Particle probe analysis of the Kehagias-Sfetsos black hole spacetime of Hořava-Lifshitz gravity is extended to wave probe analysis within the framework of quantum mechanics. The time-like naked singularity that develops when ωM2 < 1/2 is probed with quantum fields obeying Klein-Gordon and Chandrasekhar-Dirac equations. The quantum field probe of the naked singularity has revealed that both the spatial part of the wave and the Hamiltonian operators of Klein-Gordon and Chandrasekhar-Dirac equations are essentially self-adjoint, and thus, the naked singularity in the Kehagias-Sfetsos spacetime becomes quantum mechanically non-singular.
REFERENCES
1.
G. T.
Horowitz
, “Spacetime in string theory
,” New J. Phys.
7
, 201
(2005
).2.
3.
A.
Ashtekar
, “Singularity resolution in loop quantum cosmology: A brief overview
,” J. Phys.: Conf. Ser.
189
, 012003
(2009
).4.
P.
Hořava
, “Membranes at quantum criticality
,” J. High Energy Phys.
2009
(03
), 020
.5.
P.
Hořava
, “Quantum gravity at a Lifshitz point
,” Phys. Rev. D
79
, 084008
(2009
).6.
A.
Wang
, “Hořava gravity at a Lifshitz point: A progress report
,” Int. J. Mod. Phys. D
26
, 1730014
(2017
); e-print arXiv:1701.06087.7.
A.
Kehagias
and K.
Sfetsos
, “The black hole and FRW geometries of non-relativistic gravity
,” Phys. Lett. B
678
, 123
–126
(2009
).8.
M. I.
Park
, “The black hole and cosmological solutions in IR modified Hořava gravity
,” J. High Energy Phys.
2009
(9
), 123
.9.
A.
Hakimov
, B.
Turimov
, A.
Abdujabbarov
, and B.
Ahmedov
, “Quantum interference effects in Hořava-Lifshitz gravity
,” Mod. Phys. Lett. A
25
, 3115
–3127
(2010
).10.
A.
Abdujabbarov
, B.
Ahmedov
, and A.
Hakimov
, “A particle motion around black hole in Hořava-Lifshitz gravity
,” Phys. Rev. D
83
, 044053
(2011
).11.
A. N.
Aliev
and Ç.
Şentürk
, “Slowly rotating black hole solutions to Hořava-Lifshitz gravity
,” Phys. Rev. D
82
, 104016
(2010
).12.
L.
Iorio
and M. L.
Ruggiero
, “Hořava-Lifshitz gravity: Tighter constraints for the Kehagias-Sfetsos solution from new solar system data
,” Int. J. Mod. Phys. D
20
, 1079
–1093
(2011
).13.
V.
Enolskii
, B.
Hartmann
, V.
Kagramanova
, J.
Kunz
, C.
Lammerzahl
, and P.
Sirimachan
, “Particle motion in Hořava-Lifshitz black hole space-times
,” Phys. Rev. D
84
, 084011
(2011
).14.
J.
Chen
and Y.
Wang
, “The timelike geodesic motion in Hořava-Lifshitz space-times
,” Int. J. Mod. Phys. A
25
, 1439
(2010
).15.
B.
Gwak
and B.-H.
Lee
, “Particle probe of Hořava-Lifshitz gravity
,” J. Cosmol. Astropart. Phys.
2010
, 031
.16.
R.
Konoplya
, “Towards constraining of the Hořava-Lifshitz gravities
,” Phys. Lett. B
679
, 499
(2009
).17.
L.
Iorio
and M. L.
Ruggiero
, “Phenomenological constraints on the Kehagias-Sfetsos solution in the Hořava-Lifshitz gravity from solar system orbital motions
,” Int. J. Mod. Phys. A
25
, 5399
–5408
(2010
).18.
M.
Liu
, J.
Lu
, B.
Yu
, and J.
Lu
, “Solar system constraints on asymptotically flat IR modified Hořava gravity through light deflection
,” Gen. Relativ. Gravitation
43
, 1401
–1415
(2011
).19.
Z.
Stuchlik
and J.
Schee
, “Optical effects related to Keplerian discs orbiting Kehagias-Sfetsos naked singularities
,” Classical Quantum Gravity
31
, 195013
(2014
).20.
R. S. S.
Vieira
, J.
Schee
, W.
Kluzniak
, Z.
Stuchlik
, and M.
Abramowicz
, “Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava’s gravity
,” Phys. Rev. D
90
, 024035
(2013
).21.
R. M.
Wald
, “Dynamics in nonglobally hyperbolic, static space-times
,” J. Math. Phys.
21
, 2802
(1980
).22.
G. T.
Horowitz
and D.
Marolf
, “Quantum probes of spacetime singularities
,” Phys. Rev. D
52
, 5670
(1995
).23.
A.
Ishibashi
and A.
Hosoya
, “Who’s afraid of naked singularities? Probing timelike singularities with finite energy waves
,” Phys. Rev. D
60
, 104028
(1999
).24.
T. M.
Helliwell
, D. A.
Konkowski
, and V.
Arndt
, “Quantum singularity in quasiregular spacetime, as indicated by Klein-Gordon, Maxwell and Dirac fields
,” Gen. Relativ. Gravitation
35
, 79
(2003
).25.
J. P. M.
Pitelli
and P. S.
Letelier
, “Quantum singularities in static spacetimes
,” Int. J. Mod. Phys. D
20
, 729
–743
(2011
).26.
H.
Weyl
, “Über gewöhnliche differentialgleichungen mit singularitäten und die zugehörigen entwicklungen willkürlicher funktionen
,” Math. Ann.
68
, 220
–269
(1910
).27.
J.
von Neumann
, “Allgemeine eigenwerttheorie hermitescher funktionaloperatoren
,” Math. Ann.
102
, 49
–131
(1929
).28.
S.
Chandrasekhar
, The Mathematical Theory of Black Holes
(Oxford University Press
, 1992
).29.
O.
Gurtug
and T.
Tahamtan
, “Quantum singularities in a model of f(R) gravity
,” Eur. Phys. J. C
72
, 2091
(2012
).30.
O.
Gurtug
, M.
Halilsoy
, and S.
Habib Mazharimousavi
, “Quantum probes of timelike naked singularities in the weak field regime of f(R) global monopole spacetime
,” J. High Energy Phys.
01
, 178
(2014
).31.
J. P. M.
Pitelli
and A.
Saa
, “Quantum singularities in Hořava-Lifshitz cosmology
,” Phys. Rev. D
86
, 063506
(2012
).32.
T. M.
Helliwell
and D. A.
Konkowski
, “Quantum healing of classical singularities in power law spacetimes
,” Classical Quantum Gravity
24
, 3377
–3390
(2007
).33.
T. M.
Helliwell
and D. A.
Konkowski
, “Quantum singularities in spherically symmetric, conformally static spacetimes
,” Phys. Rev. D
87
, 104041
(2013
).34.
D. A.
Konkowski
and T. M.
Helliwell
, “Understanding singularities—Classical and quantum
,” Int. J. Mod. Phys. A
31
, 1641007
(2016
).35.
M.
Reed
and B.
Simon
, Fourier Analysis and Self-Adjointness
(Academic Press
, New York
, 1972
).© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.
