Change in Energy of Non-Spinning Black Holes w.r.t. the Change in Mass

Affiliation(s)

Department of Physics, Marwari College, T. M. B. U., Bhagalpur, India.

University Department of Mathematics, T. M. B. U., Bhagalpur, India.

Department of Mathematics, N. D. A., Khadakwasala, Pune, India.

Department of Physics, S. S. V. College, Kahalgaon, T. M. B. U., Bhagalpur, India.

Department of Physics, Marwari College, T. M. B. U., Bhagalpur, India.

University Department of Mathematics, T. M. B. U., Bhagalpur, India.

Department of Mathematics, N. D. A., Khadakwasala, Pune, India.

Department of Physics, S. S. V. College, Kahalgaon, T. M. B. U., Bhagalpur, India.

ABSTRACT

The present work discusses the derivation of the formula for the change in energy of non-spinning black holes with respect to the change in mass (d*E*/d*M*), which gives a constant quantity equal to 8.9998 x 10^{16 }Joule/kg in both categories of X-ray binaries (XRBs) and Active Galactic Nuclei (AGN). This formula can be used to justify the life time of black hole given by Γ = 2.098(*M*/*M*_{ο})^{3 }x 10^{67 }years as proposed by Stephen Hawking, where *M* and *M*_{ο} are the mass of the black hole and the sun respectively. The authors also calculate the change in energy and mass of non-spinning black holes with respect to the change in the radius of event horizon as well as (d*E*/d*M*) for different test non-spinning black holes in X-ray binaries (XRBs) and Active Galactic Nuclei (AGN).

Cite this paper

D. Mahto, R. Mehta, N. Pant and R. Sah, "Change in Energy of Non-Spinning Black Holes w.r.t. the Change in Mass,"*International Journal of Astronomy and Astrophysics*, Vol. 3 No. 1, 2013, pp. 49-56. doi: 10.4236/ijaa.2013.31006.

D. Mahto, R. Mehta, N. Pant and R. Sah, "Change in Energy of Non-Spinning Black Holes w.r.t. the Change in Mass,"

References

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[2] R. M. Wald, “The Thermodynamics of Black Holes. Living Reviews in Relativity,” 2001.

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[6] D. Mahto, K. Kumari, R. K. Sah and V. Prakash, “Study of Schwarzschild’s Radius with Reference to the Spinning Black Holes,” Bulletin of Pure and Applied Sciences, Vol. 30D, No. 1, 2011, pp. 157-162.

[7] D. Mahto, K. Kumari, R. K. Sah and K. M. Singh, “Study of Non-Spinning Black Holes with Reference to the Change in Energy and Entropy,” Astrophysics and Space Science, Vol. 337, No. 2, 2011, pp. 685-691. doi:10.1007/s10509-011-0883-7

[8] A. Dabholkar, “Black Hole Entropy in String Theory. A Window in to the Quantum Structure of Gravity,” Current Science, Vol. 89, No. 12, 2005, p. 25.

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[10] J. D. Bekenstein, “Bekenstein-Hawking Entropy,” Scholarpedia, Vol. 3 No. 10, 2008, p. 7375

[11] D. Mahto, V. Prakash, B. K. Singh and K. M. Singh, “Change in Entropy of Non-Spinning Black Holes w.r.t. the Radius of Event Horizon in XRBs,” Astrophysics and Space Science, Vol. 343, No. 1, 2013, pp. 153-159. doi:10.1007/s10509-012-1219-y

[12] J. Transchen, “An Introduction to Black Hole Evaporation,” 2000.

[1] R. Narayan, “Black Holes in Astrophysics,” New Journal of Physics, Vol. 7, No. 1, 2005, pp. 1-31.

[2] R. M. Wald, “The Thermodynamics of Black Holes. Living Reviews in Relativity,” 2001.

[3] S. W. Hawking, “A Black Hole Explosion?” Nature, Vol. 248, 1974, pp. 30-31. http://www.nature. com/nature/journal/v248/n5443/abs/248030a0.html

[4] C. Rose, “A Conversation with Dr. Stephen Hawking and Lucy Hawking.” http://www.charlie rose.com/guest/view/6294

[5] K. Kumari, D. Mahto, G. Chandra, R. K. Sah and K. M. Singh, “Study of Schwarzschild’s Radius with Reference to the Non-Spinning Black Holes,” Bulletin of Pure and Applied Sciences, Vol. 29D, No. 2, 2010, pp. 183-187.

[6] D. Mahto, K. Kumari, R. K. Sah and V. Prakash, “Study of Schwarzschild’s Radius with Reference to the Spinning Black Holes,” Bulletin of Pure and Applied Sciences, Vol. 30D, No. 1, 2011, pp. 157-162.

[7] D. Mahto, K. Kumari, R. K. Sah and K. M. Singh, “Study of Non-Spinning Black Holes with Reference to the Change in Energy and Entropy,” Astrophysics and Space Science, Vol. 337, No. 2, 2011, pp. 685-691. doi:10.1007/s10509-011-0883-7

[8] A. Dabholkar, “Black Hole Entropy in String Theory. A Window in to the Quantum Structure of Gravity,” Current Science, Vol. 89, No. 12, 2005, p. 25.

[9] P. G. Bergmann, “Introduction to the Theory of Relativity,” Prentice-Hall of India, New Delhi, 1969.

[10] J. D. Bekenstein, “Bekenstein-Hawking Entropy,” Scholarpedia, Vol. 3 No. 10, 2008, p. 7375

[11] D. Mahto, V. Prakash, B. K. Singh and K. M. Singh, “Change in Entropy of Non-Spinning Black Holes w.r.t. the Radius of Event Horizon in XRBs,” Astrophysics and Space Science, Vol. 343, No. 1, 2013, pp. 153-159. doi:10.1007/s10509-012-1219-y

[12] J. Transchen, “An Introduction to Black Hole Evaporation,” 2000.