormal modes of the charged Vaidya metric	2011	Cecilia Chirenti Alberto Saa	3
+ PDF Chat	Black hole in three-dimensional spacetime	1992	Máximo Bañados Claudio Teitelboim Jorge Zanelli	3