Stephen Hawking gave a formula for the temperature of black holes as given by . Some of the black holes have their spinning velocity from 50% to 99% of the velocity of light. Due to this velocity, the mass of black holes will vary which cause the variation in the temperature of black holes. In the present research article, we have applied the variation of mass with velocity to obtain the rate of change in temperature of the black holes with respect to velocity. We have also calculated their values for super dense stars like black holes existing in XRBs and AGN and concluded that for super dense stars like black holes of lower velocity as well as the velocity comparable to the velocity of light, the rate of change in temperature with respect to velocity is directly proportional to their velocities. This work will help us to find out the variation in temperature of different black holes spinning with different velocity percentage related to light speed and can be used as the references for other research works.
References
[1]
Wald, R.M. (2001) The Thermodynamics of Black Holes. Living Reviews in Relativity, 4, 6. https://doi.org/10.12942/lrr-2001-6
[2]
Mahto, D., Prakash, V., Singh, B.K. and Singh, K.M. (2012) Change in Entropy of Non-Spinning Black Holes w.r.t. the Radius of Event Horizon in XRBs. Astrophysics and Space Science, 343, 153-159. https://doi.org/10.1007/s10509-012-1219-y
[3]
Dabholkar, A. (2005) Black Hole Entropy in String Theory—A Window into the Quantum Structure of Gravity. Current Science, 89, 25.
[4]
Hawking, S.W. (1975) Particle Creation by Black Holes. Communications in Mathematical Physic, 43, 199-220. https://doi.org/10.1007/BF02345020
[5]
Hawking, S.W. (1974) Black Hole Explosions? Nature, 248, 30-31. https://doi.org/10.1038/248030a0
[6]
Hawking, S.W. (1988) A Brief History of Time. Bantam Books, New York.
[7]
Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) The Four Laws of Black Hole Mechanics. Communications in Mathematical Physics, 31, 161-170. https://doi.org/10.1007/BF01645742
[8]
Mehta, R.N., Prasad, U., Kumar, A. and Mahto, D. (2013) Study of Variation of Temperature of Black Holes with Respect to Mass in XRBs. International Journal of Astrophysics and Space Science , 1, 61-63. https://doi.org/10.11648/j.ijass.20130104.18
[9]
Silva, P.R. (2006) A Note on Black Hole Temperature and Entropy. General Relativity and Quantum Cosmology. arXiv.org/pdf/gr-qc/0605051
[10]
Prakash, V., Mahto, D., Kumar, V. and Das, B.K. (2013) Statistical Analysis of Life-Time and Temperature of Black Holes. American Journal of Theoretical and Applied Statistics, 2, 228-232. https://doi.org/10.11648/j.ajtas.20130206.20
[11]
Mahto, D., Jha, B.K., Singh, K.M. and Ram, M. (2015) Study of Temperature of Black Holes in Terms of Chandrasekhar Limit. International Letters of Chemistry, Physics and Astronomy, 40, 43-50. https://doi.org/10.18052/www.scipress.com/ILCPA.40.43
[12]
Zee, A. (2003) Quantum Field Theory in a Nutshell. Princeton University Press, Princeton.
[13]
Dolan, B.P. (2012) Where Is the PdV Term in the First Law of Black-Hole Thermodynamics? 9th Vienna Central European Seminar on Particle Physics and Quantum Field Theory, Vienna, 30 November-2 December 2012, 1-13.
[14]
Reich, E.S. (2013) Spin Rate of Black Holes Pinned Down. Nature, 500, 135. https://doi.org/10.1038/500135a
[15]
Bergmann, P.G. (1969) Introduction to the Theory of Relativity. Prentice-Hall of India, New Delhi.
[16]
Narayan, R. (2005) Black Holes in Astrophysics. New Journal Physics, 7, 1-31. https://doi.org/10.1088/1367-2630/7/1/199
[17]
Mahto, D., Nadeem, M.S., Prasad, U., Kumar, A. and Singh, K.M. (2013) Change in Entropy of Non-Spinning Black Holes w.r.t. the Radius of Event Horizon in AGN. Journal of Modern Physics, 4, 321-326. https://doi.org/10.4236/jmp.2013.43043
[18]
Madejski, G. (2003) Black Holes in Active Galactic Nuclei. SLAC-PUB-9702. https://doi.org/10.2172/812998
[19]
Sargent, W.L.W. (1978) Dynamical Evidence for a Central Mass Concentration in the Galaxy M87. The Astrophysical Journal, 221, 731-744. https://doi.org/10.1086/156077
[20]
Ferrarese, L. and Ford, H. (2005) Super Massive Black Holes in Galactic Nuclei: Past Present & Future Research. Space Science Reviews, 116, 523-624. https://doi.org/10.1007/s11214-005-3947-6
[21]
Blandford, R.D. (1999) Recent Results on Active Galactic Nuclei. Astrophysics and Space Science, 261, 245-252. https://doi.org/10.1023/A:1002093710287
![\"\"](\"Edit_0e9c9c1d-5196-49d1-b5a2-eee0ba70c0f7.bmp\")
. Some of the black holes have their spinning velocity from 50% to 99% of the velocity of light. Due to this velocity, the mass of black holes will vary which cause the variation in the temperature of black holes. In the present research article, we have applied the variation of mass with velocity ![\"\"](\"Edit_2499e5e2-f2a8-48e2-bca8-61edf5d66c56.bmp\")
to obtain the rate of change in temperature of the black holes with respect to velocity. We have also calculated their values for super dense stars like black holes existing in XRBs and AGN and concluded that for super dense stars like black holes of lower velocity as well as the velocity comparable to the velocity of light, the rate of change in temperature with respect to velocity is directly proportional to their velocities. This work will help us to find out the variation in temperature of different black holes spinning with different velocity percentage related to light speed and can be used as the references for other research works.
