Bounding the Greybody Factor, Temperature and Entropy of Black Holes in dRGT Massive Gravity
American Journal of Physics and Applications
Volume 4, Issue 2, March 2016, Pages: 64-70
Received: Apr. 8, 2016;
Published: Apr. 9, 2016
Views 3541 Downloads 125
Tritos Ngampitipan, Faculty of Science, Chandrakasem Rajabhat University, Bangkok, Thailand
Petarpa Boonserm, Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
Pitayuth Wongjun, The institute for Fundamental Study, Naresuan University, Phitsanulok, Thailand
A black hole greybody factor is the quantum quantity of a black hole. It is the fraction of Hawking radiation that can reach spatial infinity. The greybody factor may contain the necessary information to support the theory of quantum gravity. An understanding of the greybody factor helps us gain insight, not only into the nature of the black hole itself, but also into the theory of quantum gravity, which is currently being developed via numerous attempts. In this paper, we calculate the bound on the greybody factor for scalar field emitted from black holes in dRGT massive gravity. The bound on the reflection probability is also determined. Moreover, the effects of massive gravity on the greybody factors are explored. The results show that the bound on the greybody factor for the dRGT black holes is less than the bound for the Schwarzschild-de-Sitter black hole. The Hawking temperature is also calculated, both in the dRGT case and in the Schwarzschild-de-Sitter case. It is found that the Hawking temperature of the dRGT black hole is higher than that of the Schwarzschild-de-Sitter black hole. The increase in the Hawking temperature probably results from the mass of graviton. Finally, the black hole entropy is also determined. We found that the entropy of the Schwarzschild-de-Sitter black hole is more than the entropy of the dRGT black hole.
Bounding the Greybody Factor, Temperature and Entropy of Black Holes in dRGT Massive Gravity, American Journal of Physics and Applications.
Vol. 4, No. 2,
2016, pp. 64-70.
S. W. Hawking, “Particle creation by black holes”, Commun. Math. Phys. 43, 199 (1975).
S. Fernando, “Greybody factors of charged dilaton black holes in 2 + 1 dimensions”, Gen. Relativ. Gravit. 37, 461-481 (2005).
W. Kim and J. J. Oh, “Greybody Factor and Hawking Radiation of Charged Dilatonic Black Holes”, JKPS 52, 986 - 991 (2008).
J. Escobedo, “Greybody Factors Hawking Radiation in Disguise”, Master’s Thesis, University of Amsterdam (2008). 6
M. K. Parikh and F. Wilczek, “Hawking Radiation as Tunneling”, Phys. Rev. Lett. 85, 5042-5045 (2000) [arXiv: hep-th/9907001].
C. H. Fleming, “Hawking Radiation as Tunneling”, (2005) http://www.physics.umd.edu/grt/taj/776b/fleming. pdf.
P. Lange, “Calculation of Hawking Radiation as Quantum Mechanical Tunneling”, Thesis, Uppsala Universitet (2007).
M. Visser, “Some general bounds for 1-D scattering”, Phys. Rev. A 59, 427438 (1999) [arXiv: quant-ph/9901030].
P. Boonserm and M. Visser, “Bounding the Bogoliubov coefficients”, Annals Phys. 323, 2779 - 2798 (2008) [arXiv: 0801.0610 [quant-ph]].
P. Boonserm, “Rigorous Bounds on Transmission, Reflection, and Bogoliubov Coefficients”, Ph. D. Thesis, Victoria University of Wellington (2009) [arXiv: 0907.0045 [mathph]].
S. G. Ghosh, L. Tannukij, and P. Wongjun, “A class of black holes in dRGT massive gravity and their thermodynamical properties”, [arXiv: 1506.07119 [gr-qc]].
C. de Rham, G. Gabadadze, “Generalization of the Fierz-Pauli action”, Phys. Rev. D 82, 044020 (2010) [arXiv: 1007.0443 [hep-th]].
