Skip to main content
SpringerLink
Log in

Regular Black Holes from Loop Quantum Gravity

  • Chapter
  • First Online:
Regular Black Holes

Part of the book series: Springer Series in Astrophysics and Cosmology ((SSAC))

Abstract

There is rich literature on regular black holes from loop quantum gravity (LQG), where quantum geometry effects resolve the singularity, leading to a quantum extension of the classical space-time. As we will see, the mechanism that resolves the singularity can also trigger conceptually undesirable features that can be subtle and are often uncovered only after a detailed examination. Therefore, the quantization scheme has to be chosen rather astutely. We illustrate the new physics that emerges first in the context of the eternal black hole represented by the Kruskal space-time in classical general relativity, then in dynamical situations involving gravitational collapse, and finally, during the Hawking evaporation process. The emphasis is on novel conceptual features associated with the causal structure, trapping and anti-trapping horizons and boundedness of invariants associated with curvature and matter. This Chapter is not intended to be an exhaustive account of all LQG results on non-singular black holes. Rather, we have selected a few main-stream thrusts to anchor the discussion, and provided references where further details as well as discussions of related developments can be found. In the spirit of this Volume, the goal is to present a bird’s eye view that is accessible to a broad audience.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For the conceptual framework underlying effective equations see, e.g., Section V of [9]. Note that the term ‘effective equations’ has a very different connotation here than in standard quantum field theory. This has caused occasional confusion in the literature. In LQG one does not integrate out ‘high energy modes’; Planck scale effects are retained. In LQC, for example, there are states that remain sharply peaked even in the Planck regime and the effective equations capture the evolution of the peak of the quantum wave function in these states, ignoring the fluctuations.

  2. 2.

    Because the spatial curvature features on the right side of Einstein’s evolution equations, the quantum corrected version of the classical dynamical trajectories (7.3) and (7.4) along which \(\delta _b\) and \(\delta _c\) are to remain constant themselves feature \(\delta _b\) and \(\delta _c\) (see (7.9), (7.10) and (7.11)). Therefore the issue of finding \(\delta _b\) and \(\delta _c\) that are Dirac observables is rather subtle conceptually and quite intricate technically. These subtleties has led to some concerns [31]. This issue is analyzed in detail [35,36,37, 44]. Consistency of the final results directly follows from the effective equations (7.6)–(7.8).

  3. 3.

    This strategy of using time-like 3-manifolds to specify fields and then ‘evolving’ them in space-like directions was proposed and pursued in [39] for the Hamiltonian framework of full LQG. As discussed there, in the full theory one encounters certain non-trivial technical difficulties associated with the fact that SU(1,1) is non-compact. These issues do not arise in the homogeneous context discussed here.

  4. 4.

    In this review, we did not touch on the issue of black hole entropy that arises in LQG by counting microstates of the area operator that are compatible with parameters characterizing a given macroscopic black hole (see. e.g., [139]. The possibility of testing discreteness of area using gravitational waves has drawn considerable attention in the literature. It has been argued that the simplest area spectrum with area eigenvalues given by \(k n\, \ell _\textrm{Pl}^2\) (where n is an integer and k a constant), considered by Bekenstein and Mukhanov [140], could be ruled out using data from a sufficiently large number of compact binary mergers. But in LQG the area spectrum is not equidistant, it crowds exponentially, making the continuum an excellent approximation very quickly. However, for small black holes the area eigenvalues are grouped, exhibiting a band structure, and the separation between bands is \({O}(\ell _\textrm{Pl}^2)\). If this structure were to persist for large rotating black holes, each band would serve as a proxy of the Bekenstein-Mukhanov eigenvalues and gravitational observations would then lead to non-trivial constraints [141]. However, currently there is no evidence that points to the persistence of bands for macroscopic areas.

