Skip to main content
SpringerLink
Log in

Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity

  • Published:
Annales Henri Poincaré Aims and scope Submit manuscript

Abstract

We establish a class of area–angular momentum–charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a \(U(1)^2\) symmetry. A novel feature is the fact that such surfaces can have the non-trivial topologies \(S^1 \times S^2\) and L(p, q). In addition to two angular momenta, they may be characterized by ‘dipole charge’ as well as electric charge. We show that the unique geometries which saturate the inequalities are the horizon geometries corresponding to extreme black hole solutions. Analogous inequalities which also include contributions from a positive cosmological constant are also presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alaee, A., Khuri, M., Kunduri, H.: Relating mass to angular momentum and charge in 5-dimensional minimal supergravity. Ann. Henri Poincaré 18(5), 1703–1753 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Alaee, A., Khuri, M., Kunduri, H.: Existence and uniqueness of near-horizon geometries for 5-dimensional black holes. In preparation (2018)

  3. Breckenridge, J.C., Myers, R.C., Peet, A.W., Vafa, C.: D-branes and spinning black holes. Phys. Lett. B. 391, 93–98 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Bryden, E.T., Khuri, M.A.: The area-angular momentum–charge inequality for black holes with positive cosmological constant. Class. Quantum Gravity 34, 125017 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Chong, Z., Cvetič, M., Lü, H., Pope, C.N.: Non-extremal rotating black holes in five-dimensional gauged supergravity. Phys. Lett. B 644(2), 192–197 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Chruściel, P.T., Costa, J.L., Heusler, M.: Stationary black holes: uniqueness and beyond. Living Rev. Relativ. 15, 7 (2012)

    Article  ADS  MATH  Google Scholar 

  7. Chruściel, P.T., Nguyen, L.: A uniqueness theorem for degenerate Kerr–Newman black holes. Ann. Henri Poincaré 11, 585–609 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. Dain, S.: Geometric inequalities for axially symmetric black holes. Class. Quantum Gravity 29(7), 073001 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Dain, S., Gabach-Clement, M.E.: Geometrical inequalities bounding angular momentum and charges in general relativity. Living Rev. Relativ. to appear arXiv:1710.04457 (2017)

  10. Dain, S., Khuri, M., Weinstein, G., Yamada, S.: Lower bounds for the area of black holes in terms of mass, charge, and angular momentum. Phys. Rev. D 88(2), 024048 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  11. Elvang, H., Emparan, R., Mateos, D., Reall, H.S.: A supersymmetric black ring. Phys. Rev. Lett. 93, 211302 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  12. Emparan, R.: Rotating circular strings, and infinite nonuniqueness of black rings. JHEP 03, 064 (2004)

    Article  ADS  Google Scholar 

  13. Emparan, R., Reall, H.S.: A rotating black ring solution in five dimensions. Phys. Rev. Lett. 88(10), 101101 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  14. Emparan, R., Reall, H.S.: Black holes in higher dimensions. Living Rev. Relativ. 11(6), 0801–3471 (2008)

    MATH  Google Scholar 

  15. Fajman, D., Simon, W.: Area inequalities for stable marginally outer trapped surfaces in Einstein–Maxwell-dilaton theory. Adv. Theor. Math. Phys. 18(3), 687–707 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Gabach-Clement, M.E., Jaramillo, J.L., Reiris, M.: Proof of the area-angular momentum–charge inequality for axisymmetric black holes. Class. Quantum Gravity 30(6), 065017 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Gabach-Clement, M.E., Reiris, M., Simon, W.: The area-angular momentum inequality for black holes in cosmological spacetimes. Class. Quantum Gravity 32(14), 145006 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Galloway, G.J.: Rigidity of marginally trapped surfaces and the topology of black holes. Commun. Anal. Geom. 16(1), 217–229 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  19. Galloway, G.J., Schoen, R.: A generalization of Hawkings black hole topology theorem to higher dimensions. Commun. Math. Phys. 266(2), 571–576 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Gibbons, G.W., Kastor, D., London, L.A.J., Townsend, P.K., Traschen, J.H.: Supersymmetric selfgravitating solitons. Nucl. Phys. B 416, 850–880 (1994)

