Desingularization of Black Hole Space-Times

Authors

  • Simon Davis Research Foundation of Southern California 8861 Villa La Jolla Drive #13595 La Jolla, CA 92039, USA

DOI:

https://doi.org/10.48165/bpas.2023.42D.1.2%20

Keywords:

Desingularization, Algebraic Singularities, Higher Dimensions, Quantum Consistency

Abstract

 The desingularization of a class of black hole space-times arising as solutions to the  string equations is considered in connection with the consistency of the quantum  theory and the description of nonperturbative states with quantum numbers from the  particle spectrum. The geometry arising in an extreme limit of one of the singular  solutions to the gravitational field equations is demonstrated to be a background of N =  2 string theory. The positivity of the masses in the particle spectrum is proven through  quasilocal integrals near the resolved singularities in these limits of black hole  space-times. 

References

A. Raychaudhuri (1953). Arbitrary Concentrations of Matter and the Schwarzschild Singularity, Phys. Rev. 89,) 417-421.

R. Penrose (1965). Gravitational Collapse and Space-Time Singularities, Phys. Rev. Lett. 14, 57-59. 3. S. W. Hawking (1965). Occurrence of Singularities in Open Universes, Phys. Rev. Lett. 15, 689-690. 4. P. Candelas, G. Horowitz, A. Strominger and E. Witten (1985). Vacuum Configurations for Superstrings, Nucl. Phys. B258, 46-74.

I. Antoniadis, J. Rizos and K. Tamvakis (1994). Singularity-free Cosmological Solutions of the Superstring Effective Action, Nucl. Phys. B415, 487-514.

S. Davis (2003). The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity Theory, Class. Quantum Grav. 20, 2871-2881.

J. Borgman and L. H. Ford (2005). Stochastic Gravity and the Langevin-Raychaudhuri Equation, Int. J. Mod. Phys. A20, 2364-2373.

S. Davis (2015). Quantum Variation about Geodesics, Applied Mathematics and Sciences: An International Journal, 2(1), 1-15.

D. Ludwig (1965). Wave Propagation near a Smooth Caustic, Bull. Amer. Math. Soc. 71, 776-779. 10. H. Hironaka (1964). Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero, I, II, Ann. Math. 79 (2), 109-203; ibid. 79 (2), 205-326.

M. Ba˜ nados, C. Teitelboim and J. Zanelli (1992). The Black Hole in Three-Dimensional Spacetime, Phys. Rev. Lett. 69, 1849.

C. Krishnan and S. Roy (2014). Desingularization of the Miilne Universe, Phys. Lett. B734, 92-95. 13. A. Burinskii (2008). Twistor String Structure of the Kerr-Schild Geometry and Consistency of the Dirac-Kerr System, in: The Problems of Modern Cosmology, Proc. 5th Mathema- tical Physics Meeting, July 2008, ed. P. M. Lavrov, Tomsk State Pedagogical University Press, Moscow, 2009, pp. 129-136.

S. W. Hawking and G. F. R. Ellis (1973). The Large-Scale Structure of Space-Time, Cambridge University Press, Cambridge.

C. Ouyang and Z. Li (2000). Space-like Submanifolds with Parallel Mean Curvature, J. Aust. Math. Soc. Ser. A. 69, 1-7.

S. Capozziello, F. S. N. Lobo and J. P. Mimoso (2014). Energy Conditions in Modified Gravity, Phys. Lett. 730B, 280-283.

R. H. Brandenberger, V. F. Mukhanov and A. Sornborger (1993). A Cosmological Theory without Singularities, Phys. Rev. D48, 1629-1642.

P. H. v. Loewenfeld (2010). Resolution of Curvature Singularities in Black Holes and the Early Universe, Universität München thesis.

M. Sanchez (2009). Boundaries of Space-times: Causal and Conformal Approaches, Talk given at Institute Superior Técnico, Lisbon.

M. S. Volkov and A. Wipf (2000). Black Hole Pair Creation in de Sitter Space: A Complete One-Loop Analysis, Nucl. Phys. B582, 313-362.

H. Ooguri and C. Vafa (1991). Geometry of N = 2 Strings, Nucl. Phys. B361, 469-518. 22. A. Kostelecky and M. Perry (1994). Condensates and Singularities in String Theory, Nucl. Phys. B414, 174-190.

