# Gravitational mass and Inertial mass in relativistic physics

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Lee Sung Bin
In Newtonian mechanics, both gravitational mass and inertial mass is m. This principle is known as the principle of equivalence. However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc2. But in special relativity, it is widely known that F=γ3ma while a is acceleration. Does that means inertial mass and gravitational mass is different in general and only approximately same at non-relativistic situation? Or is inertial mass also γm? Or is the answer totally different?

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However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc2.
"I heard that" is not a valid reference. Where did you hear that? How are we supposed to examine a reference that we have not been given? Either way, what you "heard" is not correct.

But in special relativity, it is widely known that F=γ3ma while a is acceleration.
Again, where did you get this information? It is not generally correct so any inference you take from it is not going to be correct.

However, I heard that in Relativity, gravitational mass is γm
Where did you hear this? There is no such thing as "gravitational mass" in relativity, except in the sense that one can derive approximations like Newtonian gravity.

The source term in relativity is the stress-energy tensor, which does not include a ##\gamma m## term. Test objects follow geodesics determined by the geometry of spacetime; their own mass does not enter into it. In other words, gravity is not a force, so relativistic force equations aren't relevant.

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I heard that in Relativity, gravitational mass is γm
No, most definitely not. Whatever source you heard this from is wrong and you should discard it entirely or treat everything it says with extreme skepticism.

Lee Sung Bin
what you "heard" is not correct.
No, most definitely not. Whatever source you heard this from is wrong and you should discard it entirely or treat everything it says with extreme skepticism.
If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?

m4r35n357
If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?
The source of gravitation in General Relativity is the Stress-Energy Tensor.

Ibix
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r is there no gravitational mass in relativity?

Look up:

There is no such thing as "gravitational mass" in relativity

Ibix
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If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?
There is no active gravitational mass, the source of gravity in GR is the stress energy tensor. Sometimes people also talk about passive gravitational mass, but the concept doesn’t work in GR since gravity is not a force.

SiennaTheGr8
... But in special relativity, it is widely known that F=γ3ma while a is acceleration.

FYI, that equation only holds if the force vector is parallel (or antiparallel) with the object's velocity vector.

Ibix