References

  1. N. Englehardt, G.T. Horowitz, Int. J. Mod. Phys. D 25, 1643002 (2016)

    ADS  Google Scholar 

  2. S.W. Hawking, [erratum: Commun. Math. Phys. 46, 206 (1976)]. https://doi.org/10.1007/BF02345020

  3. S.W. Hawking, M.J. Perry, A. Strominger 116, 231301 (2016)

    Google Scholar 

  4. W.G. Unruh, R.M. Wald, Information loss. Rep. Prog. Phys. 80, 092002 (2017)

    ADS  Google Scholar 

  5. A. Almheiri, D. Marolf, J. Polchinski, D. Stanford, J. Sully, JHEP 09, 018 (2013)

    ADS  Google Scholar 

  6. S. Giddings, Phys. Lett. B 738, 92 (2014)

    ADS  Google Scholar 

  7. D. Marolf, Rep. Prog. Phys. 80, 092001 (2017)

    ADS  Google Scholar 

  8. A. Ashtekar, J. Pullin (eds.), Loop Quantum Gravity: The First 30 Years (World Scientific, Singapore, 2017)

    MATH  Google Scholar 

  9. A. Ashtekar, P. Singh, Class. Quantum Gravity 28, 213001 (2011)

    ADS  Google Scholar 

  10. P. Singh, Class. Quantum Gravity 26, 125005 (2009)

    ADS  Google Scholar 

  11. I. Agullo, P. Singh, in Loop Quantum Gravity: The First 30 Years, ed. by A. Ashtekar, J. Pullin (World Scientific, Singapore, 2017). arXiv: 1612.01236

