Abstract
We construct composite CFT operators from a large number of fermionic primary fields corresponding to states that are holographically dual to a zero temperature Fermi gas in AdS space. We identify a large N regime in which the fermions behave as free particles. In the hydrodynamic limit the Fermi gas forms a degenerate star with a radius determined by the Fermi level, and a mass and angular momentum that exactly matches the boundary calculations. Next we consider an interacting regime, and calculate the effect of the gravitational back-reaction on the radius and the mass of the star using the Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine the ”Chandrasekhar limit” beyond which the degenerate star (presumably) undergoes gravitational collapse towards a black hole. This is interpreted on the boundary as a high density phase transition from a cold baryonic phase to a hot deconfined phase.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [SPIRES].
J.R. Oppenheimer and G.M. Volkoff, On massive neutron cores, Phys. Rev. 55 (1939) 374 [SPIRES].
S.F. Ross and R.B. Mann, Gravitationally collapsing dust in (2 + 1)-dimensions, Phys. Rev. D 47 (1993) 3319 [hep-th/9208036] [SPIRES].
Y. Peleg and A.R. Steif, Phase transition for gravitationally collapsing dust shells in (2 + 1)-dimensions, Phys. Rev. D 51 (1995) 3992 [gr-qc/9412023] [SPIRES].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Vacua, propagators and holographic probes in AdS/CFT, JHEP 01 (1999) 002 [hep-th/9812007] [SPIRES].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Spherically collapsing matter in AdS, holography and shellons, Nucl. Phys. B 563 (1999) 279 [hep-th/9905227] [SPIRES].
S.B. Giddings and S.F. Ross, D3-brane shells to black branes on the Coulomb branch, Phys. Rev. D 61 (2000) 024036 [hep-th/9907204] [SPIRES].
U.H. Danielsson, E. Keski-Vakkuri and M. Kruczenski, Black hole formation in AdS and thermalization on the boundary, JHEP 02 (2000) 039 [hep-th/9912209] [SPIRES].
V. Balasubramanian, J. de Boer, E. Keski-Vakkuri and S.F. Ross, Supersymmetric conical defects: towards a string theoretic description of black hole formation, Phys. Rev. D 64 (2001) 064011 [hep-th/0011217] [SPIRES].
S.B. Giddings and A. Nudelman, Gravitational collapse and its boundary description in AdS, JHEP 02 (2002) 003 [hep-th/0112099] [SPIRES].
G.L. Alberghi and R. Casadio, On the gravitational collapse in Anti-de Sitter space-time, Phys. Lett. B 571 (2003) 245 [gr-qc/0306002] [SPIRES].
V.E. Hubeny, H. Liu and M. Rangamani, Bulk-cone singularities & signatures of horizon formation in AdS/CFT, JHEP 01 (2007) 009 [hep-th/0610041] [SPIRES].
S. Lin and E. Shuryak, Toward the AdS/CFT gravity dual for high energy collisions. 3. Gravitationally collapsing shell and quasiequilibrium, Phys. Rev. D 78 (2008) 125018 [arXiv:0808.0910] [SPIRES].
P.M. Chesler and L.G. Yaffe, Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma, Phys. Rev. Lett. 102 (2009) 211601 [arXiv:0812.2053] [SPIRES].
S. Bhattacharyya and S. Minwalla, Weak field black hole formation in asymptotically AdS spacetimes, JHEP 09 (2009) 034 [arXiv:0904.0464] [SPIRES].
P.M. Chesler and L.G. Yaffe, Boost invariant flow, black hole formation and far-from-equilibrium dynamics in N = 4 supersymmetric Yang-Mills theory, Phys. Rev. D 82 (2010) 026006 [arXiv:0906.4426] [SPIRES].
S.-S. Lee, A non-Fermi liquid from a charged black hole: a critical Fermi ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [SPIRES].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, arXiv:0903.2477 [SPIRES].
M. Cubrovic, J. Zaanen and K. Schalm, String theory, quantum phase transitions and the emergent Fermi-liquid, Science 325 (2009) 439 [arXiv:0904.1993] [SPIRES].
S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [SPIRES].
S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, arXiv:1008.2828 [SPIRES].
