Abstract
We initiate a systematic study of the state space of non-extremal, stationary black hole bound states in four-dimensional \( \mathcal{N} = {2} \) supergravity. Specifically, we show that an exponential multitude of classically stable “halo” bound states can be formed between large finite temperature D4-D0 black hole cores and much smaller, arbitrarily charged black holes at the same temperature. We map out in full the regions of existence for thermodynamically stable and metastable bound states in terms of the core’s charges and temperature, as well as the region of stability of the core itself. Several features of these systems, such as a macroscopic configurational entropy and exponential relaxation timescales, are similar to those of the extended family of glasses. We draw parallels between the two with a view toward understanding complex systems in fundamental physics.
Similar content being viewed by others
References
H. Weyl, The theory of gravitation, Annalen Phys. 54 (1917) 117 [INSPIRE].
S.D. Majumdar, A class of exact solutions of Einstein’s field equations, Phys. Rev. 72 (1947) 390 [INSPIRE].
A. Papaetrou, A static solution of the equations of the gravitational field for an arbitrary charge distribution, Proc. Roy. Irish Acad. A 51 (1947) 191 [INSPIRE].
J. Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in Gravitation: an introduction to current research, L. Witten ed., Wiley, New York U.S.A. (1962).
W. Israel and K.A. Khan, Collinear particles and Bondi dipoles in general relativity, Nuovo Cim. 33 (1964) 331.
W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D 2 (1970) 1359 [INSPIRE].
W.B. Bonnor, The sources of the vacuum C-metric, Gen. Rel. Grav. 15 (1983) 535.
D. Kastor and J.H. Traschen, Cosmological multi-black hole solutions, Phys. Rev. D 47 (1993) 5370 [hep-th/9212035] [INSPIRE].
K. Behrndt, D. Lu¨st and W.A. Sabra, Stationary solutions of N = 2 supergravity, Nucl. Phys. B 510 (1998) 264 [hep-th/9705169] [INSPIRE].
I.S. Booth and R.B. Mann, Cosmological pair production of charged and rotating black holes, Nucl. Phys. B 539 (1999) 267 [gr-qc/9806056] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R2 interactions, JHEP 12 (2000) 019 [hep-th/0009234] [INSPIRE].
F. Denef, Quantum quivers and Hall/hole halos, JHEP 10 (2002) 023 [hep-th/0206072] [INSPIRE].
B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, hep-th/0304094 [INSPIRE].
H.S. Tan and E. Teo, Multi-black hole solutions in five-dimensions, Phys. Rev. D 68 (2003) 044021 [hep-th/0306044] [INSPIRE].
V. Jejjala, O. Madden, S.F. Ross and G. Titchener, Non-supersymmetric smooth geometries and D1-D5-P bound states, Phys. Rev. D 71 (2005) 124030 [hep-th/0504181] [INSPIRE].
B. Chng, R.B. Mann and C. Stelea, Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions, Phys. Rev. D 74 (2006) 084031 [gr-qc/0608092] [INSPIRE].
J.B. Griffiths, P. Krtous and J. Podolsky, Interpreting the C-metric, Class. Quant. Grav. 23 (2006) 6745 [gr-qc/0609056] [INSPIRE].
H. Ishihara, M. Kimura, K. Matsuno and S. Tomizawa, Kaluza-Klein multi-black holes in five-dimensional Einstein-Maxwell theory, Class. Quant. Grav. 23 (2006) 6919 [hep-th/0605030] [INSPIRE].
S. Giusto, S.F. Ross and A. Saxena, Non-supersymmetric microstates of the D1-D5-KK system, JHEP 12 (2007) 065 [arXiv:0708.3845] [INSPIRE].
S. Giusto and A. Saxena, Stationary axisymmetric solutions of five dimensional gravity, Class. Quant. Grav. 24 (2007) 4269 [arXiv:0705.4484] [INSPIRE].
J. Ford, S. Giusto, A. Peet and A. Saxena, Reduction without reduction: adding KK-monopoles to five dimensional stationary axisymmetric solutions, Class. Quant. Grav. 25 (2008) 075014 [arXiv:0708.3823] [INSPIRE].
H. Elvang and P. Figueras, Black saturn, JHEP 05 (2007) 050 [hep-th/0701035] [INSPIRE].
M. Rogatko, First law of black saturn thermodynamics, Phys. Rev. D 75 (2007) 124015 [arXiv:0705.3697] [INSPIRE].
D. Gaiotto, W. Li and M. Padi, Non-supersymmetric attractor flow in symmetric spaces, JHEP 12 (2007) 093 [arXiv:0710.1638] [INSPIRE].
J. Camps, R. Emparan, P. Figueras, S. Giusto and A. Saxena, Black rings in Taub-NUT and D0-D6 interactions, JHEP 02 (2009) 021 [arXiv:0811.2088] [INSPIRE].