C. de Rham, G. Gabadadze, and A. J. Tolley, “Resummation of Massive Gravity”, Phys. Rev. Lett. 106, 231101 (2011) [arXiv: 1011.1232 [hep-th]].
M. S. Volkov, “Self-accelerating cosmologies and hairy black holes in ghost-free bigravity and massive gravity”, Class. Quant. Grav. 30, 184009 (2013) [arXiv: 1304.0238 [hep-th]].
G. Tasinato, K. Koyama, and G. Niz, “Exact solutions in massive gravity”, Class. Quant. Grav. 30, 184002 (2013) [arXiv: 1304.0601 [hep-th]].
P. Boonserm and M. Visser, “Bounding the greybody factors for Schwarzchild black holes”, Phys. Rev. D 78, 101502 (2008) [arXiv: 0806.2209 [gr-qc]].
T. Ngampitipan and P. Boonserm, “Bounding the greybody factors for non-rotating black holes”, Int. J. Mod. Phys. D 22, 1350058 (2013) [arXiv: 1211.4070 [math-ph]].
P. Boonserm, T. Ngampitipan and M. Visser, “Regge-Wheeler equation, linear stability and greybody factors for dirty black holes”, Phys. Rev. D 88, 041502 (2013) [arXiv: 1305.1416 [gr-qc]].
P. Boonserm, T. Ngampitipan, and M. Visser, “Bounding the greybody factors for scalar field excitations of the Kerr-Newman spacetime”, J. High Energy Phys. 113 (2014) [arXiv: 1401.0568 [gr-qc]].
P. Boonserm, A. Chatrabhuti, T. Ngampitipan, and M. Visser, “Greybody factors for Myers–Perry black holes”, J. Math. Phys. 55, 112502 (2014) [arXiv: 1405.5678[gr-qc]].
P. Kanti, “Black holes in theories with large extra dimensions: a review” Int. J. Mod. Phys. A 19, 4899 (2004) [arXiv: hep-ph/0402168].
M. Cavaglia, “Black hole and brane production in TeV gravity: A review”, Int. J. Mod. Phys. A 18, 1843 (2003) [arXiv: hep-ph/0210296].
G. Landsberg, “Black holes at future colliders and in cosmic rays”, Eur. Phys. J. C 33, 927 (2004) [arXiv: hep-ex/0310034].
K. Cheung, “Collider phenomenology for a few models of extra dimensions”, [arXiv: hep-ph/0409028].
S. Hossenfelder, “What black holes can teach us”, Focus on Black Hole Research 155, (2005) [arXiv: hep-ph/0412265].
C. M. Harris, “Physics beyond the standard model: Exotic leptons and black holes at future colliders”, Ph. D. Thesis, University of Cambridge (2003) [arXiv: hep-ph/0502005].
A. S. Majumdar and N. Mukherjee, “Braneworld black holes in cosmology and astrophysics”, Int. J. Mod. Phys. D 14, 1095 (2005) [arXiv: astro-ph/0503473].
J. Man and H. Cheng, “The greybody factor for scalar fields in the Schwarzschild spacetime with an f(R) global monopole”, [arXiv: 1402.4215 [hep-th]].
P. Kanti and J. M. Russell, “Calculable corrections to brane black hole decay. II. Greybody factors for spin 1/2 and 1”, Phys. Rev. D 67, 104019 (2003) [arXiv: hep-ph/0212199].
O. Efthimiou, “Graviton emission from a Schwarzschild black hole in the presence of extra dimensions”, J. Phys: Conf. Ser. 68, 012024 (2007) [arXiv: hep-th/0609144].
J. V. Rocha, “Evaporation of large black holes in AdS: greybody factor and decay rate”, J. High Energy Phys. 08, 027 (2009) [arXiv: 0905.4373 [hep-th]].
S. G. Ghosh and S. D. Maharaj, “A class of black holes in dRGT massive gravity and their thermodynamical properties” Phys. Rev. D 89, no. 8, 084027 (2014) [arXiv: 1506.07119 [gr-qc]].
S. Caroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley 2004.