黑洞熵起源的探讨
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摘要
1972年,Bekenstein证明:黑洞有熵,它的熵等于视界面积的四分之一。Hawcking等人也证明:黑洞事件视界的面积永不减少。黑洞面积与第二定律类似性,使得人们把黑洞面积与黑洞熵等同起来。1993年,t’Hooft提出全息原理:时空中某一区域的最大熵与它的表面积相关,而与体积无关。而传统场论里的熵是广延性的。它大大消减了传统场论中的量子态数,因而被认为是解决宇宙常数的最有力的工具。随后,Cohen等人建议:具有紫外截止频率与红外截止频率关系的有效场论使得宇宙常数经量子修正后与观测值一致。取红外截止为目前可观测宇宙的大小,所得到的暗能量为10 ?5 2cm ?2的量级,与观测值一致,缓解了宇宙常数问题。
利用全息原理我们发现一个熵就是全息荧屏的一个Planck矩形,对应着区域内的一个粒子。表面积的增加意味着区域内粒子数的增多。运用这个原理,求得宇宙的半径与观测值一致。并且重新表述了热力学第二定律:时空中某一区域的粒子数总在增加。又用Einstein场方程作了论证,也证实了真空衰减学说。利用Friedmann方程我们发现:传统的能量守恒定律遭到了破坏,如果把暗能量,暗物质,普通粒子和辐射作为一个整体,能量守恒定律可以幸存下来。暗能量和普通粒子相互转化,能量既可从暗能量流向普通物质,也可从普通物质流向暗能量。现阶段,能量主要从暗能量流向普通物质。我们认为,这个熵就是Hawcking辐射中的黑洞熵的起源。
Bekenstein(1972,1973,1974)suggested that a black hole actually carries an entropy equal to its horizon area ,4SBH = A .The area theorem(Hawcking,1971) states that the area of black hole event horizon never decreases with time: dA≥0.Assuming weak gravity ,spherical symmetry ,and other conditions one finds that the entropy in a region of space is limited by the entropy in a region of space ia limited by the area of its boundary. Based on spherical entropy bound ,’t Hooft (1993) and Sussind (1995)formulated a holographic principle: the number of independent degrees of freedom residing inside the relevant region is bounded by the surface area in Planck units, instead of by the relevant region.Such bounds establish black holes as maximally entropy objects of a give size, and postulate that the maximum entropy inside the relevant region behaves non-extensively, growing only as its surface area. Cohen and collaborators suggested sometime ago , that in quantum field theory a short distance cut-off is related to a long distance cut-off due to the limit set by formation of a black hole. An effective local quantum field theory with UV and IR cutoffs in accordance with holographic entropy bounds is capable of rendering the cosmological constant (cc) stable against quantum corrections. By setting an IR cutoff to length scales relevant to cosmology, one easily obtains the currently observedρΛ= 10 ?52cm?2, Thus alleviating the CC problem. In terms of holographic principle we analyze entropy once again , obtaining cosmological radius agree with the currently observed 10? 25m.
According to holographic principle, we think entropy is made up of the number of the particles with different scale. In conventional quantum field theories, entropy denote number of the particles with electronic scale, In a black hole entropy denote number of the particles with Planck scale. With it wo reformulate the second law: the number of particles residing inside the relevant region never decreases. We demonstrate it with Einstein field equation. We also demonstrate decaying vacuum. We find the constant energy law inviolate, but we unify dark energy, dark matter, common matter, he constant energy law survies. There exists an interaction between matter and the CC which causes a continuous transfer of energy from matter to the CC and vice versa . We think this entropy just is the Hawcking radiation entropy.
