Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros

ilustraciones, graficas

Autores:
Pulido González, Walter Alexis
Tipo de recurso:
Doctoral thesis
Fecha de publicación:
2022
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
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oai:repositorio.unal.edu.co:unal/82039
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/82039
https://repositorio.unal.edu.co/
Palabra clave:
110 - Metafísica::118 - Fuerza y energía
TERMODINAMICA
COLAPSO GRAVITACIONAL
AGUJEROS NEGROS (ASTRONOMIA)
Thermodynamics
Gravitational collapse
Black holes (astronomy)
Agujeros negros
Colapso gravitacional
Cascarones negros
Black holes
Gravitational collapse
Black shells
Rights
openAccess
License
Reconocimiento 4.0 Internacional
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oai_identifier_str oai:repositorio.unal.edu.co:unal/82039
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dc.title.spa.fl_str_mv Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
dc.title.translated.eng.fl_str_mv Relativistic observers and thermodynamics of the gravitational collapse of black shells
title Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
spellingShingle Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
110 - Metafísica::118 - Fuerza y energía
TERMODINAMICA
COLAPSO GRAVITACIONAL
AGUJEROS NEGROS (ASTRONOMIA)
Thermodynamics
Gravitational collapse
Black holes (astronomy)
Agujeros negros
Colapso gravitacional
Cascarones negros
Black holes
Gravitational collapse
Black shells
title_short Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
title_full Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
title_fullStr Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
title_full_unstemmed Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
title_sort Observadores relativistas y termodinámica del colapso gravitacional de cascarones negros
dc.creator.fl_str_mv Pulido González, Walter Alexis
dc.contributor.advisor.none.fl_str_mv Arenas Salazar, José Robel
dc.contributor.author.none.fl_str_mv Pulido González, Walter Alexis
dc.subject.ddc.spa.fl_str_mv 110 - Metafísica::118 - Fuerza y energía
topic 110 - Metafísica::118 - Fuerza y energía
TERMODINAMICA
COLAPSO GRAVITACIONAL
AGUJEROS NEGROS (ASTRONOMIA)
Thermodynamics
Gravitational collapse
Black holes (astronomy)
Agujeros negros
Colapso gravitacional
Cascarones negros
Black holes
Gravitational collapse
Black shells
dc.subject.lemb.spa.fl_str_mv TERMODINAMICA
COLAPSO GRAVITACIONAL
AGUJEROS NEGROS (ASTRONOMIA)
dc.subject.lemb.eng.fl_str_mv Thermodynamics
Gravitational collapse
Black holes (astronomy)
dc.subject.proposal.spa.fl_str_mv Agujeros negros
Colapso gravitacional
Cascarones negros
dc.subject.proposal.eng.fl_str_mv Black holes
Gravitational collapse
Black shells
description ilustraciones, graficas
publishDate 2022
dc.date.accessioned.none.fl_str_mv 2022-08-23T19:56:31Z
dc.date.available.none.fl_str_mv 2022-08-23T19:56:31Z
dc.date.issued.none.fl_str_mv 2022
dc.type.spa.fl_str_mv Trabajo de grado - Doctorado
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/doctoralThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_db06
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TD
format http://purl.org/coar/resource_type/c_db06
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/82039
dc.identifier.instname.spa.fl_str_mv Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv https://repositorio.unal.edu.co/
url https://repositorio.unal.edu.co/handle/unal/82039
https://repositorio.unal.edu.co/
identifier_str_mv Universidad Nacional de Colombia
Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.indexed.spa.fl_str_mv RedCol
LaReferencia
dc.relation.references.spa.fl_str_mv M. Alcubierre, Introduction to 3+1 numerical relativity. Oxford University Press, Oxford, UK. (2006).
J.R. Oppenheimer, H. Snyder, On continued gravitational contraction. Phys.Rev. 56, (1939) 455.
D.V Fursaev, Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?, Phys. Part. Nucl.36, (2005) 81.
J. Cano, W. Pulido, La paradoja de la pérdida de información de los agujeros negros, Revista Momento. Número 58, (2019) 59-88.
X. Calmet, (Ed.), Quantum Aspects of Black Holes, Fundamental Theories of Physics. Vol 178.
Y. Takahashi, H. Umezawa, Collective Phenomena 2, (1975) 55.
H. Umezawa. Advanced Field Theory. Micro, Macro and Thermal Physics. American Institute of Physics, 1980.
W. Pulido, H. Quevedo, Black shells and naked shells, International Journal Of Geometric Methods in Modern Physics. (2021).
