Abstract:
Mahto et al. have shown δS≥0 and M^{2}=a*J by using the first law of the black hole mechanics in the vacuum and Einstein mass-energy equivalence relation specially for spinning black holes. In the present paper, this work is extended to propose a model for the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum & half spin parameter of black holes (a* = 1 & 1/2) and calculated their values for different test black holes in XRBs and AGN. We have also shown that the change in mass of the spinning black holes due to corresponding change in the angular momentum for maximum spinning rate of black holes (a* = 1) is double to that of the spinning black holes having spinning parameter (a* = 1/2).

Abstract:
The present paper gives a theoretical model for the change in entropy of spinning black holes due to change in mass to use the first law of black hole mechanics for unit spinning parameter and angular momentum in XRBs. This shows that the entropy change with respect to the mass of uncharged spinning black holes is essentially the function of mass and their surface gravity are lesser than to that of the non-spinning black holes.

Abstract:
Mahto et al. gave an expression for the change in enthalpy and internal energy with corresponding change in the radius of the event horizon of black holes of spin parameter a* = 1 (2013). On the basis of this research work, we have proposed an expression for the change in the internal energy and enthalpy of the spinning black holes to assume spin parameter a* = 1/2 and calculated their values for different test spinning black holes existing in XRBs.

Abstract:
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.

Abstract:
The present paper discusses the
change in entropy of spinning black holes due to change in mass for AGN black
holes on the basis of the model as proposed in the case of XRBs under condition
that the black holes spin with unit spinning parameter and angular momentum and
this model gives slightly some different nature of the super-massive spinning
black holes in AGN as specified for XRBs.

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 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 (dE/dM) for different test non-spinning black holes in X-ray binaries (XRBs) and Active Galactic Nuclei (AGN).

In this research paper, we have used the formula for the change in entropy of Non-spinning black holes with respect to the change in the radius of event horizon (Mahto et al. 2012) and entropy of black holes (Hawking1973 & Mahto et al. 2012) to calculate their values in Active Galactic Nuclei(AGN) which shows that the variation of change in entropy of black holes with respect to the radius of the event horizon/entropy of black holes with increasing the values of the radius of the event horizon of different test Non-spinning black holes are like a wave-pattern.

In this research paper, we have used the formula for gravitational
force acting between the black hole and light particle passing near the radius
of event horizon of black holes (Mahto et
al. 2013) to calculate their values for different test of black
holes existing in Active Galactic Nuclei (AGN) and compared with that of the
black holes in XRBs.

Abstract:
The present research paper derives a formula for gravitational force acting between the black hole and light particle passing near the radius of event horizon of black holes and calculates also their values of different test black holes existing in only X-ray binaries (XRBs). 1. Introduction The English physicist Isaac Newton proposed Universal law of Gravitation in 1687, which states that every particle in the universe exerts a force on every particle along the line joining their centres. The magnitude of the force is directly proportional to the product of the masses of two particles and inversely proportional to the square of distance between them [1], which was successively explained by the observation on the planetary movements made by the German astronomer Kepler (1571–1630). It works perfectly well in the world of ordinary experience and has dominated for about 250 years. It, however, shows its shortcoming when explaining the unusual orbit of Mercury around the sun. It breaks down when the gravitational forces get very strong or involving bodies moving at speed near that of light (http://library.thinkquest.org/C007571/english/printback.htm). In 1915, Albert Einstein demonstrated better theory of gravitation on the basis of general relativity, which has overcome the limitations of Newton’s law of universal gravitation [2]. In 1997, Lerner discussed the problem of the deflection of light in a medium with varying refractive index applied to the motion of light in a weak Schwarzschild gravitational field [3]. In 1999-2000, Mario presented a theory which introduces new unknown relationships that may shed new light on the nature of matter. This theory allows the calculation of the gravitational constant with a precision comparable to the other atomic constants, gives a direct relation between mass and charge of the electron without the need of the ubiquitous “classical electron radius,” and generates a second fine structure constant while also offering the disconcerting possibility of an antigravitational force [4]. In 2013, Ng and Raymond Ooi analysed the gravitational force due to a pulsed Bessel beam and its effect on the probe pulse. They found that the Bessel beam generates gravitational repulsive forces at small distances and attractive forces at large distance. These forces can be coherently controlled in a medium by introducing a slow light effect through electromagnetic induced transparency [5]. In the present work, we have derived a formula for gravitational force acting between the black hole and light particle passing near the radius of

Abstract:
The Nigerian state has been fundamentally affected by two historical phenomena, colonial rule and military rule. Whereas colonial rule ended about forty-five years ago at the attainment of independence, military rule as a post-colonial instrument of conquest does not seem to have a perceivable abatement. This is in spite of the return to another civil rule since 1999. Indeed, the military conquest has reemerged in the involvement of ex-military rulers in politics. This study presents the dilemma of a post-colonial state coping with contradictory factors of development and democracy.