Noncommutative Schwarzschild Black Hole and Area Law

Using a graphical analysis, we show that for the horizon radius $r_h\gtrsim 4.8\sqrt\theta$, the standard semiclassical Bekenstein-Hawking area law for noncommutative Schwarzschild black hole exactly holds for all orders of $\theta$. We also give the corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy when $r_h<4.8\sqrt{\theta }$ till the extremal point $r_h=3.0\sqrt{\theta }$.