    Article  ADS  MATH  Google Scholar 

  21. Hollands, S.: Horizon area-angular momentum inequality in higher-dimensional spacetimes. Class. Quantum Gravity 29(6), 065006 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Hollands, S., Ishibashi, A.: All vacuum near horizon geometries in D-dimensions with (D-3) commuting rotational symmetries. Ann. Henri Poincaré 10(8), 1537–1557 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Hollands, S., Ishibashi, A.: Black hole uniqueness theorems in higher dimensional spacetimes. Class. Quantum Gravity 29(16), 163001 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Hollands, S., Ishibashi, A., Wald, R.M.: A higher dimensional stationary rotating black hole must be axisymmetric. Commun. Math. Phys. 271(3), 699–722 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. Hollands, S., Yazadjiev, S.: Uniqueness theorem for 5-dimensional black holes with two axial killing fields. Commun. Math. Phys. 283(3), 749–768 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Khuri, M., Woolgar, E.: Nonexistence of extremal de sitter black rings. Class. Quantum Gravity 34, 22LT01 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kunduri, H.K., Lucietti, J.: A classification of near-horizon geometries of extremal vacuum black holes. J. Math. Phys. 50(8), 082502 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. Kunduri, H.K., Lucietti, J.: Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes. Class. Quantum Gravity 26, 055019 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Kunduri, H.K., Lucietti, J.: Constructing near-horizon geometries in supergravities with hidden symmetry. JHEP 2011(7), 1–31 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Kunduri, H.K., Lucietti, J.: Classification of near-horizon geometries of extremal black holes. Living Rev. Relativ. 16, 8 (2013)

    Article  ADS  MATH  Google Scholar 

  31. Kunduri, H.K., Lucietti, J.: Black hole non-uniqueness via spacetime topology in five dimensions. JHEP 1410, 82 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Kunduri, H.K., Lucietti, J.: Supersymmetric black holes with lens-space topology. Phys. Rev. Lett. 113(21), 211101 (2014)

    Article  ADS  Google Scholar 

  33. Kunduri, H.K., Lucietti, J., Reall, H.S.: Near-horizon symmetries of extremal black holes. Class. Quantum Gravity 24, 4169–4190 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  34. Rácz, I.: A simple proof of the recent generalizations of Hawking’s black hole topology theorem. Class. Quantum Gravity 25(16), 162001 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Reall, H.S.: Higher dimensional black holes and supersymmetry. Phys. Rev. D 68, 024024 (2003). [Erratum: Phys. Rev. D 70, 089902 (2004)]

    Article  ADS  MathSciNet  Google Scholar 

  36. Rogatko, M.: Mass angular momentum and charge inequalities for black holes in Einstein–Maxwell-axion-dilaton gravity. Phys. Rev. D 89, 044020 (2014)

    Article  ADS  Google Scholar 

  37. Schoen, R., Zhou, X.: Convexity of reduced energy and mass angular momentum inequalities. Ann. Henri Poincaré 14(7), 1747–1773 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Strominger, A., Vafa, C.: Microscopic origin of the Bekenstein–Hawking entropy. Phys. Lett. B 379(1), 99–104 (1996)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Tomizawa, S., Nozawa, M.: Supersymmetric black lenses in five dimensions. Phys. Rev. D 94(4), 044037 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  40. Yazadjiev, S.: Area-angular momentum–charge inequality for stable marginally outer trapped surfaces in 4D Einstein–Maxwell-dilaton theory. Phys. Rev. D 87(2), 024016 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  41. Yazadjiev, S.: Horizon area-angular momentum–charge–magnetic flux inequalities in the 5D Einstein–Maxwell-dilaton gravity. Class. Quantum Gravity 30(11), 115010 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    Aghil Alaee

  2. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    Marcus Khuri

  3. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Hari Kunduri

Authors
  1. Aghil Alaee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcus Khuri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hari Kunduri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hari Kunduri.

Additional information

Communicated by Krzysztof Gawȩdzki.

Hari Kunduri: On sabbatical leave from Memorial University of Newfoundland.

A. Alaee acknowledges the support of a NSERC Postdoctoral Fellowship 502873 and PIMS Postdoctoral Fellowship. M. Khuri acknowledges the support of NSF Grants DMS-1308753 and DMS-1708798. H. Kunduri acknowledges the support of NSERC Grant 418537-2012.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alaee, A., Khuri, M. & Kunduri, H. Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity. Ann. Henri Poincaré 20, 481–525 (2019). https://doi.org/10.1007/s00023-018-0749-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00023-018-0749-4

Search

Navigation