G. W. Gibbons, G. T. Horowitz and P. K. Townsend (1995). Resolution of Dilatonic Higher-Dimensional Black Hole Singularities, Class. Quantum Grav. 12, 297-318. 24. M. Natsuume (2001). The Singularity Problem in String Theory, in Frontiers of Cosmology and Gravitation, Proc. Intl. Workshop at Yukawa Institute of Theoretical Physics, Kyoto, April 25-27, 2001, ed. M. Sakagami, Yukawa Institute Press, Kyoto, 2001, p. 55-69.

C. Duval, Z. Horváth and P. A. Horváthy (1993).Vanishing of the Conformal Anomaly for Strings in a Gravitational Wave, Phys. Lett. B313, 10.

R. Güven (2006). The Conformal Penrose Limit and the Resolution of the pp-Curvature Singularities, Class. Quantum Grav. 23, 295-308.

D. Sadri and M. M. Sheikh-Jabbari (2003). String Theory on Parallelizable PP-Waves, J. High Energy Phys. 306(5), 1-34.

G. Papadopoulos, J. G. Russo and A. A. Tseytlin (2003). Solvable Model of Strings in a Time Dependent Plane Wave Background, Class. Quantum Grav. 20, 969-1016.

K. Narayan (2011). Null Cosmological Singularities and Free Strings: II, J. High Energy Phys. 1101 (145), 1-25.

C. Hull and P. Townsend (1995). Unity of Superstring Dualities, Nucl. Phys. B438, 109-137. 31. R. Dijkgraaf (1998). Instanton Strings and HyperKaehler Geometry, Nucl. Phys. B543, 545-571. 32. S. Davis (2017). The Intersection Forms of Four-Manifolds and Exceptional Group Symmetries, Quantum Phys. Lett. 6, 91-93.

S. Deser, R. Jackiw and G.’t Hooft (1984). Three-Dimensional Einstein Gravity: Dynamics of Flat Space, Ann. Phys. 152, 220-235.

L. Alvarez-Gaumé, G. Moore and C. Vafa (1986). Theta Functions, Modular Invariance and Strings, Commun. Math. Phys. 106, 1-40.

Yu. Manin (1991). Three-Dimensional Hyperbolic Geometry as ∞-Adic Arakelov Geometry, Invent. Math. 104, 223-244.

G. T. Horowitz and A. A. Tseytlin (1994). Extremal Black Holes as Exact String Solutions, Phys. Rev. Lett. 73, 3351-3354.

G. W. Gibbons and K. Maeda (1988). Black Holes and Membranes in Higher-Dimensional Theories with Dilaton Fields, Nucl. Phys. B298, 741-775.

A. Dabholkar (2005). Exact Counting of Black Hole Microsates, Phys. Rev. Lett. 94, 241301:1-4. 39. A. Sen (1995). Extremal Black Holes and Elementary String States, Mod. Phys. Lett. A10, 2081-2094. 40. S. Davis (2010). The Quasilocal Supercharge and Energy of Matter in a Space-Time of Approximately Constant Curvature, Hadr. J. 33, 71-98.

R. Penrose (1982). Quasi-local Mass and Angular Momentum in General Relativity, Proc. Roy. Soc. Lond. A381, 53-63.

C. Vafa (1987). Operator Formulation on Riemann Surfaces, Phys. Lett. B190, 47-54. 43. T. Ortin (1998). Extremality versus Supersymmetry in Stringy Black Holes, Phys. Lett. B422, 93-100. 44. S. Cecotti, L. Girardello and A. Pasquinucci (1991). Singularity Theory and N=2 Supersymmetry, Int. J. Mod. Phys. A6, 3427-3496.

S. Kachru and C. Vafa (1995). Exact Results for N=2 Compactifications of Heterotic Strings, Nucl. Phys. B450, 69-89.

S. Davis (2013). Supersymmetric Fixed Points for Elementary Particle Masses, Balkan Phys. Lett. 21, 1-15.

G. W. Gibbons, C. M. Hull and N. P. Warner (1983). The Stability of Gauged Supergravity, Nucl. Phys. B218, 173-190.

S. Davis (2001). Scalar Field Theory and the Definition of Momentum in Curved Space, Class. Quantum Grav. 18, 3395-3427.

S. Davis (2022). Summation over the Gravitational Instantons and the Temperature of the Cosmic Background Radiation, Int. J. Mod. Phys. A37, 2250022: 1-24.

S. W. Hawking, D, N. Page and C. N. Pope (1980). Quantum Gravitational Bubbles, Nucl. Phys. B170, 283-306.

Published

2023-06-17

How to Cite

Desingularization of Black Hole Space-Times . (2023). Bulletin of Pure and Applied Sciences – Physics, 42(1), 6–34. https://doi.org/10.48165/bpas.2023.42D.1.2