the higher you go the slower is ageing as per to einstein as we go far from the earth the TIME tends to slow down , so it means when I am one metre above the earth's surface , the time has slow down for me as per http://en.wikipedia.org/wiki/Gravitational_time_dilation 
what would happen if I am at the centre of earth 
 A: To a good approximation the time measured far from a gravitational field, $t_\infty$, and the time measured within the gravitational field, $t_0$, are related by:
$$ \Delta t_\infty = \Delta t_0 \left( 1 + \frac{2 \Phi}{c^2}\right)^{-1/2} $$
where $\Phi$ is the Newtonian gravitational potential. So for example outside the Earth at some distance $r$ the gravitational potential is:
$$ \Phi = -\frac{GM}{r} $$
and therefore:
$$ \Delta t_\infty = \Delta t_0 \left( 1 - \frac{2 GM}{c^2r}\right)^{-1/2} $$
which is actually the same result we get from the Schwarzschild metric, though you should note that the Schwarzschild $r$ co-ordinate is subtly different from the $r$ co-ordinate used in Newton's law.
Anyhow, inside the Earth at a distance $r$ from the centre the gravitational potential is:
$$ \Phi = -\frac{GM}{2R^3} (3R^2 - r^2) $$
where $R$ is the radius of the Earth (assuming the Earth is a perfect sphere of uniform density). So the gravitational time dilation is given by:
$$ \Delta t_\infty = \Delta t_0 \left( 1 - \frac{GM}{c^2R^3} (3R^2 - r^2)\right)^{-1/2} $$
or at the centre where $r$ is zero:
$$ \Delta t_\infty = \Delta t_0 \left( 1 - \frac{3GM}{c^2R} \right)^{-1/2} $$
So time at the centre runs more slowly than time at the surface. This shouldn't surprise you as the gravitational potential at the centre is obviously higher than at the surface otherwise objects wouldn't fall down mine shafts. Note that it's the potential that matters not the gravitational acceleration. The gravitational acceleration at the centre of the Earth is actually zero i.e. you would be weightless. However the time dilation is not zero.