W. Israel, Thermo- eld dynamics of black holes, Phys. Lett.A57, (1976) 107.
S. Mukohyama, W. Israel, Black holes, brick walls, and the Boulware state, Phys. Rev.D58, (1998) 104005.
W. Israel, Black hole thermodynamics, in current trends in relativistic astrophysics. Ed. L. Fernández, L.M. González. Springer Lectures notes in Physics LNP 617, (2003) 15.
W. Israel. A massless rewall, (2014).
J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cimento. 4, (1972) 737.
J.D. Bekenstein, Black Holes and Entropy, Phys. Rev. D7, (1973) 2333.
J.D. Bekenstein, Generalized second law of thermodynamics in black-hole physics, Phys. Rev. D9, (1974) 3292.
J.D. Bekenstein, Statistical black-hole thermodynamics, Phys. Rev. D12, (1975) 3077.
J.M. Bardeen, B. Carter, S. Hawking, The four laws of black hole mechanics, Comm. Math. Phys. 31, (1973) 161.
S.W. Hawking, Particle creation by black holes, Commun. Math, Phys. 43, (1975) 199.
J.R Arenas, W. Pulido, Agujeros negros cuánticos y el efecto Hawking, Revista Momento. Número 59E, (2019) 1-13.
B. Carter, General relativity, an Einstein Centenary Survey. Ed. by. S.W. Hawking and W. Israel. (Cambridge University Press, 1979) Cap 6.
S.D. Sorkin, Black holes and relativistic stars. (The university of Chicago Press, 1998) Cap.9.
G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D15, (1977) 2752.
G. t'Hooft, On the quantum structure of a black hole, Nucl.Phys B256, (1985) 727.
A. Strominger, C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett. B379 (1996) 99.
J.M. Maldacena, A. Strominger, Statistical Entropy of Four-Dimensional Extremal Black Holes, Phys. Rev. Lett. 77 (1996) 428.
C.G. Callan, J.M. Maldacena, D-brane Approach to Black Hole Quantum Mechanics, Nucl. Phys. B472 (1996) 591.
E.T. Akhmedov, Black Hole Thermodynamics from the Point of View of Superstring Theory, Int. J. Mod. Phys. A15 (2000) 1.
A. Corichi, Black holes and entropy in loop quantum gravity: An overview. (2009).
S. Mukohyama, The origin of black hole entropy, PhD. Thesis, Kyoto University, (1998).
L. Bombelli, R.K. Koul, J. Lee, and R.D, Sorkin, Quantum source of entropy for black holes, Phys. Rev. D34, (1986) 373.
M. Srednicki, Entropy and area, Phys. Rev. Lett. 71, (1993) 666.
J.R. Arenas, J.M. Tejeiro, Black Hole Entanglement Entropy. XXVIII Spanish Relativity Meeting. ERE (2005) 385.
J. M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity Adv. Theor. Math. Phys. 2, (1998) 231.
J. M. Maldacena, Int. J. Theor. Phys. 38, (1999) 1113.
L. Susskind, J. Lindesay, An introduction to black holes, information and the string theory revolution, (World Scienti c Publishing Co. 2005) Cap. 12.
Papantonopoulos, E., (Ed.), Physics of Black Holes: A Guided Tour, Lect. Notes Phys. 769 (Springer, Berlin Heidelberg 2009).
J.M. Maldacena, Eternal Black Holes in AdS JHEP 04, (2003) 021.
A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, Black Holes: Complementarity or Firewalls?, J High Energy Phys 2013, 62 (2013).
J. Preskill, Do Black Holes Destroy Information?, (1992).
G. Horowitz, D. Marolf, Where is the Information Stored in Black Holes?, Phys, Rev. D55, (1997) 3654.
G. Horowitz, Quantum States of Black Holes, (1997).
V. Mashkevich, Conservative Model of Black Hole and Lifting of the Information Loss Paradox, (1997).
G. Horowitz, J. Maldacena, The black hole nal state, JHEP 02 (2004) 008.
P.Kraus, F. Wilczek, Self-Interaction Correction to Black Hole Radiance,Nucl. Phys. B433 (1995) 403.
P.Kraus, F. Wilczek, Effect of Self-Interaction on Charged Black Hole Radiance, Nucl. Phys. B437 (1995) 231.
M. Parikh, F. Wilczek, Hawking Radiation as Tunneling, Phys. Rev. Lett. 85 (2000) 5042.
B. Zhang, Q. Cai, M. Zhan, L. You, Hidden messenger revealed in Hawking radiation: A resolution to the paradox of black hole information loss, Phys. Lett. B675 (2009) 98.