J. de Boer, K. Papadodimas and E. Verlinde, Holographic neutron stars, JHEP 10 (2010) 020 [arXiv:0907.2695] [SPIRES].
R. Jost, The general theory of quantized fields, American Mathematical Society, U.S.A. (1965).
T. Banks, M.R. Douglas, G.T. Horowitz and E.J. Martinec, AdS dynamics from conformal field theory, hep-th/9808016 [SPIRES].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [SPIRES].
E.H. Lieb and W.E. Thirring, Gravitational collapse in quantum mechanics with relativistic kinetic energy, Ann. Phys. 155 (1984) 494 [SPIRES].
E.H. Lieb and H.-T. Yau, The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Comm. Math. Phys. 112 (1987) 147 [SPIRES].
R. Ruffini and S. Bonazzola, Systems of selfgravitating particles in general relativity and the concept of an equation of state, Phys. Rev. 187 (1969) 1767 [SPIRES].
R.H. Boyer and R. Lindquist, A variational principle for a rotating relativistic fluid, Phys. Lett. 20 (1966) 504.
J.B. Hartle and D.H. Sharp, Variational principle for the equilibrium of a relativistic, rotating star, Astrophys. J. 147 (1967) 317.
F.E. Schunck and E.W. Mielke, General relativistic boson stars, Class. Quant. Grav. 20 (2003) R301 [arXiv:0801.0307] [SPIRES].
D.N. Page and K.C. Phillips, Selfgravitating radiation in Anti-de Sitter space, Gen. Rel. Grav. 17 (1985) 1029 [SPIRES].
J.A. Wheeler, Geons, Phys. Rev. 97 (1955) 511 [SPIRES].
S. Shapiro and S. Teukolsky, Black holes, white dwarfs and neutron stars: the physics of compact objects, Wiley, U.S.A. (1983).
C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, Freeman, U.S.A. (1973).
J.M. Heinzle, N. Rohr and C. Uggla, Spherically symmetric relativistic stellar structures, Class. Quant. Grav. 20 (2003) 4567 [gr-qc/0304012] [SPIRES].
P.-H. Chavanis, Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes, arXiv:0707.2292 [SPIRES].
V. Vaganov, Self-gravitating radiation in AdS(d), arXiv:0707.0864 [SPIRES].
J. Hammersley, A critical dimension for the stability of perfect fluid spheres of radiation, Class. Quant. Grav. 25 (2008) 205010 [SPIRES].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
L. Álvarez-Gaumé, C. Gomez and M.A. Vazquez-Mozo, Scaling phenomena in gravity from QCD, Phys. Lett. B 649 (2007) 478 [hep-th/0611312] [SPIRES].
L. Álvarez-Gaumé, C. Gomez, A. Sabio Vera, A. Tavanfar and M.A. Vazquez-Mozo, Critical gravitational collapse: towards a holographic understanding of the Regge region, Nucl. Phys. B 806 (2009) 327 [arXiv:0804.1464] [SPIRES].
L. Álvarez-Gaumé, C. Gomez, A. Sabio Vera, A. Tavanfar and M.A. Vazquez-Mozo, Critical formation of trapped surfaces in the collision of gravitational shock waves, JHEP 02 (2009) 009 [arXiv:0811.3969] [SPIRES].
A. Avgoustidis, R. Jimenez, L. Álvarez-Gaumé and M.A. Vazquez-Mozo, Powering AGNs with super-critical black holes, arXiv:0905.2109 [SPIRES].
J. Novak, Velocity-induced collapses of stable neutron stars, Astron. Astrophys. 376 (2001) 606 [gr-qc/0107045] [SPIRES].
S.C. Noble and M.W. Choptuik, Type II critical phenomena of neutron star collapse, Phys. Rev. D 78 (2008) 064059 [arXiv:0709.3527] [SPIRES].
L.-Y. Hung, D.P. Jatkar and A. Sinha, Non-relativistic metrics from back-reacting fermions, Class. Quant. Grav. 28 (2011) 015013 [arXiv:1006.3762] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1010.5784
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Arsiwalla, X., de Boer, J., Papadodimas, K. et al. Degenerate stars and gravitational collapse in AdS/CFT. J. High Energ. Phys. 2011, 144 (2011). https://doi.org/10.1007/JHEP01(2011)144
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2011)144