Abstract
We construct the first smooth bubbling geometries using the Weyl formalism. The solutions are obtained from Einstein theory coupled to a two-form gauge field in six dimensions with two compact directions. We classify the charged Weyl solutions in this framework. Smooth solutions consist of a chain of Kaluza-Klein bubbles that can be neutral or wrapped by electromagnetic fluxes, and are free of curvature and conical singularities. We discuss how such topological structures are prevented from gravitational collapse without struts. When embedded in type IIB, the class of solutions describes D1-D5-KKm solutions in the non-BPS regime, and the smooth bubbling solutions have the same conserved charges as a static four-dimensional non-extremal Cvetic-Youm black hole.
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References
K.P. Tod, All Metrics Admitting Supercovariantly Constant Spinors, Phys. Lett. B 121 (1983) 241 [INSPIRE].
W.A. Sabra, General BPS black holes in five-dimensions, Mod. Phys. Lett. A 13 (1998) 239 [hep-th/9708103] [INSPIRE].
I. Bena and N.P. Warner, One ring to rule them all . . . and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Plumbing the Abyss: Black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
I. Bena, S. Giusto, R. Russo, M. Shigemori and N.P. Warner, Habemus Superstratum! A constructive proof of the existence of superstrata, JHEP 05 (2015) 110 [arXiv:1503.01463] [INSPIRE].
P. Heidmann, Four-center bubbled BPS solutions with a Gibbons-Hawking base, JHEP 10 (2017) 009 [arXiv:1703.10095] [INSPIRE].
I. Bena, P. Heidmann and P.F. Ramirez, A systematic construction of microstate geometries with low angular momentum, JHEP 10 (2017) 217 [arXiv:1709.02812] [INSPIRE].
H. Stephani, D. Kramer, M.A.H. MacCallum, C. Hoenselaers and E. Herlt, Exact solutions of Einstein’s field equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (2003) [DOI] [INSPIRE].
W.B. Bonnor, Physical Interpretation of Vacuum Solutions of Einstein’s Equations. Part I. Time-independent Solutions, Gen. Rel. Grav. 24 (1992) 551.
H. Weyl, The theory of gravitation, Annalen Phys. 54 (1917) 117 [INSPIRE].
R. Emparan and H.S. Reall, Generalized Weyl solutions, Phys. Rev. D 65 (2002) 084025 [hep-th/0110258] [INSPIRE].
H. Elvang and G.T. Horowitz, When black holes meet Kaluza-Klein bubbles, Phys. Rev. D 67 (2003) 044015 [hep-th/0210303] [INSPIRE].
E. Witten, Instability of the Kaluza-Klein Vacuum, Nucl. Phys. B 195 (1982) 481 [INSPIRE].
S. Stotyn and R.B. Mann, Magnetic charge can locally stabilize Kaluza-Klein bubbles, Phys. Lett. B 705 (2011) 269 [arXiv:1105.1854] [INSPIRE].
I. Bah and P. Heidmann, Topological Stars, Black holes and Generalized Charged Weyl Solutions, arXiv:2012.13407 [INSPIRE].
M.S. Costa and M.J. Perry, Interacting black holes, Nucl. Phys. B 591 (2000) 469 [hep-th/0008106] [INSPIRE].
I. Bah and P. Heidmann, Bubble Bag End: A Bubbly Resolution of Curvature Singularity, arXiv:2107.13551 [INSPIRE].
W. Israel and K.A. Khan, Collinear Particles and Bondi Dipoles in General Relativity, Nuovo Cim. 33 (1964) 331.
G.W. Gibbons and M.J. Perry, New Gravitational Instantons and Their Interactions, Phys. Rev. D 22 (1980) 313 [INSPIRE].
R. Emparan and H.S. Reall, Black Holes in Higher Dimensions, Living Rev. Rel. 11 (2008) 6 [arXiv:0801.3471] [INSPIRE].
C. Charmousis and R. Gregory, Axisymmetric metrics in arbitrary dimensions, Class. Quant. Grav. 21 (2004) 527 [gr-qc/0306069] [INSPIRE].
A. Papapetrou, Eine rotationssymmetrische losung in der allgemeinen relativitatstheorie, Annals Phys. 12 (1953) 309 [INSPIRE].
T. Regge, General relativity without coordinates, Nuovo Cim. 19 (1961) 558 [INSPIRE].
I. Bah and P. Heidmann, Topological Stars and Black Holes, Phys. Rev. Lett. 126 (2021) 151101 [arXiv:2011.08851] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
D.M. Eardley, Observable effects of a scalar gravitational field in a binary pulsar, Astrophys. J. Lett. 196 (1975) 59.
T. Damour and G. Esposito-Farese, Tensor multiscalar theories of gravitation, Class. Quant. Grav. 9 (1992) 2093 [INSPIRE].
S. Mirshekari and C.M. Will, Compact binary systems in scalar-tensor gravity: Equations of motion to 2.5 post-Newtonian order, Phys. Rev. D 87 (2013) 084070 [arXiv:1301.4680] [INSPIRE].
F.-L. Julié, On the motion of hairy black holes in Einstein-Maxwell-dilaton theories, JCAP 01 (2018) 026 [arXiv:1711.10769] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [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, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].
G.W. Gibbons and S.W. Hawking, Gravitational Multi-Instantons, Phys. Lett. B 78 (1978) 430 [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].
S. Giusto, S.D. Mathur and A. Saxena, Dual geometries for a set of 3-charge microstates, Nucl. Phys. B 701 (2004) 357 [hep-th/0405017] [INSPIRE].
S. Giusto, O. Lunin, S.D. Mathur and D. Turton, D1-D5-P microstates at the cap, JHEP 02 (2013) 050 [arXiv:1211.0306] [INSPIRE].
G.W. Gibbons and M.J. Perry, Quantizing Gravitational Instantons, Nucl. Phys. B 146 (1978) 90 [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].
J.W. York Jr., Black hole thermodynamics and the Euclidean Einstein action, Phys. Rev. D 33 (1986) 2092 [INSPIRE].
A.R. Brown, Decay of hot Kaluza-Klein space, Phys. Rev. D 90 (2014) 104017 [arXiv:1408.5903] [INSPIRE].
U. Miyamoto and H. Kudoh, New stable phase of non-uniform charged black strings, JHEP 12 (2006) 048 [gr-qc/0609046] [INSPIRE].
D.D.K. Chow and G. Compère, Black holes in N = 8 supergravity from SO(4, 4) hidden symmetries, Phys. Rev. D 90 (2014) 025029 [arXiv:1404.2602] [INSPIRE].
I. Bena, S. Giusto, C. Ruef and N.P. Warner, Supergravity Solutions from Floating Branes, JHEP 03 (2010) 047 [arXiv:0910.1860] [INSPIRE].
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Bah, I., Heidmann, P. Smooth bubbling geometries without supersymmetry. J. High Energ. Phys. 2021, 128 (2021). https://doi.org/10.1007/JHEP09(2021)128
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DOI: https://doi.org/10.1007/JHEP09(2021)128