J. Evslin and C. Krishnan, Metastable black saturns, JHEP 09 (2008) 003 [arXiv:0804.4575] [INSPIRE].
B. Chng, R.B. Mann, E. Radu and C. Stelea, Charging black saturn?, JHEP 12 (2008) 009 [arXiv:0809.0154] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Multi-center non-BPS black holes: the solution, JHEP 11 (2009) 032 [arXiv:0908.2121] [INSPIRE].
J.H. Al-Alawi and S.F. Ross, Spectral flow of the non-supersymmetric microstates of the D1-D5-KK system, JHEP 10 (2009) 082 [arXiv:0908.0417] [INSPIRE].
C. Stelea, K. Schleich and D. Witt, Charged Kaluza-Klein double-black holes in five dimensions, Phys. Rev. D 83 (2011) 084037 [arXiv:0909.3835] [INSPIRE].
S. Ferrara, A. Marrani and E. Orazi, Split attractor flow in N = 2 minimally coupled supergravity, Nucl. Phys. B 846 (2011) 512 [arXiv:1010.2280] [INSPIRE].
R. Emparan and P. Figueras, Multi-black rings and the phase diagram of higher-dimensional black holes, JHEP 11 (2010) 022 [arXiv:1008.3243] [INSPIRE].
D. Anninos and T. Anous, A de Sitter hoedown, JHEP 08 (2010) 131 [arXiv:1002.1717] [INSPIRE].
C. Stelea, C. Dariescu and M.-A. Dariescu, Static charged double-black rings in five dimensions, Phys. Rev. D 84 (2011) 044009 [arXiv:1107.3484] [INSPIRE].
I. Bena, B.D. Chowdhury, J. de Boer, S. El-Showk and M. Shigemori, Moulting black holes, arXiv:1108.0411 [INSPIRE].
C. Stelea, K. Schleich and D. Witt, Non-extremal multi-Kaluza-Klein black holes in five dimensions, arXiv:1108.5145 [INSPIRE].
E. Andriyash, F. Denef, D.L. Jafferis and G.W. Moore, Wall-crossing from supersymmetric galaxies, arXiv:1008.0030 [INSPIRE].
A. Adams and S. Yaida, Disordered holographic systems I: functional renormalization, arXiv:1102.2892 [INSPIRE].
S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].
J. Kurchan, Glasses, in Séminaire Poincaré XIII. Verres & Grains, Paris France (2009).
M. Mezard, G. Parisi and M.A. Virasoro, Lecture Notes in Physics. Volume 9: Spin glass theory and beyond, World Scientific (1987) [ISBN 9971501155].
A. Amir, Y. Oreg and Y. Imry, Electron glass dynamics, Annu. Rev. Cond. Mat. Phys. 2 (2011) 235 [arXiv:1010.5767].
A. Amir, Localization, anomalous diffusion and slow relaxations in disordered systems, http://online.kitp.ucsb.edu/online/electroglass10/amir/.
X. Du, G. Li, E.Y. Andrei, M. Greenblatt and P. Shuk, Ageing memory and glassiness of a driven vortex system, Nat. Phys. 3 (2007) 111.
http://en.wikipedia.org/wiki/Ice cream. Using liquid nitrogen.
P.W. Anderson, Through the glass lightly, Science 267 (1995) 1615.
D. Kennedy and C. Norman, What don’t we know?, Science 309 (2005) 5731.
F. Denef, TASI lectures on complex structures, arXiv:1104.0254 [INSPIRE].
D. Anninos, Classical and quantum symmetries of de Sitter space, Ph.D. Thesis, Harvard University, Cambridge U.S.A. (2011).
J. Gomis, F. Marchesano and D. Mateos, An open string landscape, JHEP 11 (2005) 021 [hep-th/0506179] [INSPIRE].
F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, hep-th/0702146 [INSPIRE].
P. Kraus and F. Wilczek, Selfinteraction correction to black hole radiance, Nucl. Phys. B 433 (1995) 403 [gr-qc/9408003] [INSPIRE].
P. Kraus and F. Wilczek, Effect of selfinteraction on charged black hole radiance, Nucl. Phys. B 437 (1995) 231 [hep-th/9411219] [INSPIRE].
E. Keski-Vakkuri and P. Kraus, Microcanonical D-branes and back reaction, Nucl. Phys. B 491 (1997) 249 [hep-th/9610045] [INSPIRE].
M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 (2000) 5042 [hep-th/9907001] [INSPIRE].
B. Vercnocke, Hidden structures of black holes, arXiv:1011.6384 [INSPIRE].
J. Barandes, Special geometry and black holes, to appear.
P. Galli, T. Ortín, J. Perz and C.S. Shahbazi, Non-extremal black holes of N = 2, D = 4 supergravity, JHEP 07 (2011) 041 [arXiv:1105.3311] [INSPIRE].
