Greybody factors for perfect fluid black hole

Abstract

The Einstein equation is a field equation which describes gravity in terms of the curvature of spacetime. It states how matter curves spacetime. The solutions of the Einstein field equation are the metrics of spacetime from which the curvature of spacetime can be found. The field equations are non-linear, which are complicated to solve. Therefore, some assumptions are needed to reduce the complexity of the Einstein equation. One of these assumptions is a perfect fluid sphere. Perfect fluid sphere satisfies the following: no viscosity, no heat conduction, and isotropy. Perfect fluid black holes are black hole solutions of the Einstein field equation, which are classified according to the Schwarzschild radius. Perfect fluid spheres that have a radius smaller than the Schwarzschild radius will be transformed into black holes. In this work, we are interested in studying a black hole solution of the Einstein field equation. Greybody factors are the transmission and reflection probabilities of the Hawking radiation which are emitted from a black hole. Greybody factors can be obtained from their structure of potential. We then calculated the Hawking radiation temperature and entropy, which are the properties of thermodynamics. Temperature is expressed in terms of the surface gravity of a black hole, while entropy is expressed in terms of the area of the event horizon. Finally, we are interested in the entropy composition of the black hole systems, and then we calculated it for each system of black holes.