Abstract
We present a D-dimensional charged Anti-de-Sitter black hole solutions in f (T) gravity, where f (T) = T + βT 2 and D ≥ 4. These solutions are characterized by flat or cylindrical horizons. The interesting feature of these solutions is the existence of inseparable electric monopole and quadrupole terms in the potential which share related momenta, in contrast with most of the known charged black hole solutions in General Relativity and its extensions. Furthermore, these solutions have curvature singularities which are milder than those of the known charged black hole solutions in General Relativity and Teleparallel Gravity. This feature can be shown by calculating some invariants of curvature and torsion tensors. Furthermore, we calculate the total energy of these black holes using the energy-momentum tensor. Finally, we show that these charged black hole solutions violate the first law of thermodynamics in agreement with previous results.
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References
S. Carlip, Black hole thermodynamics, Int. J. Mod. Phys. D 23 (2014) 1430023 [arXiv:1410.1486] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, gr-qc/9310026 [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
C. Rovelli, Quantum gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K., (2007).
T. Jacobson, Thermodynamics of space-time: the Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004] [INSPIRE].
E.P. Verlinde, On the origin of gravity and the laws of Newton, JHEP 04 (2011) 029 [arXiv:1001.0785] [INSPIRE].
A. Einstein, Einheitliche Feldtheorie von Gravitation und Elektrizität Unified Field Theory of Gravity and Electricity (in German), Pruss. Acad. Sci. (1925) 414.
A. Einstein, Riemanngeometrie mit Aufrechterhaltung des Begriffes des Fern-Parallelismus (in German), Pruss. Acad. Sci. (1928) 217.
A. Einstein, Auf die Riemann-Metrik und den Fern-Parallelismus gegründete einheitliche Feldtheorie (in German), Math. Ann. 102 (1930) 685.
A. Unzicker and T. Case, Translation of Einstein’s attempt of a unified field theory with teleparallelism, physics/0503046 [INSPIRE].
K. Hayashi and T. Shirafuji, New general relativity, Phys. Rev. D 19 (1979) 3524 [Addendum ibid. D 24 (1982) 3312] [INSPIRE].
R. Ferraro and F. Fiorini, Modified teleparallel gravity: inflation without inflaton, Phys. Rev. D 75 (2007) 084031 [gr-qc/0610067] [INSPIRE].
R. Ferraro and F. Fiorini, On Born-Infeld gravity in Weitzenböck spacetime, Phys. Rev. D 78 (2008) 124019 [arXiv:0812.1981] [INSPIRE].
G.R. Bengochea and R. Ferraro, Dark torsion as the cosmic speed-up, Phys. Rev. D 79 (2009) 124019 [arXiv:0812.1205] [INSPIRE].
Y.-F. Cai, S. Capozziello, M. De Laurentis and E.N. Saridakis, f (T) teleparallel gravity and cosmology, Rept. Prog. Phys. 79 (2016) 106901 [arXiv:1511.07586] [INSPIRE].
G.G.L. Nashed, Stationary axisymmetric solutions and their energy contents in teleparallel equivalent of Einstein theory, Astrophys. Space Sci. 330 (2010) 173 [arXiv:1503.01379] [INSPIRE].
R. Aldrovandi, J.G. Pereira and K.H. Vu, Selected topics in teleparallel gravity, Braz. J. Phys. 34 (2004) 1374 [gr-qc/0312008] [INSPIRE].
R. Aldrovandi and J.G. Pereira, Teleparallel gravity: an introduction, Springer, Dordrecht The Netherlands, (2012).
R. Aldrovandi and J.G. Pereira, Teleparallel gravity, http://www.ift.unesp.br/users/jpereira/tele.pdf.
J.W. Maluf, Localization of energy in general relativity, J. Math. Phys. 36 (1995) 4242 [gr-qc/9504010] [INSPIRE].
J.W. Maluf, The teleparallel equivalent of general relativity, Annalen Phys. 525 (2013) 339 [arXiv:1303.3897] [INSPIRE].
K. Bamba, S. Capozziello, S. Nojiri and S.D. Odintsov, Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests, Astrophys. Space Sci. 342 (2012) 155 [arXiv:1205.3421] [INSPIRE].
S. Basilakos, S. Capozziello, M. De Laurentis, A. Paliathanasis and M. Tsamparlis, Noether symmetries and analytical solutions in f (T )-cosmology: a complete study, Phys. Rev. D 88 (2013) 103526 [arXiv:1311.2173] [INSPIRE].
Y.-F. Cai, S.-H. Chen, J.B. Dent, S. Dutta and E.N. Saridakis, Matter bounce cosmology with the f (T) gravity, Class. Quant. Grav. 28 (2011) 215011 [arXiv:1104.4349] [INSPIRE].