利用全息原理我们发现一个熵就是全息荧屏的一个Planck矩形,对应着区域内的一个粒子。表面积的增加意味着区域内粒子数的增多。运用这个原理,求得宇宙的半径与观测值一致。并且重新表述了热力学第二定律:时空中某一区域的粒子数总在增加。又用Einstein场方程作了论证,也证实了真空衰减学说。利用Friedmann方程我们发现:传统的能量守恒定律遭到了破坏,如果把暗能量,暗物质,普通粒子和辐射作为一个整体,能量守恒定律可以幸存下来。暗能量和普通粒子相互转化,能量既可从暗能量流向普通物质,也可从普通物质流向暗能量。现阶段,能量主要从暗能量流向普通物质。我们认为,这个熵就是Hawcking辐射中的黑洞熵的起源。
Bekenstein(1972,1973,1974)suggested that a black hole actually carries an entropy equal to its horizon area ,4SBH = A .The area theorem(Hawcking,1971) states that the area of black hole event horizon never decreases with time: dA≥0.Assuming weak gravity ,spherical symmetry ,and other conditions one finds that the entropy in a region of space is limited by the entropy in a region of space ia limited by the area of its boundary. Based on spherical entropy bound ,’t Hooft (1993) and Sussind (1995)formulated a holographic principle: the number of independent degrees of freedom residing inside the relevant region is bounded by the surface area in Planck units, instead of by the relevant region.Such bounds establish black holes as maximally entropy objects of a give size, and postulate that the maximum entropy inside the relevant region behaves non-extensively, growing only as its surface area. Cohen and collaborators suggested sometime ago , that in quantum field theory a short distance cut-off is related to a long distance cut-off due to the limit set by formation of a black hole. An effective local quantum field theory with UV and IR cutoffs in accordance with holographic entropy bounds is capable of rendering the cosmological constant (cc) stable against quantum corrections. By setting an IR cutoff to length scales relevant to cosmology, one easily obtains the currently observedρΛ= 10 ?52cm?2, Thus alleviating the CC problem. In terms of holographic principle we analyze entropy once again , obtaining cosmological radius agree with the currently observed 10? 25m.
According to holographic principle, we think entropy is made up of the number of the particles with different scale. In conventional quantum field theories, entropy denote number of the particles with electronic scale, In a black hole entropy denote number of the particles with Planck scale. With it wo reformulate the second law: the number of particles residing inside the relevant region never decreases. We demonstrate it with Einstein field equation. We also demonstrate decaying vacuum. We find the constant energy law inviolate, but we unify dark energy, dark matter, common matter, he constant energy law survies. There exists an interaction between matter and the CC which causes a continuous transfer of energy from matter to the CC and vice versa . We think this entropy just is the Hawcking radiation entropy.
引文
[1]S. Weinberg, The cosmological constant problem [J]. Rev. Mod. Phys. 1989, 61: 1-23.
[2]M. Tegmak, M. Zaldarriaga, and A. J. S. Hamilton, Towards a refined cosmic concordance model: joint 11-Parameter constraints from CMB and Large–scale structure [J]. Phys. Rev. D 2001, 043007: 63-78.
[3] J. D. Bekenstein, Generalized second law of thermodynamics in black-hole physics [J]. Phys. Rev. D 1974, 9: 3292-3300.
[4] S. W. Hawcking, Commun. Math. Phys. Black holes and Thermodynamics[J]. Phys. Rev. D, 1976, 13: 191-197.
[5] A. Cohen, D. Kaplan, and A. Nelson, Effective Field Theory, Black Hole, and the Cosmological Constant [J]. Phys. Rev. Lett.1999, 82: 4971-4974.
[6] S. Thomas, Holography Stabilizes the Vacuum Energy [J]. Phys. Rev. Lett. 2002, 89: 081301-081305.
[7] S. D. H. Hsu, Entropy Bounds and Dark Energy [J]. Phys. Lett. B, 2004, 594: 13-16.
[8] M. Li, A model of holographic dark energy[J]. Phys. Lett. B, 2004, 603: 1-5.
[9] R. Bousso, The holographic principle[J]. Rev. Mod. Phys. 2002, 74: 825-874.
[10] P. Wang and X. Meng, Class. Quant. Grav. 2005, 283: 22.
[11] Richard Easther and David Lowe, Holography, cosmology, and the Second Law of Thermodynamics Physical Review Letters.1999, 82:25.
[12] R. Horvart, holography and Variable Cosmological Constant, arXiv: astrop-ph/0404204 v4 8 Sep 2004.