B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [INSPIRE].
L. Andrianopoli et al., N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: symplectic covariance, gaugings and the momentum map, J. Geom. Phys. 23 (1997) 111 [hep-th/9605032] [INSPIRE].
M. Billó et al., The 0-brane action in a general D = 4 supergravity background, Class. Quant. Grav. 16 (1999) 2335 [hep-th/9902100] [INSPIRE].
G.W. Gibbons, Antigravitating black hole solitons with scalar hair in N = 4 supergravity, Nucl. Phys. B 207 (1982) 337 [INSPIRE].
A. Ceresole and G. Dall’Agata, Flow equations for non-BPS extremal black holes, JHEP 03 (2007) 110 [hep-th/0702088] [INSPIRE].
J. Perz, P. Smyth, T. Van Riet and B. Vercnocke, First-order flow equations for extremal and non-extremal black holes, JHEP 03 (2009) 150 [arXiv:0810.1528] [INSPIRE].
S. Ferrara, A. Gnecchi and A. Marrani, D = 4 attractors, effective horizon radius and fake supergravity, Phys. Rev. D 78 (2008) 065003 [arXiv:0806.3196] [INSPIRE].
E.G. Gimon, F. Larsen and J. Simon, Constituent model of extremal non-BPS black holes, JHEP 07 (2009) 052 [arXiv:0903.0719] [INSPIRE].
S. Ferrara, G.W. Gibbons and R. Kallosh, Black holes and critical points in moduli space, Nucl. Phys. B 500 (1997) 75 [hep-th/9702103] [INSPIRE].
D.I. Olive, Classical solutions in gauge theories — spherically symmetric monopoles — Lax pairs and Toda lattices, in Proceedings of the International Summer Institute on Theoretical Physics. Current Topics in Elementary Particle Physics, Bad Honnef Germany, 1–12 Sept 1980, pg. 199–217 [INSPIRE].
P. Davies, Thermodynamics of black holes, Proc. Roy. Soc. Lond. A 353 (1977) 499 [INSPIRE].
M. Shmakova, Calabi-Yau black holes, Phys. Rev. D 56 (1997) 540 [hep-th/9612076] [INSPIRE].
J. de Boer, F. Denef, S. El-Showk, I. Messamah and D. Van den Bleeken, Black hole bound states in AdS 3 × S2 , JHEP 11 (2008) 050 [arXiv:0802.2257] [INSPIRE].
D.J. Thouless, P.W. Anderson and R.G. Palmer, Solution of ‘Solvable model of a spin glass’, Phil. Mag. 35 (1977) 593.
A.J. Bray and M.A. Moore, Metastable states in spin glasses, J. Phys. C 13 (1980) L469.
R. Monasson, Structural glass transition and the entropy of the metastable states, Phys. Rev. Lett. 75 (1995) 2847 [cond-mat/9503166] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].
P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, The foaming three-charge black hole, Phys. Rev. D 75 (2007) 124026 [hep-th/0604110] [INSPIRE].
V. Balasubramanian, E.G. Gimon and T.S. Levi, Four dimensional black hole microstates: from D-branes to spacetime foam, JHEP 01 (2008) 056 [hep-th/0606118] [INSPIRE].
A. Saxena, G. Potvin, S. Giusto and A.W. Peet, Smooth geometries with four charges in four dimensions, JHEP 04 (2006) 010 [hep-th/0509214] [INSPIRE].
M.C. Cheng, More bubbling solutions, JHEP 03 (2007) 070 [hep-th/0611156] [INSPIRE].
S. Hawking, Black holes and thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
D.J. Gross, M.J. Perry and L.G. Yaffe, Instability of flat space at finite temperature, Phys. Rev. D 25 (1982) 330 [INSPIRE].
D.N. Page, Black hole formation in a box, Gen. Rel. Grav. 13 (1981) 1117 [INSPIRE].
S. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
S. Carlip and S. Vaidya, Phase transitions and critical behavior for charged black holes, Class. Quant. Grav. 20 (2003) 3827 [gr-qc/0306054] [INSPIRE].
I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Wilsonian approach to fluid/gravity duality, JHEP 03 (2011) 141 [arXiv:1006.1902] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Metastable supertubes and non-extremal black hole microstates, arXiv:1109.5180 [INSPIRE].
B.D. Chowdhury and B. Vercnocke, New instability of non-extremal black holes: spitting out supertubes, arXiv:1110.5641 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1108.5821
Rights and permissions
About this article
Cite this article
Anninos, D., Anous, T., Barandes, J. et al. Hot halos and galactic glasses (carbonado). J. High Energ. Phys. 2012, 3 (2012). https://doi.org/10.1007/JHEP01(2012)003
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2012)003