Abstract
We extend the ideas introduced in the previous work to a more general space-time. In particular we consider the Kantowski-Sachs space time with space section with topology \(R \times S^2\). In this way we want to study a general space time that we think to be the space time inside the horizon of a black hole. In this case the phase space is four dimensional and we simply apply the quantization procedure suggested by loop quantum gravity and based on an alternative to the Schroedinger representation introduced by H. Halvorson. Through this quantization procedure we show that the inverse of the volume density and the Schwarzschild curvature invariant are upper bounded and so the space time is singularity free. Also in this case we can extend dynamically the space time beyond the classical singularity.
Similar content being viewed by others
References
Ashtekar, A. (2004). Background independent quantum gravity: A status report. Classical and Quantum Gravity 21, R53.
Ashtekar, A. and Bojovald, M. (2005). Black hole evaporation: A paradigm. Classical and Quantum Gravity 22, 3349–3362.
Ashtekar, A., Fairhurst, S., and Willis, J. (2003). Quantum gravity, shadow states, and quantum mechanics. Classical and Quantum Gravity 20, 1031–1062.
Ashtekar, A., Bojowald, M., and Lewandowski, J. (2003). Mathematical structure of loop quantum cosmology. Advancement in Theoretical and Mathematical Physics 7 233–268.
Bojowald, M. (2001a). Inverse scale factor in isotropic quantum geometry. Physical Review D 64, 084018.
Bojowald, M. (2001b). Loop quantum cosmology IV: Discrete time evolution. Classical and Quantum Gravity 18, 1071.
Christodoulakis, T. (2002). Lectures on quantum cosmology. Lecture Notes in Physics 592, 318–350, gr-qc/0109059.
Gambini, R., Lewandowski, J., Marolf, D., and Pullin, J. (1998). On the consistency of the constraint algebra in spin network quantum gravity. International Journal of Modern Physics D 7, 97–109.
Halliwell, J. and Louko, J. (1990). Steeps-descent contours in the path-integral approach to quantum cosmology. III. A general method with applications to anisotropic minisuperspace models. Physical Review D 42, 3997.
Halvorson, H. (2001). Complementary of representations in quantum mechanics, quant-ph/0110102.
Kantowski, R. and Sachs, R. K. (1966). Journal of Mathematical Physics 7, 443.
Leonardo, M. (2004). Disappearance of the black hole singularity in quantum gravity. Physical Review D 70, 124009, gr-qc/0407097.
Luca, B. and Torrence, R. J. (1990). Perfect fluids and Ashtekar variables, with application to Kantowski-Sachs models. Classical and Quantum Gravity 7, 1747–1745.
Rovelli, C. (2002). Partial observables. Phyical Review D 65, 124013, gr-qc/0110035.
Rovelli, C. (2004). Quantum Gravity, Cambridge University Press, Cambridge.
Thiemann, T. (1996). Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity. Physical Letters B 380, 257–264.
Thiemann, T. (1998a). Quantum spin dynamics. Classical and Quantum Gravity 15, 839.
Thiemann, T. (1998b). QSD III: Quantum constraint algebra and physical scalar product in quantum general relativity. Classical and Quantum Gravity 15, 1207–1247.
Thiemann, T. (2001). Introduction to Modern Canonical Quantum General Relativity, gr-qc/0110034.
Thiemann, T. (2003). Lectures on Loop Quantum Gravity, gr-qc/0210094.
Viqar, H. and Oliver, W. (2003). On singularity resolution in quantum gravity, gr-qc/0312094.
Author information
Authors and Affiliations
Additional information
PACS number: 04.60.Pp, 04.70.Dy
Rights and permissions
About this article
Cite this article
Modesto, L. The Kantowski-Sachs Space-Time in Loop Quantum Gravity. Int J Theor Phys 45, 2235–2246 (2006). https://doi.org/10.1007/s10773-006-9188-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9188-y