R. Ferraro and F. Fiorini, Spherically symmetric static spacetimes in vacuum f (T) gravity, Phys. Rev. D 84 (2011) 083518 [arXiv:1109.4209] [INSPIRE].
G.G.L. Nashed, Vacuum nonsingular black hole solutions in tetrad theory of gravitation, Gen. Rel. Grav. 34 (2002) 1047 [gr-qc/0109033] [INSPIRE].
P.A. Gonzalez, E.N. Saridakis and Y. Vasquez, Circularly symmetric solutions in three-dimensional teleparallel, f (T) and Maxwell-f (T) gravity, JHEP 07 (2012) 053 [arXiv:1110.4024] [INSPIRE].
G.G.L. Nashed and W. El Hanafy, A built-in inflation in the f (T)-cosmology, Eur. Phys. J. C 74 (2014) 3099 [arXiv:1403.0913] [INSPIRE].
M.E. Rodrigues, M.J.S. Houndjo, J. Tossa, D. Momeni and R. Myrzakulov, Charged black holes in generalized teleparallel gravity, JCAP 11 (2013) 024 [arXiv:1306.2280] [INSPIRE].
G.G.L. Nashed, Kerr-Newman solution in modified teleparallel theory of gravity, Int. J. Mod. Phys. D 24 (2014) 1550007 [INSPIRE].
E.L.B. Junior, M.E. Rodrigues and M.J.S. Houndjo, Regular black holes in f (T) gravity through a nonlinear electrodynamics source, JCAP 10 (2015) 060 [arXiv:1503.07857] [INSPIRE].
K. Bamba, G.G.L. Nashed, W. El Hanafy and S.K. Ibraheem, Bounce inflation in f (T) cosmology: a unified inflaton-quintessence field, Phys. Rev. D 94 (2016) 083513 [arXiv:1604.07604] [INSPIRE].
R. Ferraro and F. Fiorini, Cosmological frames for theories with absolute parallelism, Int. J. Mod. Phys. Conf. Ser. 3 (2011) 227 [arXiv:1106.6349] [INSPIRE].
R. Ferraro and F. Fiorini, On Born-Infeld gravity in Weitzenböck spacetime, Phys. Rev. D 78 (2008) 124019 [arXiv:0812.1981] [INSPIRE].
P. Wu and H.W. Yu, Observational constraints on f (T) theory, Phys. Lett. B 693 (2010) 415 [arXiv:1006.0674] [INSPIRE].
A. Awad and G. Nashed, Generalized teleparallel cosmology and initial singularity crossing, JCAP 02 (2017) 046 [arXiv:1701.06899] [INSPIRE].
G. Farrugia, J.L. Said and M.L. Ruggiero, Solar system tests in f(T) gravity, Phys. Rev. D 93 (2016) 104034 [arXiv:1605.07614] [INSPIRE].
C. Bejarano, R. Ferraro and M.J. Guzmán, Kerr geometry in f (T) gravity, Eur. Phys. J. C 75 (2015) 77 [arXiv:1412.0641] [INSPIRE].
G.G.L. Nashed, Vacuum nonsingular black hole in tetrad theory of gravitation, Nuovo Cim. B 117 (2002) 521 [gr-qc/0109017] [INSPIRE].
M. Krššák, Holographic renormalization in teleparallel gravity, Eur. Phys. J. C 77 (2017) 44 [arXiv:1510.06676] [INSPIRE].
M. Krššák and E.N. Saridakis, The covariant formulation of f (T) gravity, Class. Quant. Grav. 33 (2016) 115009 [arXiv:1510.08432] [INSPIRE].
C.G. Boehmer, A. Mussa and N. Tamanini, Existence of relativistic stars in f (T) gravity, Class. Quant. Grav. 28 (2011) 245020 [arXiv:1107.4455] [INSPIRE].
H. Dong, Y.-B. Wang and X.-H. Meng, Extended Birkhoff ’s theorem in the f (T ) gravity, Eur. Phys. J. C 72 (2012) 2002 [arXiv:1203.5890] [INSPIRE].
S. Capozziello, O. Luongo and E.N. Saridakis, Transition redshift in f (T ) cosmology and observational constraints, Phys. Rev. D 91 (2015) 124037 [arXiv:1503.02832] [INSPIRE].
L. Iorio and E.N. Saridakis, Solar system constraints on f (T) gravity, Mon. Not. Roy. Astron. Soc. 427 (2012) 1555 [arXiv:1203.5781] [INSPIRE].