W. Israel, Z. Yun, Band-aid for information loss from black holes, Phys. Rev. D 82, 124036.
L. Susskind, Black holes and the information paradox. Scienti c American, Volume 276, April 1997, p. 40-45.
J. D. Bekenstein, Information in the Holographic Universe. Scienti c American, Volume 289, Number 2, August 2003, p. 61.
I. Klebanov, J. Maldacena, Solving quantum eld theories via curved spacetimes. Physics Today, Volume 62, January 2009. p.28.
L. Susskind, L. Thorlacius, J. Uglum, The Stretched Horizon and Black Hole Complementarity, Phys, Rev. D48 (1993) 3743.
S.W. Hawking, Information Loss in Black Holes, Phys.Rev. D72 (2005) 084013.
Z. Merali, Fire in the hole. Nature, Volume 496, April 2013, p. 21-23.
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dc.publisher.spa.fl_str_mv Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv Bogotá - Ciencias - Doctorado en Ciencias - Física
dc.publisher.department.spa.fl_str_mv Departamento de Física
dc.publisher.faculty.spa.fl_str_mv Facultad de Ciencias
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dc.publisher.branch.spa.fl_str_mv Universidad Nacional de Colombia - Sede Bogotá
institution Universidad Nacional de Colombia
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spelling Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Arenas Salazar, José Robelef9c9f40f98f012478a028312f2e76adPulido González, Walter Alexise2a539016f1fc54c16f712cfd6fd587e2022-08-23T19:56:31Z2022-08-23T19:56:31Z2022https://repositorio.unal.edu.co/handle/unal/82039Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, graficasSe estudia el colapso de un cascarón de polvo delgado desde dos enfoques diferentes: clásico y semiclásico. En el enfoque clásico se identifican superficies críticas cuyas coordenadas de tiempo y espacio intercambian sus papeles, las cuales se asocian con la presencia de horizontes cuasi-locales, sobre los que se realiza un estudio de las propiedades gravitacionales y termodinámicas. A continuación, para el enfoque semiclásico se incorpora un campo escalar, para el cascarón en colapso, con el que se calculan la densidad de energía y entropía asociadas al observador relativista FREFOS, en contraste con el observador FIDO. Con lo anterior se discute e interpretan los resultados a luz de la existencia de una densidad de energía negativa ante la presencia de un campo gravitacional fuerte. (Texto tomado de la fuente)The collapse of a thin dust shell is studied from two different approaches: classical and semiclassical. In the classical approach, critical surfaces are identified whose coordinates of time and space exchange their roles, which are associated with the presence of quasi-local horizons, on which a study of the gravitational and thermodynamic properties is carried out. Next, for the semiclassical approach, a scalar field is incorporated, for the collapsing shell, with which the energy density and entropy associated with the relativistic observer FREFOS are calculated , in contrast to the FIDO observer. With the above, the results are discussed and interpreted in light of the existence of a negative energy density in the presence of a strong gravitational field.DoctoradoDoctor en Ciencias - Física194 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - FísicaDepartamento de FísicaFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá110 - Metafísica::118 - Fuerza y energíaTERMODINAMICACOLAPSO GRAVITACIONALAGUJEROS NEGROS (ASTRONOMIA)ThermodynamicsGravitational collapseBlack holes (astronomy)Agujeros negrosColapso gravitacionalCascarones negrosBlack holesGravitational collapseBlack shellsObservadores relativistas y termodinámica del colapso gravitacional de cascarones negrosRelativistic observers and thermodynamics of the gravitational collapse of black shellsTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDRedColLaReferenciaM. Alcubierre, Introduction to 3+1 numerical relativity. Oxford University Press, Oxford, UK. (2006).J.R. Oppenheimer, H. Snyder, On continued gravitational contraction. Phys.Rev. 56, (1939) 455.D.V Fursaev, Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?, Phys. Part. Nucl.36, (2005) 81.J. Cano, W. Pulido, La paradoja de la pérdida de información de los agujeros negros, Revista Momento. Número 58, (2019) 