  12. A. Ashtekar, M. Bojowald, Class. Quantum Gravity 23, 391 (2006)

    ADS  Google Scholar 

  13. L. Modesto, Class. Quantum Gravity 23, 5587 (2006)

    ADS  Google Scholar 

  14. M. Campiglia, R. Gambini, J. Pullin, AIP Conf. Proc. 977, 52–63 (2008)

    Google Scholar 

  15. R. Gambini, J. Pullin, Phys. Rev. Lett. 110, 211301 (2013)

    ADS  Google Scholar 

  16. D. Cartin, G. Khanna, Phys. Rev. D 73, 104009 (2006)

    ADS  MathSciNet  Google Scholar 

  17. C.G. Boehmer, K. Vandersloot, Phys. Rev. D 76, 1004030 (2007)

    Google Scholar 

  18. D.W. Chiou, Phys. Rev. D 78, 064040 (2008)

    ADS  Google Scholar 

  19. A. Corichi, P. Singh, Class. Quantum Gravity 33, 055006 (2016)

    ADS  Google Scholar 

  20. J. Olmedo, S. Saini, P. Singh, Class. Quantum Gravity 34, 225011 (2017)

    ADS  Google Scholar 

  21. J. Cortez, W. Cuervo, H.A. Morales-Técotl, J.C. Ruelas, Phys. Rev. D 95, 064041 (2017)

    ADS  MathSciNet  Google Scholar 

  22. A. Yonika, G. Khanna, P. Singh, Class. Quantum Gravity 35, 045007 (2018)

    ADS  Google Scholar 

  23. A. Joe, P. Singh, Class. Quantum Gravity 32, 015009 (2015)

    ADS  Google Scholar 

  24. D.-W. Chiou, Phys. Rev. D 78, 044019 (2008)

    Google Scholar 

  25. J. Brannlund, S. Kloster, A. DeBenedictis, Phys. Rev. D 79, 084023 (2009)

    ADS  MathSciNet  Google Scholar 

  26. R. Gambini, J. Olmedo, J. Pullin, Class. Quantum Gravity 31, 095009 (2014)

    ADS  Google Scholar 

  27. N. Dadhich, A. Joe, P. Singh, Class. Quantum Gravity 32, 185006 (2015)

    ADS  Google Scholar 

  28. A. Ashtekar, J. Olmedo, P. Singh, Phys. Rev. Lett. 121, 241301 (2018)

    ADS  Google Scholar 

  29. A. Ashtekar, J. Olmedo, P. Singh, Phys. Rev. D 98, 126003 (2018)

    ADS  MathSciNet  Google Scholar 

  30. A. Ashtekar, J. Olmedo, Int. J. Mod. Phys. 29, 2050076 (2020)

    ADS  Google Scholar 

  31. N. Bodendorfer, F.M. Mele, J. Münch, Class. Quantum Gravity 36, 187001 (2019)

    ADS  Google Scholar 

  32. C. Zhang, Y. Ma, S. Song, X. Zhang, Phys. Rev. Phys. Rev. D 105, 024069 (2020)

    ADS  Google Scholar 

  33. R. Gambini, J. Olmedo, J. Pullin, Front. Astron. Space Sci. 8, 74 (2021)

    ADS  Google Scholar 

  34. C. Zhang, Y. Ma, S. Song, X. Zhang, Phys. Rev. D 105, 024069 (2022)

    ADS  Google Scholar 

  35. B.E. Navascués, A. García-Quismondo, G.A. Mena Marugán, Phys. Rev. D 106, 063516 (2022)

    Google Scholar 

  36. A. García-Quismondo, G. A. Mena Marugán, Phys. Rev. D 106, 023532 (2022)

    Google Scholar 

  37. B. E. Navascués, A. García-Quismondo, G. A. Mena Marugán, Phys. Rev. D106, 043531 (2022)

    Google Scholar 

  38. M. Han, H. Liu. arXiv:2212.04605

  39. H. Liu, K. Noui, Class. Quantum Gravity 34, 135008 (2017)

    ADS  Google Scholar 

  40. A. Ashtekar, M. Bojowald, Class. Quantum Gravity 22, 3349 (2005)

    ADS  Google Scholar 

  41. A. Ashtekar, B. Krishnan, Phys. Rev. D 68, 104030 (2003)

    ADS  MathSciNet  Google Scholar 

  42. A. Ashtekar, B. Krishnan, Liv. Rev. (Relativ.) 7(10) (2004)

    Google Scholar 

  43. I. Booth, Can. J. Phys. 83, 1073 (2005)

    ADS  Google Scholar 

  44. G. Ongole, H. Zhang, T. Zhu, A. Wang, B. Wang, Universe 8, 543 (2022)

    ADS  Google Scholar 

  45. A. Ashtekar, T. Pawlowski, P. Singh, Phys. Rev. D 74, 084003 (2006)

    ADS  MathSciNet  Google Scholar 

  46. A. Ashtekar, M. Bojowald, J. Lewandowski, Adv. Theo. Math. Phys. 7, 233–268 (2003)

    Google Scholar 

  47. J. Willis, On the low energy ramifications and a mathematical extension of loop quantum gravity; Ph.D. Dissertation, The Pennsylvaina State University (2004)

    Google Scholar 

  48. V. Taveras, Phys. Rev. D 78, 064072 (2008)

    ADS  MathSciNet  Google Scholar 

  49. G.W. Gibbons, M.J. Perry, Proc. Roy. Soc. Lond. A 358, 467 (1978)

    ADS  Google Scholar 

  50. S.A. Fulling, S.N.M. Ruijsenaars, Phys. Rep. 152, 135 (1987)

    ADS  MathSciNet  Google Scholar 

  51. T. Levi-Civita, Il sottocaso B2: soluzioni oblique, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Nat. Rend. 27, 343 (1918)

