Abstract
The Eguchi-Hanson-AdS5 family of spacetimes are a class of static, geodesically complete asymptotically locally AdS5 soliton solutions of the vacuum Einstein equations with negative cosmological constant. They have negative mass and are parameterized by an integer p ≥ 3 with a conformal boundary with spatial topology L(p, 1). We investigate mode solutions of the scalar wave equation on this background and show that, similar to AdS5, the geometry admits a normal mode spectrum (i.e. solutions that neither grow or decay in time). In addition, we also discuss other geometric properties of these soliton spacetimes, including the behaviour of causal geodesics and their thermodynamic properties. We also point out a surprising connection with the AdS soliton.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
X. Dong Wang, On the Uniqueness of the ADS Spacetime, Acta Math. Sin. (Engl. Ser.) 21 (2005) 917.
W. Boucher, G.W. Gibbons and G.T. Horowitz, A Uniqueness Theorem for Anti-de Sitter Space-time, Phys. Rev. D 30 (1984) 2447 [INSPIRE].
J. Qing, On the uniqueness of the AdS space-time in higher dimensions, Annales Henri Poincare 5 (2004) 245 [math/0310281] [INSPIRE].
P. Bizon and A. Rostworowski, On weakly turbulent instability of anti-de Sitter space, Phys. Rev. Lett. 107 (2011) 031102 [arXiv:1104.3702] [INSPIRE].
P. Bizoń, M. Maliborski and A. Rostworowski, Resonant Dynamics and the Instability of Anti-de Sitter Spacetime, Phys. Rev. Lett. 115 (2015) 081103 [arXiv:1506.03519] [INSPIRE].
G.J. Galloway, S. Surya and E. Woolgar, A Uniqueness theorem for the AdS soliton, Phys. Rev. Lett. 88 (2002) 101102 [hep-th/0108170] [INSPIRE].
G.J. Galloway, S. Surya and E. Woolgar, On the geometry and mass of static, asymptotically AdS space-times, and the uniqueness of the AdS soliton, Commun. Math. Phys. 241 (2003) 1 [hep-th/0204081] [INSPIRE].
R. Clarkson and R.B. Mann, Soliton solutions to the Einstein equations in five dimensions, Phys. Rev. Lett. 96 (2006) 051104 [hep-th/0508109] [INSPIRE].
R. Clarkson and R.B. Mann, Eguchi-Hanson solitons in odd dimensions, Class. Quant. Grav. 23 (2006) 1507 [hep-th/0508200] [INSPIRE].
D. Dold, Global dynamics of asymptotically locally AdS spacetimes with negative mass, Class. Quant. Grav. 35 (2018) 095012 [arXiv:1711.06700] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
S. Andrews, R.A. Hennigar and H.K. Kunduri, Chemistry and complexity for solitons in AdS5, Class. Quant. Grav. 37 (2020) 204002 [arXiv:1912.07637] [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
G. Holzegel and J. Smulevici, Quasimodes and a lower bound on the uniform energy decay rate for Kerr-AdS spacetimes, Anal. Part. Diff. Eq. 7 (2014) 1057 [arXiv:1303.5944] [INSPIRE].
G. Benomio, The stable trapping phenomenon for black strings and black rings and its obstructions on the decay of linear waves, Anal. Part. Diff. Eq. 14 (2021) 2427 [arXiv:1809.07795] [INSPIRE].
J. Keir, Wave propagation on microstate geometries, Annales Henri Poincare 21 (2019) 705 [arXiv:1609.01733] [INSPIRE].
S. Gunasekaran and H.K. Kunduri, Slow decay of waves in gravitational solitons, Annales Henri Poincare 22 (2021) 821 [arXiv:2007.04283] [INSPIRE].
J. Keir, Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars, Class. Quant. Grav. 33 (2016) 135009 [arXiv:1404.7036] [INSPIRE].
T. Eguchi and A.J. Hanson, Asymptotically Flat Selfdual Solutions to Euclidean Gravity, Phys. Lett. B 74 (1978) 249 [INSPIRE].
G.T. Horowitz and R.C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity, Phys. Rev. D 59 (1998) 026005 [hep-th/9808079] [INSPIRE].
D.N. Page, Phase transitions for gauge theories on tori from the AdS/CFT correspondence, JHEP 09 (2008) 037 [hep-th/0205001] [INSPIRE].
E. Shaghoulian, Modular Invariance of Conformal Field Theory on S1 × S3 and Circle Fibrations, Phys. Rev. Lett. 119 (2017) 131601 [arXiv:1612.05257] [INSPIRE].
H.K. Kunduri and J. Lucietti, The first law of soliton and black hole mechanics in five dimensions, Class. Quant. Grav. 31 (2014) 032001 [arXiv:1310.4810] [INSPIRE].
S. Mbarek and R.B. Mann, Thermodynamic Volume of Cosmological Solitons, Phys. Lett. B 765 (2017) 352 [arXiv:1611.01131] [INSPIRE].
A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quant. Grav. 1 (1984) L39 [INSPIRE].
D. Kubiznak, R.B. Mann and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav. 34 (2017) 063001 [arXiv:1608.06147] [INSPIRE].
S. Gunasekaran, U. Hussain and H.K. Kunduri, Soliton mechanics, Phys. Rev. D 94 (2016) 124029 [arXiv:1609.08500] [INSPIRE].