[13] Yun Soo Myung, Holographic principle and dark energy, Physics Letter B, 2005, 610: 18-22.
[14] B. Guberina and R. Horvat, Hint for Quintessense-like Scalars from Holographic Dark Energy,arXiv: astro-ph/0503495 v2 4 May 2005.
[15] Edward Witten, When Symmetry breaks down, Nature, 2004, 429: 507.
[16] Raphael Bousso, The holographic principle, arXiv: hep-th/0203101 v229 Jun/2002.
[17] Petra Horava and Djordje Minic, Probable Values of the Cosmological Constant in a Holographic Theory, Physical Review Letters, 2000, 85:8.
[18] Scott Thomas, Holography Stablizea the Vacuum Energy, Physical Review Letters,89: 8.
[19]Saulo Carneiro, Holography and the Cosmic Coinidence, arXiv: gr-qc/0206064-v120 Jun 2002.
[20] Kayll Lake, The Flatness Problem and∧, Physical Review Letters, 2005, 94: 20.
[21] German Olivares, Fernando Atrio-Barandela, Observational constraints on interacting quintessense models, Physical Review D, 2005, 71:6.
[22] Robert R.Caldwell, Marc Kamionkowski, and Nevin N. Weinberg, Phantom Energy: Dark Energy withω<-1 Causes a Cosmic Doomsday, Physical Review Letters, 91: 7.
[23] J. S. Alcaniz and N. Piers, Cosmic acceleration in brane cosmology, 2004, 70: 4.
[24] Gia Dvali and Mchael S. Turner, Dark Energy as a Modification of the Friedmann Equation, arXiv: astro-ph/0301510v1 25 Jan 2003.
[25] J. S. Alcaniz, and J.A.S. Lima, Interpreting cosmological vacuum decay, Physical Review D, 2006, 72: 6.
[26] Alexander A. Andrianov, Francesco Cannata, and Alexander Y. Kamenshchik, Smooth dynamical crossing of the phantom divide of a scalar field in simple cosmological models, 2005, 72: 4.
[27] P. J. E. Peebles, Bharat Ratra, The cosmological constant and dark energy, Review Modern Physics, 75: 2.
[28] T. Banks,W. Fischler, An Holographic Cosmology, arXiv: hep-th0111142v1 15 Nov 2001.
[29] R. R. Caldwell and Eric V.Linder, Limits of Quintessense, Physical Review Letters, 2005, 95: 14.
[30] Raphael Bouss, Flat space physics from holography, arXiv: hep-th/0402058v1 6 Feb 2004.
[31] Gerard’t Hooft, The Holographic Principle, arXiv: hep-th/0003004v216 May 2000.
[32] Kari Enqvist and Martin S. Sloth, Possible Connection between the Location of the Cutoff in the Comic Microwave Background Spectrum and the Equation of State of Dark Energy, Physical Review Letters, 2004, 93: 22.
[33] Marian Douspis, Alian Riazuelo, Zolnierowski, Alain Blanchard, Archeops collaboration, Cosmological constraints in∧-CDM and quintness paradigms with Archeops, New Astronomy Review, 2003, 47: 755-760.
[34] Joan Sola, The Cosmological Constant in Brief, Nuclear B, 2001, 9529-37.
[35] T. Backs, W. Fischler, An Holographic Cosmology, arXiv: hep-th/0111142v1 15 Nov 2001.
[36] R. R. Caldwell and Eric V. Linder, Limts of Quintessense, Physical Review Letters, 2005, 95: 14.
[37] Marian Douspis, Alian Riazuelo, Yves Zolnierowski, Alain blanchard, Archeops collaboration, Cosmological constraints in∧-CDM and quintesssense paradigms with Archeops, New Astronomy Reviews, 2003, 47: 755-760.
[38] J. S. Alcainz, D. Jain and A. Dev, Age, Constraints on brane Models of Dark Energy, arXiv: astro-ph/0206448v2 20 Sep 2002.
