# Why times runs slowy when gravity is high?

Jan 1, 2018

Strong gravity means that spacetime is curved which means that time passes more slowly.

#### Explanation:

Einstein's field equations show that mass, energy and momentum cause four dimensional spacetime to curve. Curved spacetime causes gravity. It also causes time to pass slower.

The equation which gives the factor by which time slows due to a mass $M$ is:

$\sqrt{1 - \frac{2 G M}{{c}^{2} r}}$

Where $G$ is the gravitational constant,, $c$ is the speed of light and $r$ is the distance from the centre of the massive object. The equation is only valid if $r$ is greater than the radius of the massive object.

Notice that if the mass is zero or the radius is very large, the factor is one and time runs at its fastest. Now, as the mass gets bigger and the radius gets smaller the factor gets smaller and time slows.

Also notice that there is a special value of the radius where the factor is zero which means that time stops.

${r}_{s} = \frac{2 G M}{c} ^ 2$

The value ${r}_{s}$ is called the Schwarzschild radius which describes the event horizon of a black hole.