M. Appels, R. Gregory and D. Kubiznak, Thermodynamics of Accelerating Black Holes, Phys. Rev. Lett. 117 (2016) 131303 [arXiv:1604.08812] [INSPIRE].
A.B. Bordo, F. Gray, R.A. Hennigar and D. Kubizňák, Misner Gravitational Charges and Variable String Strengths, Class. Quant. Grav. 36 (2019) 194001 [arXiv:1905.03785] [INSPIRE].
R. Emparan, C.V. Johnson and R.C. Myers, Surface terms as counterterms in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 104001 [hep-th/9903238] [INSPIRE].
V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
Y. Hikida, Phase Transitions of Large N Orbifold Gauge Theories, JHEP 12 (2006) 042 [hep-th/0610119] [INSPIRE].
E. Shaghoulian, Emergent gravity from Eguchi-Kawai reduction, JHEP 03 (2017) 011 [arXiv:1611.04189] [INSPIRE].
S. Surya, K. Schleich and D.M. Witt, Phase transitions for flat AdS black holes, Phys. Rev. Lett. 86 (2001) 5231 [hep-th/0101134] [INSPIRE].
H.K. Kunduri and J. Lucietti, Notes on non-extremal, charged, rotating black holes in minimal D = 5 gauged supergravity, Nucl. Phys. B 724 (2005) 343 [hep-th/0504158] [INSPIRE].
R.C. Myers, M. Rozali and B. Way, Holographic Quenches in a Confined Phase, J. Phys. A 50 (2017) 494002 [arXiv:1706.02438] [INSPIRE].
T.T. Wu and C.N. Yang, Dirac Monopole Without Strings: Monopole Harmonics, Nucl. Phys. B 107 (1976) 365 [INSPIRE].
N.P. Warner, The Spectra of Operators on CPN, Proc. Roy. Soc. Lond. A 383 (1982) 217 [INSPIRE].
P. Hoxha, R.R. Martinez-Acosta and C.N. Pope, Kaluza-Klein consistency, Killing vectors, and Kahler spaces, Class. Quant. Grav. 17 (2000) 4207 [hep-th/0005172] [INSPIRE].
C.M. Bender and S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill (1978).
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
J.P. Boyd, Chebyshev and Fourier Spectral Methods, Dover Publications (2001).
C. Canuto, M. Hussaini, A. Quarteroni and T. Zang, Spectral Methods: Fundamentals in Single Domains, Scientific Computation, Springer Berlin Heidelberg (2006) [https://doi.org/10.1007/978-3-540-30726-6].
Ó.J.C. Dias, J.E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav. 33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].
K. Murata and J. Soda, Stability of Five-dimensional Myers-Perry Black Holes with Equal Angular Momenta, Prog. Theor. Phys. 120 (2008) 561 [arXiv:0803.1371] [INSPIRE].
T. Ishii, K. Murata, J.E. Santos and B. Way, Superradiant instability of black resonators and geons, JHEP 07 (2020) 206 [arXiv:2005.01201] [INSPIRE].
M. Garbiso, T. Ishii and K. Murata, Resonating AdS soliton, JHEP 08 (2020) 136 [arXiv:2006.12783] [INSPIRE].
N.R. Constable and R.C. Myers, Spin two glueballs, positive energy theorems and the AdS/CFT correspondence, JHEP 10 (1999) 037 [hep-th/9908175] [INSPIRE].
R.C. Myers, Stress tensors and Casimir energies in the AdS/CFT correspondence, Phys. Rev. D 60 (1999) 046002 [hep-th/9903203] [INSPIRE].
A.W.C. Wong and R.B. Mann, Five-Dimensional Eguchi-Hanson Solitons in Einstein-Gauss-Bonnet Gravity, Phys. Rev. D 85 (2012) 046010 [arXiv:1112.2229] [INSPIRE].
C. Corral, G. Giribet and R. Olea, Self-dual gravitational instantons in conformal gravity: Conserved charges and thermodynamics, Phys. Rev. D 104 (2021) 064026 [arXiv:2105.10574] [INSPIRE].
C. Corral, D. Flores-Alfonso, G. Giribet and J. Oliva, Higher-curvature generalization of Eguchi-Hanson spaces, Phys. Rev. D 106 (2022) 084055 [arXiv:2207.04014] [INSPIRE].
M. Cvetic, G.W. Gibbons, D. Kubiznak and C.N. Pope, Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume, Phys. Rev. D 84 (2011) 024037 [arXiv:1012.2888] [INSPIRE].
G.W. Gibbons, M.J. Perry and C.N. Pope, The First law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav. 22 (2005) 1503 [hep-th/0408217] [INSPIRE].
A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav. 17 (2000) L17 [hep-th/9911230] [INSPIRE].
S. Hollands, A. Ishibashi and D. Marolf, Comparison between various notions of conserved charges in asymptotically AdS-spacetimes, Class. Quant. Grav. 22 (2005) 2881 [hep-th/0503045] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.12685
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Durgut, T., Hennigar, R.A., Kunduri, H.K. et al. Phase transitions and stability of Eguchi-Hanson-AdS solitons. J. High Energ. Phys. 2023, 114 (2023). https://doi.org/10.1007/JHEP03(2023)114
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)114