[39] Justin Khoury and Ren-Jie Zhang, The Friedmann Equation in Brane-world Scenarios, Physical Review Letters, 89: 6.
[40] E. Elizalde, S. Nojiri, S. D. Odintsov and Peng Wang, Dark energy: Vacuum fluctuations, the effective phantomphase, and holography, Physical Review D, 2005, 71.
[41] John D. Fearns, A Physical Quantum Model in a Smooth Topos, arXiv: quant-ph/0202079v1 14 Feb 2002.
[42] Nima Arkani-Hamed, Savas Dimopoulos, Gia Divali and Nemanja Kaloper, manifold universe, arXiv: hep-ph/9911386v1 17 Nov 1999.
[43] Alexander A. Andrianov, Francesco Cannanta, and Alexander Y. Kamenshchik, Smooth dynamical crossing of the phantom divide line of a scalar field in simple cosmological models, Physical Review D, 2005, 72.
[44] Daniel R. Terno, Entropy, Holographic, and the Second Law, Physical Review Letters, 2004, 93.
[45] Yun Wang and Max Tegmark, New Dark Energy Constrainrts Supernovae, Microwave Background, and Galaxy Clustering, Physical Review Letters, 2004, 92
[47] Saulo Carneiro, Holography and the Cosmic Coincidence, arXiv: gr-qc/0206064-v1 20 Jun 2002.
[47] L. Perivolaropoulos, Constraints on linear negative potentials in quintessense and phantom models from recent supernova data, Physical Review D, 2005, 71.
[48] Lisa Randall, and Raman Sundrum, An Alternative to Compactification, Physical Review Letters, 1999, 83.
[49] John Schwarz, and Nathan Seiberg, String theory, supersymmetry,unification, and all that, Reviews of Modem Physics, 1999, 71.
[50] Lisa Randall, Extra Dimensions and Warped Geometries, Science, 2002, 296.
[51] Ashoke Sen, Developments in superstring Theory, arXiv: hep-ph/9810356v2 16 Oct 1998.
[52] David Langlois, Cosmology with an Extra-dimension, arXiv: astro-ph/0301021v1 2 Jan 2003.
[53] Gia Dvali and Michael S. Tuner, Dark Energy as a Modification of the Friedmann Equation, arXiv: astro-ph/0301510v1 25 Jan 2003.
[54] J. S. Alcaniz, Some Obervational Consequences of Brane World Cosmologies, arXiv: astro-ph/0202492 v2 17 May 2002.
[55] E. I. Guendelman, Conformally invariant braneworld the cosmological constant, Physics Letter B, 2004, 580: 87-92.
[56] M. Doran and Wetterich, Quintessense and the costant, Nuclear Physics B, 2003, 124: 57-62.
[57] Adam G. Riess, Louis-Gregory Strolger, John Tonnry, Stefano Casertano, Henry C. Ferguson, Bahram Mobasher, Peter Challis, Alexei V. Filippenko, Saurabh Jha, Weidong Li, Ryan Chornock, Robert P. Kirshner, Bruno Leibundgut, Mark Dickinson, Mario Livio, Mauro Giavalisco, Charles C. Steidel, Narciso Benitez and Zlatan Tsvetanov, Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution, arXiv: astro-ph/0402512v2 31 Mar 2004.
[2]M. Tegmak, M. Zaldarriaga, and A. J. S. Hamilton, Towards a refined cosmic concordance model: joint 11-Parameter constraints from CMB and Large–scale structure [J]. Phys. Rev. D 2001, 043007: 63-78.
[3] J. D. Bekenstein, Generalized second law of thermodynamics in black-hole physics [J]. Phys. Rev. D 1974, 9: 3292-3300.
[4] S. W. Hawcking, Commun. Math. Phys. Black holes and Thermodynamics[J]. Phys. Rev. D, 1976, 13: 191-197.
[5] A. Cohen, D. Kaplan, and A. Nelson, Effective Field Theory, Black Hole, and the Cosmological Constant [J]. Phys. Rev. Lett.1999, 82: 4971-4974.