    Google Scholar 

  52. W. Kinnersley, M. Walker, Phys. Rev. D 2, 1359 (1970)

    Google Scholar 

  53. A. Ashtekar, T. Dray, Commun. Math. Phys. 79, 581 (1981)

    ADS  Google Scholar 

  54. M. Bouhmadi-López, S. Brahma, C.-Y. Chen, P. Chen, D.-H. Chen, Phys. Dark Univ. 30, 100701 (2020)

    Google Scholar 

  55. A. Ashtekar, A. Magnon, J. Math. Phys. 25, 2682 (1984)

    ADS  MathSciNet  Google Scholar 

  56. R. Schoen, Localizing solutions of the Einstein equations, Lectures at the Institut Henri Poincaré, General Relativity: A Celebration of the 100th Anniversary (2015). https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-richardschoen.pdf

  57. T. Thiemann, Class. Quantum Gravity 12, 181 (2003)

    ADS  MathSciNet  Google Scholar 

  58. M. Bojowald, R. Swiderski, Class. Quantum Gravity 23, 2129 (2006)

    ADS  Google Scholar 

  59. D.-W. Chiou, W.-T. Ni, A. Tang. arXiv:1212.1265

  60. J. Ben Achour, F. Lamy, H. Liu, K. Noui, Euro. Phys. Lett. 123, 20006 (2018)

    Google Scholar 

  61. J.G. Kelly, R. Santacruz, E. Wilson-Ewing, Phys. Rev. D 102, 106024 (2020)

    ADS  MathSciNet  Google Scholar 

  62. J.G. Kelly, R. Santacruz, E. Wilson-Ewing, Class. Quant. Grav. 38, 04LT01 (2021)

    Google Scholar 

  63. R. Gambini, J. Olmedo, J. Pullin, Class. Quantum Gravity 37, 205012 (2020)

    ADS  Google Scholar 

  64. M. Han, H. Liu, Class. Quantum Gravity 39, 035011 (2022)

    ADS  Google Scholar 

  65. V. Husain, J.G. Kelly, R. Santacruz, E. Wilson-Ewing, Phys. Rev. Lett. 128, 121301 (2021)

    ADS  Google Scholar 

  66. C. Zhang, Phys. Rev. D 104, 126003 (2021)

    ADS  Google Scholar 

  67. V. Husain, J.G. Kelly, R. Santacruz, E. Wilson-Ewing, Phys. Rev. D 106, 024014 (2022)

    ADS  Google Scholar 

  68. K. Giesel, M. Han, B. Li, H. Liu, P. Singh, Phys. Rev. D 107, 044047 (2023)

    Google Scholar 

  69. L. Modesto, Int. J. Theor. Phys. 47, 357 (2008)

    Google Scholar 

  70. S. Hossenfelder, L. Modesto, I. Premont-Schwarz, Phys. Rev. D 81, 044036 (2010)

    ADS  Google Scholar 

  71. Y. Tavakoli, J. Marto, A. Dapor, Int. J. Mod. Phys. D 23, 1450061 (2014)

    ADS  Google Scholar 

  72. C. Bambi, D. Malafarina, L. Modesto, Phys. Rev. D 88, 044009 (2013)

    ADS  Google Scholar 

  73. Y. Liu, D. Malafarina, L. Modesto, C. Bambi, Phys. Rev. D 90, 044040 (2014)

    ADS  Google Scholar 

  74. J. Ben Achour, S. Brahma, J.-P. Uzan, JCAP 2003, 041 (2020)

    Google Scholar 

  75. B.F. Li, P. Singh, Universe 7(11), 406 (2021)

    ADS  Google Scholar 

  76. A. Corichi, P. Singh, Phys. Rev. D 78, 024034 (2008)

    ADS  MathSciNet  Google Scholar 

  77. P. Hájíček, Quantum Gravity: Quantum Theory of Gravitational Collapse. Lecture Notes on Quantum Conchology, Springer Berlin Heidelberg, pp. 255–299 (2003)

