In this research paper, we have derived the formula for both the changes in energy (δE) and entropy (δS) and thereafter calculated the change in entropy (δS) with corresponding change in energy (δE) taking account the first law of the black hole mechanics relating the change in mass M, angular momentum J , horizon area A and charge Q, of a stationary black hole, when it is perturbed, given by formula satisfying in the vacuum as δM = k 8π δA + δJ − υδQ, specially for Non-spinning black holes.

Neeraj Pant et al.(2010) gave a detailed study of BCT First solution (Tewari,1988) representing time dependent balls of perfect fluid with matter-radiation in general relativity to assume the life time of quasar 7 9 5 10 M × ⊙ as well as the radiative efficiency of black hole is smaller than the same mass of quasars.

In the present paper, we have derived an expression for change in entropy of non-spinning black holes on the basis of formula ( BH

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 (dE/dM), which gives a constant quantity equal to 8.9998 x 10¹⁶ 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 10⁶⁷ 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 (dE/dM) for different test non-spinning black holes in X-ray binaries (XRBs) and Active Galactic Nuclei (AGN).  

In the present paper, we have derived an expression for change in entropy of non-spinning black holes on the basis of formula (EBH=KBHR5) as proposed by Kanak Kumari et al. (2010) and the formula δSbh=(2П/(kc2) ( Mahto et al., 2011) and calculated their values for different test non-spinning black holes.