[6] S. Thomas, Holography Stabilizes the Vacuum Energy [J]. Phys. Rev. Lett. 2002, 89: 081301-081305.
[7] S. D. H. Hsu, Entropy Bounds and Dark Energy [J]. Phys. Lett. B, 2004, 594: 13-16.
[8] M. Li, A model of holographic dark energy[J]. Phys. Lett. B, 2004, 603: 1-5.
[9] R. Bousso, The holographic principle[J]. Rev. Mod. Phys. 2002, 74: 825-874.
[10] P. Wang and X. Meng, Class. Quant. Grav. 2005, 283: 22.
[11] Richard Easther and David Lowe, Holography, cosmology, and the Second Law of Thermodynamics Physical Review Letters.1999, 82:25.
[12] R. Horvart, holography and Variable Cosmological Constant, arXiv: astrop-ph/0404204 v4 8 Sep 2004.
[13] Yun Soo Myung, Holographic principle and dark energy, Physics Letter B, 2005, 610: 18-22.
[14] B. Guberina and R. Horvat, Hint for Quintessense-like Scalars from Holographic Dark Energy,arXiv: astro-ph/0503495 v2 4 May 2005.
[15] Edward Witten, When Symmetry breaks down, Nature, 2004, 429: 507.
[16] Raphael Bousso, The holographic principle, arXiv: hep-th/0203101 v229 Jun/2002.
[17] Petra Horava and Djordje Minic, Probable Values of the Cosmological Constant in a Holographic Theory, Physical Review Letters, 2000, 85:8.
[18] Scott Thomas, Holography Stablizea the Vacuum Energy, Physical Review Letters,89: 8.
[19]Saulo Carneiro, Holography and the Cosmic Coinidence, arXiv: gr-qc/0206064-v120 Jun 2002.
[20] Kayll Lake, The Flatness Problem and∧, Physical Review Letters, 2005, 94: 20.
[21] German Olivares, Fernando Atrio-Barandela, Observational constraints on interacting quintessense models, Physical Review D, 2005, 71:6.
[22] Robert R.Caldwell, Marc Kamionkowski, and Nevin N. Weinberg, Phantom Energy: Dark Energy withω<-1 Causes a Cosmic Doomsday, Physical Review Letters, 91: 7.
[23] J. S. Alcaniz and N. Piers, Cosmic acceleration in brane cosmology, 2004, 70: 4.
[24] Gia Dvali and Mchael S. Turner, Dark Energy as a Modification of the Friedmann Equation, arXiv: astro-ph/0301510v1 25 Jan 2003.
[25] J. S. Alcaniz, and J.A.S. Lima, Interpreting cosmological vacuum decay, Physical Review D, 2006, 72: 6.
[26] Alexander A. Andrianov, Francesco Cannata, and Alexander Y. Kamenshchik, Smooth dynamical crossing of the phantom divide of a scalar field in simple cosmological models, 2005, 72: 4.
[27] P. J. E. Peebles, Bharat Ratra, The cosmological constant and dark energy, Review Modern Physics, 75: 2.
[28] T. Banks,W. Fischler, An Holographic Cosmology, arXiv: hep-th0111142v1 15 Nov 2001.
[29] R. R. Caldwell and Eric V.Linder, Limits of Quintessense, Physical Review Letters, 2005, 95: 14.
[30] Raphael Bouss, Flat space physics from holography, arXiv: hep-th/0402058v1 6 Feb 2004.
[31] Gerard’t Hooft, The Holographic Principle, arXiv: hep-th/0003004v216 May 2000.
[32] Kari Enqvist and Martin S. Sloth, Possible Connection between the Location of the Cutoff in the Comic Microwave Background Spectrum and the Equation of State of Dark Energy, Physical Review Letters, 2004, 93: 22.
[33] Marian Douspis, Alian Riazuelo, Zolnierowski, Alain Blanchard, Archeops collaboration, Cosmological constraints in∧-CDM and quintness paradigms with Archeops, New Astronomy Review, 2003, 47: 755-760.
[34] Joan Sola, The Cosmological Constant in Brief, Nuclear B, 2001, 9529-37.