    Google Scholar 

  78. M. Campiglia, R. Gambini, J. Olmedo, J. Pullin, Class. Quantum Gravity33, LT01 (2016)

    Google Scholar 

  79. J. Ziprick, J. Gegenberg, G. Kunstatter, Phys. Rev. D 94, 104076 (2016)

    ADS  MathSciNet  Google Scholar 

  80. K. Giesel, B.-F. Li, P. Singh, Phys. Rev. D 104, 106017 (2021)

    ADS  Google Scholar 

  81. M. Bojowald, T. Harada, R. Tibrewala, Phys. Rev. D 78, 064057 (2008)

    ADS  MathSciNet  Google Scholar 

  82. M. Bojowald, J.D. Reyes, R. Tibrewala, Phys. Rev. D 80, 084002 (2009)

    ADS  MathSciNet  Google Scholar 

  83. A. Alonso-Bardaji, D. Brizuela, Phys. Rev. D 104, 084064 (2021)

    ADS  Google Scholar 

  84. A. Alonso-Bardaji, D. Brizuela, R. Vera, Phys. Lett. B 829, 137075 (2022)

    Google Scholar 

  85. M.W. Choptuik, Phys. Rev. Lett. 70, 9 (1993)

    ADS  Google Scholar 

  86. V. Husain, O. Winkler, Class. Quantum Gravity 22, L127 (2005)

    ADS  Google Scholar 

  87. V. Husain. arXiv:0808.0949

  88. J. Ziprick, G. Kunstatter, Phys. Rev. D 80, 024032 (2009)

    ADS  Google Scholar 

  89. A. Kreienbuehl, V. Husain, S.S. Seahra, Class. Quantum Gravity 29, 095008 (2012)

    ADS  Google Scholar 

  90. F. Benitez, R. Gambini, L. Lehner, S. Liebling, J. Pullin, Phys. Rev. Lett. 124, 071301 (2020)

    ADS  MathSciNet  Google Scholar 

  91. F. Benitez, R. Gambini, S. Liebling, J. Pullin, Phys. Rev. D 104, 024008 (2021)

    ADS  Google Scholar 

  92. F. Benitez, R. Gambini, J. Pullin, Universe 8, 10 (2022)

    Google Scholar 

  93. C. Barceló, R. Carballo-Rubio, L.J. Garay, Int. J. Mod. Phys. D 23, 1442022 (2014)

    ADS  Google Scholar 

  94. C. Barcelo, R. Carballo-Rubio, L.J. Garay, G. Jannes, Class. Quantum Gravity 32, 035012 (2015)

    ADS  Google Scholar 

  95. C. Barceló, R. Carballo-Rubio, L.J. Garay, JHEP 01, 157 (2016)

    ADS  Google Scholar 

  96. R. Carballo-Rubio, F. Di Filippo, S. Liberati, M. Visser, Class. Quantum Gravity 37, 14 (2020)

    Google Scholar 

  97. K. Giesel, B.F. Li, P. Singh, S.A. Weigl, Phys. Rev. D 105, 066023 (2022)

    ADS  Google Scholar 

  98. S. Hod, T. Piran, Phys. Rev. D 55, 440 (1997)

    ADS  Google Scholar 

  99. T. Thiemann, Class. Quantum Gravity 15, 839 (1998)

    ADS  Google Scholar 

  100. A. Ashtekar, J. Lewandowski, H. Sahlmann, Class. Quantum Gravity 20, L11 (2003)

    ADS  Google Scholar 

  101. M. Bojowald, R. Goswami, R. Maartens, P. Singh, Phys. Rev. Lett. 95, 091302 (2005)

    ADS  MathSciNet  Google Scholar 

  102. K. Vandersloot, Phys. Rev. D 75, 023523 (2007)

