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Added BE19B019.tex file and updated main.tex #66

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52 changes: 52 additions & 0 deletions BE19B019.tex
Original file line number Diff line number Diff line change
@@ -0,0 +1,52 @@
\subsection{What is Hawking Radiation?}
{

Hawking radiation is thermal radiation thought to be emitted by black holes due to quantum effects. Black holes are sites of immense gravitational attraction into which surrounding matter is drawn by gravitational forces.


By doing a calculation in the framework of quantum field theory in curved spacetimes, Hawking showed that quantum effects allow black holes to emit radiations in a thermal spectrum.
}

\subsection{Equations}
{

A black hole emits thermal radiation at a temperature:

\begin{equation}
T_H = \frac{\kappa}{2 \pi}
\end{equation}

in natural units with G, c, $\hbar$ and $\kappa$ equal to 1, and where $\kappa$ is the surface gravity of the horizon. \newline



The radiation from a Schwarzschild black hole is black-body radiation with temperature:

\begin{equation}
T={\hbar\,c^3\over8\pi G M k}
\end{equation}

where $\hbar$ is the reduced Planck constant, c is the speed of light, k is the Boltzmann constant, G is the gravitational constant, and M is the mass of the black hole.
\newline



The power emitted by a black hole in the form of Hawking radiation can easily be estimated for the simplest case of a nonrotating, non-charged Schwarzschild black hole of mass M:

\begin{equation}
P={\hbar\,c^6\over15360\,\pi\,G^2M^2}
\end{equation}

where P is the energy outflow, $\hbar$ is the reduced Planck constant, c is the speed of light, and G is the gravitational constant.
\newline



The time that the black hole takes to evaporate is:

\begin{equation}
t_{ev}={5120\,\pi\,G^2M_0^{\,3}\over\hbar\,c^4}
\end{equation}

where G is gravitational constant, $M_0$ is Mass of Black hole at time 0, $\hbar$ is planck's constant and c is the speed of light.
}
2 changes: 2 additions & 0 deletions main.tex
Original file line number Diff line number Diff line change
Expand Up @@ -17,4 +17,6 @@ \section{Introduction}
% \section{ME20B001}
% \include{me20b001}

\section{BE19B019}
\include{BE19B019}
\end{document}