[35] T. Backs, W. Fischler, An Holographic Cosmology, arXiv: hep-th/0111142v1 15 Nov 2001.
[36] R. R. Caldwell and Eric V. Linder, Limts of Quintessense, Physical Review Letters, 2005, 95: 14.
[37] Marian Douspis, Alian Riazuelo, Yves Zolnierowski, Alain blanchard, Archeops collaboration, Cosmological constraints in∧-CDM and quintesssense paradigms with Archeops, New Astronomy Reviews, 2003, 47: 755-760.
[38] J. S. Alcainz, D. Jain and A. Dev, Age, Constraints on brane Models of Dark Energy, arXiv: astro-ph/0206448v2 20 Sep 2002.
[39] Justin Khoury and Ren-Jie Zhang, The Friedmann Equation in Brane-world Scenarios, Physical Review Letters, 89: 6.
[40] E. Elizalde, S. Nojiri, S. D. Odintsov and Peng Wang, Dark energy: Vacuum fluctuations, the effective phantomphase, and holography, Physical Review D, 2005, 71.
[41] John D. Fearns, A Physical Quantum Model in a Smooth Topos, arXiv: quant-ph/0202079v1 14 Feb 2002.
[42] Nima Arkani-Hamed, Savas Dimopoulos, Gia Divali and Nemanja Kaloper, manifold universe, arXiv: hep-ph/9911386v1 17 Nov 1999.
[43] Alexander A. Andrianov, Francesco Cannanta, and Alexander Y. Kamenshchik, Smooth dynamical crossing of the phantom divide line of a scalar field in simple cosmological models, Physical Review D, 2005, 72.
[44] Daniel R. Terno, Entropy, Holographic, and the Second Law, Physical Review Letters, 2004, 93.
[45] Yun Wang and Max Tegmark, New Dark Energy Constrainrts Supernovae, Microwave Background, and Galaxy Clustering, Physical Review Letters, 2004, 92
[47] Saulo Carneiro, Holography and the Cosmic Coincidence, arXiv: gr-qc/0206064-v1 20 Jun 2002.
[47] L. Perivolaropoulos, Constraints on linear negative potentials in quintessense and phantom models from recent supernova data, Physical Review D, 2005, 71.
[48] Lisa Randall, and Raman Sundrum, An Alternative to Compactification, Physical Review Letters, 1999, 83.
[49] John Schwarz, and Nathan Seiberg, String theory, supersymmetry,unification, and all that, Reviews of Modem Physics, 1999, 71.
[50] Lisa Randall, Extra Dimensions and Warped Geometries, Science, 2002, 296.
[51] Ashoke Sen, Developments in superstring Theory, arXiv: hep-ph/9810356v2 16 Oct 1998.
[52] David Langlois, Cosmology with an Extra-dimension, arXiv: astro-ph/0301021v1 2 Jan 2003.
[53] Gia Dvali and Michael S. Tuner, Dark Energy as a Modification of the Friedmann Equation, arXiv: astro-ph/0301510v1 25 Jan 2003.
[54] J. S. Alcaniz, Some Obervational Consequences of Brane World Cosmologies, arXiv: astro-ph/0202492 v2 17 May 2002.
[55] E. I. Guendelman, Conformally invariant braneworld the cosmological constant, Physics Letter B, 2004, 580: 87-92.
[56] M. Doran and Wetterich, Quintessense and the costant, Nuclear Physics B, 2003, 124: 57-62.
[57] Adam G. Riess, Louis-Gregory Strolger, John Tonnry, Stefano Casertano, Henry C. Ferguson, Bahram Mobasher, Peter Challis, Alexei V. Filippenko, Saurabh Jha, Weidong Li, Ryan Chornock, Robert P. Kirshner, Bruno Leibundgut, Mark Dickinson, Mario Livio, Mauro Giavalisco, Charles C. Steidel, Narciso Benitez and Zlatan Tsvetanov, Type Ia Supernova Discoveries at z>1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution, arXiv: astro-ph/0402512v2 31 Mar 2004.