Units for Entropy of Simple Black Holes

[muzukashi suginaiyo]

Hello. I recently discovered Gerard 't Hooft's (what a complicated name to type, isn't it?*apostrophe*apostrophe*apostrophe) equation for the entropy of a simple black hole (what is meant by "simple" I have no idea). It is:

Where "S" is the entropy of a simple black hole
A is the area of the black hole's event horizon
h is (reduced?) Planck's Constant
G is the gravitational constant

S = A/(4hG)

Unless there is a conversion constant missing in this equation (is there?), I get units for entropy as (s^3)/(m^3).

That is,

Entropy = [m^2]/[(kg*m^2/s)*(m^3/kg*s^2)]

= seconds cubed per meters cubed? What does this signify? Is there some "speed" associated with entropy such that entropy is inversely proportional to the cube of this "speed"?

Or am I way off track here?

 

[TJGilb]

I've never heard of entropy referred to in $\frac {s^3} {m^3}$. Generally it's given as $\frac J K$.

 

[Chalnoth]

Hello. I recently discovered Gerard 't Hooft's (what a complicated name to type, isn't it?*apostrophe*apostrophe*apostrophe) equation for the entropy of a simple black hole (what is meant by "simple" I have no idea). It is:

Where "S" is the entropy of a simple black hole
A is the area of the black hole's event horizon
h is (reduced?) Planck's Constant
G is the gravitational constant

S = A/(4hG)

Unless there is a conversion constant missing in this equation (is there?), I get units for entropy as (s^3)/(m^3).

That is,

Entropy = [m^2]/[(kg*m^2/s)*(m^3/kg*s^2)]

= seconds cubed per meters cubed? What does this signify? Is there some "speed" associated with entropy such that entropy is inversely proportional to the cube of this "speed"?

Or am I way off track here?

You're missing a factor of $k_B c^3$. The three factors of $c$ cancel out the $s^3/m^3$, while the Boltzmann constant $k_B$ has units of energy per unit temperature (typically J/K, as TJGilb mentioned). You can see this at the Wikipedia page here:
https://en.wikipedia.org/wiki/Black_hole_thermodynamics

 

[muzukashi suginaiyo]

Ah. Okay. So there was a couple constants missing. Thanks.