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I think so. But I wold like to know another opinions to confirm.

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  • $\begingroup$ Yes, and it's not an opinion. $\endgroup$ – Aaron Stevens Aug 20 '18 at 3:00
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    $\begingroup$ Inertia and mass are related, but different concepts. Inertia is expressed by the Newton's 2nd law as $F=\dfrac{\text{d}p}{\text{d}t}$ while mass is the energy localized in the rest frame as $E=mc^2$. $\endgroup$ – safesphere Aug 20 '18 at 4:50
  • $\begingroup$ @safesphere Yes. but you also said this: "A quantum effect at the horizon dissolves the infalling matter whose energy has transferred to the gravitational field. " physics.stackexchange.com/questions/413222/… So, I can synthesize and to say that mass and inertia are exactly the same thing, because only gravitacional field has this properties. Matters mass belongs to its gravitational field. Right? $\endgroup$ – João Bosco Aug 21 '18 at 14:56
  • $\begingroup$ No, mass comes from the energy of all fields combined, gravity, electromagnetism, strong, and weak (plus Higgs, if it exists). Normally gravity is weak and 99% of mass is the energy of the strong field (virtual gluons). As gravity increases, the time dilation converts this energy into the energy of the gravitational field. The conversion is complete at the event horizon, but for an external observer this takes an infinite time, so it is never really complete and all charge conservation laws still hold. $\endgroup$ – safesphere Aug 21 '18 at 15:40
  • $\begingroup$ Also see my calculation of how gravity reduces mass (the energy of mass is converted to the energy of gravity). Formula (2) here plus the last formula: physics.stackexchange.com/questions/423533/… $\endgroup$ – safesphere Aug 21 '18 at 15:54
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Yes, but. I would say that mass is the property that underlies inertia - And also underlies gravity. I'm not sure if these distinctions matter to you.

Mass is the amount of stuff there is. It's a property of the object. Post-Einstein, it's the rest-energy of the stuff, rather than its "amount".

It so-happens that inertial mass, the property of matter that resists change in velocity (the $m$ in $F=ma$) is equal to this amount. It didn't have to be this way, philosophically, the two concepts are different. So as a matter of empirical fact we found that mass is the property of matter that resists changing velocity, i.e. it is the property that underlies inertia.

At the same time, we also found that mass is the property of matter that underlies gravity. Again, this needen't be the case philosophically. It's not like that the idea of "amount of rest energy" or "amount of stuff" is the same as the idea of "what causes gravity". But in practice, the same thing is both.

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