59-88.X. Calmet, (Ed.), Quantum Aspects of Black Holes, Fundamental Theories of Physics. Vol 178.Y. Takahashi, H. Umezawa, Collective Phenomena 2, (1975) 55.H. Umezawa. Advanced Field Theory. Micro, Macro and Thermal Physics. American Institute of Physics, 1980.W. Pulido, H. Quevedo, Black shells and naked shells, International Journal Of Geometric Methods in Modern Physics. (2021).W. Israel, Thermo- eld dynamics of black holes, Phys. Lett.A57, (1976) 107.S. Mukohyama, W. Israel, Black holes, brick walls, and the Boulware state, Phys. Rev.D58, (1998) 104005.W. Israel, Black hole thermodynamics, in current trends in relativistic astrophysics. Ed. L. Fernández, L.M. González. Springer Lectures notes in Physics LNP 617, (2003) 15.W. Israel. A massless rewall, (2014).J.D. Bekenstein, Black holes and the second law, Lett. Nuovo Cimento. 4, (1972) 737.J.D. Bekenstein, Black Holes and Entropy, Phys. Rev. D7, (1973) 2333.J.D. Bekenstein, Generalized second law of thermodynamics in black-hole physics, Phys. Rev. D9, (1974) 3292.J.D. Bekenstein, Statistical black-hole thermodynamics, Phys. Rev. D12, (1975) 3077.J.M. Bardeen, B. Carter, S. Hawking, The four laws of black hole mechanics, Comm. Math. Phys. 31, (1973) 161.S.W. Hawking, Particle creation by black holes, Commun. Math, Phys. 43, (1975) 199.J.R Arenas, W. Pulido, Agujeros negros cuánticos y el efecto Hawking, Revista Momento. Número 59E, (2019) 1-13.B. Carter, General relativity, an Einstein Centenary Survey. Ed. by. S.W. Hawking and W. Israel. (Cambridge University Press, 1979) Cap 6.S.D. Sorkin, Black holes and relativistic stars. (The university of Chicago Press, 1998) Cap.9.G.W. Gibbons and S.W. Hawking, Action integrals and partition functions in quantum gravity, Phys. Rev. D15, (1977) 2752.G. t'Hooft, On the quantum structure of a black hole, Nucl.Phys B256, (1985) 727.A. Strominger, C. Vafa, Microscopic Origin of the Bekenstein-Hawking Entropy, Phys. Lett. B379 (1996) 99.J.M. Maldacena, A. Strominger, Statistical Entropy of Four-Dimensional Extremal Black Holes, Phys. Rev. Lett. 77 (1996) 428.C.G. Callan, J.M. Maldacena, D-brane Approach to Black Hole Quantum Mechanics, Nucl. Phys. B472 (1996) 591.E.T. Akhmedov, Black Hole Thermodynamics from the Point of View of Superstring Theory, Int. J. Mod. Phys. A15 (2000) 1.A. Corichi, Black holes and entropy in loop quantum gravity: An overview. (2009).S. Mukohyama, The origin of black hole entropy, PhD. Thesis, Kyoto University, (1998).L. Bombelli, R.K. Koul, J. Lee, and R.D, Sorkin, Quantum source of entropy for black holes, Phys. Rev. D34, (1986) 373.M. Srednicki, Entropy and area, Phys. Rev. Lett. 71, (1993) 666.J.R. Arenas, J.M. Tejeiro, Black Hole Entanglement Entropy. XXVIII Spanish Relativity Meeting. ERE (2005) 385.J. M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity Adv. Theor. Math. Phys. 2, (1998) 231.J. M. Maldacena, Int. J. Theor. Phys. 38, (1999) 1113.L. Susskind, J. Lindesay, An introduction to black holes, information and the string theory revolution, (World Scienti c Publishing Co. 2005) Cap. 12.Papantonopoulos, E., (Ed.), Physics of Black Holes: A Guided Tour, Lect. Notes Phys. 769 (Springer, Berlin Heidelberg 2009).J.M. Maldacena, Eternal Black Holes in AdS JHEP 04, (2003) 021.A. Almheiri, D. Marolf, J. Polchinski, and J. Sully, Black Holes: Complementarity or Firewalls?, J High Energy Phys 2013, 62 (2013).J. Preskill, Do Black Holes Destroy Information?, (1992).G. Horowitz, D. 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D 77, 084004 (2008).InvestigadoresLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.unal.edu.co/bitstream/unal/82039/1/license.txt8a4605be74aa9ea9d79846c1fba20a33MD51ORIGINAL79750439.2022.pdf79750439.2022.pdfTesis de Doctorado en Ciencias - Físicaapplication/pdf4600812https://repositorio.unal.edu.co/bitstream/unal/82039/2/79750439.2022.pdfc54ec87212d354cf557e0eac7d70d090MD52THUMBNAIL79750439.2022.pdf.jpg79750439.2022.pdf.jpgGenerated Thumbnailimage/jpeg4459https://repositorio.unal.edu.co/bitstream/unal/82039/3/79750439.2022.pdf.jpge4f4d6b16b08c46c9fca58c58dbce89fMD53unal/82039oai:repositorio.unal.edu.co:unal/820392023-08-07 23:04:23.984Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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