    ADS  MathSciNet  Google Scholar 

  103. P. Singh, E. Wilson-Ewing, Class. Quantum Gravity 31, 035010 (2014)

    ADS  Google Scholar 

  104. T. Schmitz, Phys. Rev. D 101, 026016 (2020)

    ADS  MathSciNet  Google Scholar 

  105. R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems (Cambridge University Press, Cambridge, 2002)

    Google Scholar 

  106. C. Vaz, L. Witten, Gen. Rel. Gravity 43, 3429 (2011)

    ADS  Google Scholar 

  107. C. Kiefer, T. Schmitz, Phys. Rev. D 99, 126010 (2019)

    ADS  MathSciNet  Google Scholar 

  108. W. Piechocki, T. Schmitz, Phys. Rev. D 102, 046004 (2020)

    ADS  MathSciNet  Google Scholar 

  109. T. Schmitz, Phys. Rev. D 103, 064074 (2021)

    ADS  Google Scholar 

  110. J. Münch, Class. Quantum Gravity 38, 175015 (2021)

    ADS  Google Scholar 

  111. J. Ben Achour, S. Brahma, S. Mukohyama, J.P. Uzan, JCAP 09, 020 (2020)

    Google Scholar 

  112. S.W. Hawking, Phys. Rev. D 14, 2460 (1976)

    ADS  MathSciNet  Google Scholar 

  113. P. Hajicek, Phys. Rev. D 36, 1066 (1987)

    ADS  Google Scholar 

  114. A. Ashtekar, The issue of information loss: the current status, ILQG seminar of February 23rd (2015). http://relativity.phys.lsu.edu/ilqgs/ashtekar022316.pdf

  115. A. Ashtekar, Universe 6, 21 (2020)

    ADS  Google Scholar 

  116. S. Hayward, arXiv:gr-qc/0504038

  117. S. Hayward, arXiv:gr-qc/0504037

  118. D. Page, Phys. Rev. Lett. 71, 3743–3746 (1993)

    ADS  MathSciNet  Google Scholar 

  119. M. Christodoulou, T. De Lorenzo, Phys. Rev. D 94, 104002 (2016)

    ADS  Google Scholar 

  120. M. Christodoulou, C. Rovelli, Phys. Rev. D 91, 064046 (2015)

    ADS  Google Scholar 

  121. A. Ashtekar, V. Taveras, M. Varadarajan, Phys. Rev. Lett. 100, 211302 (2008)

    ADS  MathSciNet  Google Scholar 

  122. S.A. Hayward, Phys. Rev. Lett. 96, 031103 (2006)

    ADS  Google Scholar 

  123. V.P. Frolov, JHEP 1405, 049 (2014)

    ADS  Google Scholar 

  124. J.M. Bardeen, arXiv:1406.4098

  125. C. Rovelli, F. Vidotto, Int. J. Mod. Phys. D 23, 1442026 (2014)

    Google Scholar 

  126. E. Bianchi, M. Smerlak, Gen. Relativ. Gravit. 46, 1809 (2014)

    ADS  Google Scholar 

  127. E. Bianchi, T. De Lorenzo, M. Smerlak, JHEP 06, 180 (2015)

    ADS  Google Scholar 

  128. H.M. Haggard, C. Rovelli, Phys. Rev. D 92, 104020 (2015)

    ADS  MathSciNet  Google Scholar 

  129. M. Christodoulou, Geometry transition in covariant LQG: black to white. http://relativity.phys.lsu.edu/ilqgs/christodoulou102417.pdf

