Revisiting Laws of Black Hole Mechanics and Violation of Null Energy Condition

Abstract

Most of the important and powerful theorems in General Relativity such as singularity theorems and the theorems applied for null horizons depend strongly on the energy conditions. However, the energy conditions on which these theorems are based on, are beginning to look at less secure if one takes into accounts quantum effects which can violate these energy conditions. Even there are classical systems that can violate these energy conditions which would be problematic in validation of those theorems. In this article, we revisit to a class of such important theorems, the laws of black hole mechanics which are meant to be developed on null like killing horizons using null energy condition. Then we show some classical and quantum mechanical systems which violate null energy condition based on which the above theorem stands.

Share and Cite:

Mandal, S. (2019) Revisiting Laws of Black Hole Mechanics and Violation of Null Energy Condition. Journal of High Energy Physics, Gravitation and Cosmology, 5, 82-111. doi: 10.4236/jhepgc.2019.51004.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

References

[1] Visser, M. (1995) Lorentzian Wormholes: From Einstein to Hawking.
[2] Flanagan, E.E and Wald, R.M. (1996) Does Back Reaction Enforce the Averaged Null Energy Condition in Semiclassical Gravity? Physical Review D, 54, 6233.
https://doi.org/10.1103/PhysRevD.54.6233
[3] Barcelo, C. and Visser, M. (2000) Scalar Fields, Energy Conditions and Traversable Wormholes. Classical and Quantum Gravity, 17, 3843.
https://doi.org/10.1088/0264-9381/17/18/318
[4] Hawking, S.W. and Ellis, G.F.R. (1973) The Large Scale Structure of Space-Time. Vol. 1, Cambridge University Press.
[5] Lock, M.P.E. and Fuentes, I. (2017) Dynamical Casimir Effect in Curved Spacetime. New Journal of Physics, 19, 073005.
https://doi.org/10.1088/1367-2630/aa7651
[6] Saharian, A.A. (2001) Scalar Casimir Effect for D-Dimensional Spherically Symmetric Robin Boundaries. Physical Review D, 63, 125007.
https://doi.org/10.1103/PhysRevD.63.125007
[7] Kandrup, H.E. (1992) Violations of the Strong Energy Condition for Interacting Systems of Particles. Physical Review D, 46, 5360.
https://doi.org/10.1103/PhysRevD.46.5360
[8] Xiong, H.H. and Zhu, J.Y. (2007) Violation of Strong Energy Condition in Effective Loop Quantum Cosmology. International Journal of Modern Physics A, 22, 3137- 3146.
https://doi.org/10.1142/S0217751X07036658
[9] Dowker, F. (2013) Black Holes. Imperial College London, MSc Quantum Fields and Fundamental Forces, Lecture Notes.
[10] Gourgoulhon, é. (2018) Geometry and Physics of Black Holes Lecture Notes. Les Houches.
[11] Reall, H. (2014) Part 3 Black Holes. Lecture Notes Given as Part of the Cambridge University Mathematical Tripos.
[12] Adamson, R. Black Holes and Thermodynamics.
[13] Wald, R.M. (1984) General Relativity. Chicago University Press, Chicago.
https://doi.org/10.7208/chicago/9780226870373.001.0001
[14] Kar, S. and Sengupta, S. (2007) The Raychaudhuri Equations: A Brief Review. Pramana, 69, 49-76.
https://doi.org/10.1007/s12043-007-0110-9
[15] Sjøstrøm, Dag-Morten. Bosons and Fermions in Curved Spacetime. Master’s thesis, Institutt for fysikk, 2013.
[16] Myrzakulov, R., Sebastiani, L. and Zerbini, S. (2013) Inhomogeneous Viscous Fluids in a Friedmann-Robertson-Walker (FRW) Universe. Galaxies, 1, 83-95.
https://doi.org/10.3390/galaxies1020083
[17] Sebastiani, L. (2010) Dark Viscous Fluid Coupled with Dark Matter and Future Singularity. The European Physical Journal C, 69, 547-553.
https://doi.org/10.1140/epjc/s10052-010-1398-z
[18] Nojiri, S. and Odintsov, S.D. (2005) Inhomogeneous Equation of State of the Universe: Phantom Era, Future Singularity, and Crossing the Phantom Barrier. Physical Review D: Particles and Fields, 72, Article ID: 023003.
[19] Barceló, C. and Visser, M. (2000) Scalar Fields, Energy Conditions and Traversable Wormholes. Classical and Quantum Gravity, 17, 3843-3864.
https://doi.org/10.1088/0264-9381/17/18/318
[20] Ford, L.H. and Roman, T.A. (2001) Classical Scalar Fields and the Generalized Second Law. Physical Review D, 64, Article ID: 024023.
https://doi.org/10.1103/PhysRevD.64.024023
[21] Weinberg, S. (1972) Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York.
[22] Dubovsky, S., Grégoire, T., Nicolis, A. and Rattazzi, R. (2006) Null Energy Condition and Superluminal Propagation. Journal of High Energy Physics, No. 3, 025.
[23] Buniy, R.V., Hsu, S.D.H. and Murray, B.M. (2006) The Null Energy Condition and Instability. Physical Review D, 74, Article ID: 063518.
[24] Buniy, R.V. and Hsu, S.D.H. (2006) Instabilities and the Null Energy Condition. Physics Letters B, 632, 543-546.
https://doi.org/10.1016/j.physletb.2005.10.075
[25] Elder, B., Joyce, A. and Khoury, J. (2014) From Satisfying to Violating the Null Energy Condition. Physical Review D, 89, Article ID: 044027.
https://doi.org/10.1103/PhysRevD.89.044027
[26] Winitzki, S. (2001) Null Energy Condition Violations in Eternal Inflation. arXiv preprint gr-qc/0111109
[27] Baldi, M., Finelli, F. and Matarrese, S. (2005) Inflation with Violation of the Null Energy Condition. Physical Review D, 72, Article ID: 083504.
https://doi.org/10.1103/PhysRevD.72.083504
[28] Rubakov, V.A. (2014) The Null Energy Condition and Its Violation. Physics-Uspekhi, 57, 128.
https://doi.org/10.3367/UFNe.0184.201402b.0137
[29] Visser, M. (2008) Traversable Wormholes from Surgically Modified Schwarzschild Spacetimes. arXiv preprint arXiv:0809.0927
[30] Visser, M., Kar, S. and Dadhich, N. (2003) Traversable Wormholes with Arbitrarily Small Energy Condition Violations. Physical Review Letters, 90, Article ID: 201102.
https://doi.org/10.1103/PhysRevLett.90.201102
[31] Barcelo, C. and Visser, M. (1999) Traversable Wormholes from Massless Conformally Coupled Scalar Fields. Physics Letters B, 466, 127-134.
https://doi.org/10.1016/S0370-2693(99)01117-X
[32] Kar, S., Dadhich, N. and Visser, M. (2004) Quantifying Energy Condition Violations in Traversable Wormholes. Pramana, 63, 859-864.
https://doi.org/10.1007/BF02705207
[33] Barceló, C. and Visser, M. (2000) Brane Surgery: Energy Conditions, Traversable Wormholes, and Voids. arXiv preprint hep-th/0004022
[34] Ambrus, V.E. (2014) Dirac Fermions on Rotating Space-Times. PhD Thesis, University of Sheffield, Sheffield.
[35] Ambrus, V.E. and Winstanley, E. (2014) Rotating Quantum States. Physics Letters B, 734, 296-301.
https://doi.org/10.1016/j.physletb.2014.05.031
[36] Pfenning, M.J. (1998) Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes. PhD Thesis, Tufts University, Medford.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.