G.G.L. Nashed, Spherically symmetric solutions on a non-trivial frame in f (T ) theories of gravity, Chin. Phys. Lett. 29 (2012) 050402.
K. Bamba, S. Nojiri and S.D. Odintsov, Trace-anomaly driven inflation in f (T ) gravity and in minimal massive bigravity, Phys. Lett. B 731 (2014) 257 [arXiv:1401.7378] [INSPIRE].
Y. Xie and X.-M. Deng, f (T ) gravity: effects on astronomical observation and solar system experiments and upper-bounds, Mon. Not. Roy. Astron. Soc. 433 (2013) 3584 [arXiv:1312.4103] [INSPIRE].
G.G.L. Nashed and W. El Hanafy, Analytic rotating black hole solutions in N -dimensional f (T) gravity, Eur. Phys. J. C 77 (2017) 90 [arXiv:1612.05106] [INSPIRE].
G.G.L. Nashed, Spherically symmetric charged-dS solution in f (T) gravity theories, Phys. Rev. D 88 (2013) 104034 [arXiv:1311.3131] [INSPIRE].
S. Capozziello, P.A. González, E.N. Saridakis and Y. Vásquez, Exact charged black-hole solutions in D-dimensional f (T) gravity: torsion vs curvature analysis, JHEP 02 (2013) 039 [arXiv:1210.1098] [INSPIRE].
G.G.L. Nashed, A special exact spherically symmetric solution in f (T) gravity theories, Gen. Rel. Grav. 45 (2013) 1887 [arXiv:1502.05219] [INSPIRE].
R.B. Mann, Topological black holes: outside looking in, Annals Israel Phys. Soc. 13 (1997) 311 [gr-qc/9709039] [INSPIRE].
J.P.S. Lemos, Cylindrical black hole in general relativity, Phys. Lett. B 353 (1995) 46 [gr-qc/9404041] [INSPIRE].
A.M. Awad, Higher dimensional charged rotating solutions in (A)dS space-times, Class. Quant. Grav. 20 (2003) 2827 [hep-th/0209238] [INSPIRE].
A.M. Awad, Higher dimensional Taub-NUTS and Taub-Bolts in Einstein-Maxwell gravity, Class. Quant. Grav. 23 (2006) 2849 [hep-th/0508235] [INSPIRE].
A.M. Awad and C.V. Johnson, Holographic stress tensors for Kerr-AdS black holes, Phys. Rev. D 61 (2000) 084025 [hep-th/9910040] [INSPIRE].
A.M. Awad and C.V. Johnson, Scale versus conformal invariance in the AdS/CFT correspondence, Phys. Rev. D 62 (2000) 125010 [hep-th/0006037] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
R. Weitzenböck, Invariance theorie, Nordhoff, Groningen The Netherlands, (1923).
S.C. Ulhoa and E.P. Spaniol, On the gravitational energy-momentum vector in f (T ) theories, Int. J. Mod. Phys. D 22 (2013) 1350069 [arXiv:1303.3144] [INSPIRE].
J.W. Maluf, J.F. da Rocha-Neto, T.M.L. Toribio and K.H. Castello-Branco, Energy and angular momentum of the gravitational field in the teleparallel geometry, Phys. Rev. D 65 (2002) 124001 [gr-qc/0204035] [INSPIRE].
F.J. Tipler, Singularities in conformally flat spacetimes, Phys. Lett. A 64 (1977) 8 [INSPIRE].
C. Clarke and A. Krolak, Conditions for the occurence of strong curvature singularities, J. Geom. Phys. 2 (1985) 127.
R.-X. Miao, M. Li and Y.-G. Miao, Violation of the first law of black hole thermodynamics in f (T) gravity, JCAP 11 (2011) 033 [arXiv:1107.0515] [INSPIRE].
M. Akbar and R.-G. Cai, Thermodynamic behavior of Friedmann equations at apparent horizon of FRW universe, Phys. Rev. D 75 (2007) 084003 [hep-th/0609128] [INSPIRE].
A. Awad and A.F. Ali, Minimal length, Friedmann equations and maximum density, JHEP 06 (2014) 093 [arXiv:1404.7825] [INSPIRE].
K. Bamba, S. Capozziello, M. De Laurentis, S. Nojiri and D. Sáez-Gómez, No further gravitational wave modes in F (T) gravity, Phys. Lett. B 727 (2013) 194 [arXiv:1309.2698] [INSPIRE].
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Awad, A., Capozziello, S. & Nashed, G. D-dimensional charged Anti-de-Sitter black holes in f (T) gravity. J. High Energ. Phys. 2017, 136 (2017). https://doi.org/10.1007/JHEP07(2017)136
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DOI: https://doi.org/10.1007/JHEP07(2017)136