  130. E. Bianchi, M. Christodoulou, F. D’Ambrosio, H. M Haggard, C. Rovelli, Class. Quantum Grav. 35, 225003 (2018)

    Google Scholar 

  131. P. Martin-Dessuad, C. Rovelli, Class. Quantum Gravity 36, 245002 (2019)

    ADS  Google Scholar 

  132. A. Ori, Personal communication

    Google Scholar 

  133. I. Agullo, A. Ashtekar, W. Nelson, Class. Quantum Gravity 30, 085014 (2013)

    ADS  Google Scholar 

  134. L. Amadei, A. Perez, Phys. Rev. D 106, 063528 (2022)

    ADS  Google Scholar 

  135. P. Diener, B. Gupt, P. Singh, Class. Quantum Gravity 31, 105015 (2014)

    ADS  Google Scholar 

  136. P. Diener, A. Joe, M. Megevand, P. Singh, Class. Quantum Gravity 34, 094004 (2017)

    ADS  Google Scholar 

  137. V. Faraoni, A. Giusti, Symmetry 12, 1264 (2020)

    ADS  Google Scholar 

  138. M. Bojowald, Universe 6, 125 (2020)

    ADS  Google Scholar 

  139. A. Perez, Rept. Prog. Phys. 80, 126901 (2017)

    ADS  Google Scholar 

  140. J.D. Bekenstein, V.F. Mukhanov, Phys. Lett. B 360, 7–12 (1995)

    Google Scholar 

  141. I. Agullo, V. Cardoso, A. del Rio, M. Maggiore, J. Pullin Phys. Rev. Lett. 126, 041302 (2021)

    Google Scholar 

  142. R.G. Daghigh, M.D. Green, G. Kunstatter, Phys. Rev. D 103, 084031 (2021)

    Google Scholar 

  143. D. del-Corral, J. Olmedo, Phys. Rev. D 105, 064053 (2022)

    Google Scholar 

  144. M. Bojowald. arXiv: 1906.04650

  145. G. Olmo, P. Singh, JCAP 0901, 030 (2009)

    ADS  Google Scholar 

  146. R. Dijkgraaf, H. Verlinde, E. Verlinde, Null. Phys. B 371, 269–314 (2002)

    ADS  Google Scholar 

  147. D. Grumiller, JHEP 0211, 018 (2002)

    ADS  Google Scholar 

  148. D. Grumiller, JHEP 0505, 028 (2005)

    ADS  Google Scholar 

  149. A. Ashtekar, F. Pretorius, F. Ramazanoglu, Phys. Rev. D 83, 044040 (2011)

    ADS  Google Scholar 

  150. A. Ori, Gen. Relativ. Gravit. 48, 9 (2016)

    ADS  MathSciNet  Google Scholar 

  151. W.C. Gan, G. Ongole, E. Alesci, Y. An, F.W. Shu, A. Wang, Phys. Rev. D. 106, 126013 (2022)

    ADS  Google Scholar 

  152. M. Assanioussi, A. Dapor, K. Liegener, Phys. Rev. D 101, 026002 (2020)

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the NSF grant PHY-1806356, PHY-1912274 and PHY-2110207, Penn State research funds associated with the Eberly Chair and Atherton professorship, and by Projects PID2020-118159GB-C43, PID2019-105943GB-I00 (with FEDER contribution), by the Spanish Government, and also by the “Operative Program FEDER2014-2020 Junta de Andalucía-Consejería de Economía y Conocimiento” under project E-FQM-262-UGR18 by Universidad de Granada. We would like to thank Eugenio Bianchi, Kristina Giesel, Muxin Han, Bao-Fei Li, Guillermo Mena, Sahil Saini and Ed Wilson-Ewing for discussions, and Tommaso De Lorenzo for Figures 4–6.

Author information

Authors and Affiliations

  1. Physics Department, and, Institute for Gravitation & the Cosmos, Penn State, University Park, PA, 16802, USA

    Abhay Ashtekar

  2. Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, 18071, Spain

    Javier Olmedo

  3. Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, 70803, USA

    Parampreet Singh

Authors
  1. Abhay Ashtekar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Javier Olmedo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Parampreet Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abhay Ashtekar .

Editor information

Editors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ashtekar, A., Olmedo, J., Singh, P. (2023). Regular Black Holes from Loop Quantum Gravity. In: Bambi, C. (eds) Regular Black Holes. Springer Series in Astrophysics and Cosmology. Springer, Singapore. https://doi.org/10.1007/978-981-99-1596-5_7

Download citation

Publish with us

Policies and ethics

Search

Navigation