0

According to relative mass effect predicted by Einstein's relativity theory, the mass of an object increases with increase in it velocity given by the equation

$$ M = \frac{M_0}{\sqrt{(1 - v^2 / c^2)}}. $$ This is also one of the reason why an object can never attain the speed of light. This phenomena has also been experimentally observed in particle accelerators. My question is, with increase in mass of the objet say at 98% speed of light, will their be an increase in its gravitational strength or Field around the object? If so, has this been experimentally observed and confirmed?

Qmechanic
  • 201,751
Tushar Sharma
  • 315

1 Answers1

0

No. The kinetic energy of an object does not gravitate, only the rest mass, $M_0^2 = M^2- p^2/c^2$.

(The formula you wrote above for $M$ is a little obsolete. It is the rest mass plus the kinetic energy of the object, from the famous formula $E=Mc^2$. Nowadays people would just call it $E/c^2$, and use the symbol $M$ to mean $M_0$.)

As an example of this answer, consider the stress-tensor for a pressureless fluid: $$T^{\mu\nu} = \rho u^\mu u^\nu.$$ Now the Einstein equation says $$R= -4\pi G T,$$ and here $$T={\rm tr}T^{\mu\nu} = g_{\mu\nu}T^{\mu\nu} = \rho u^2 = \rho$$ where $u^2=1$ by normalization of 4-velocity. Thus the curvature scalar is always given by $-4\pi G\rho$, independent of the object's velocity.

Eric David Kramer
  • 1,627
  • 8
  • 21
  • 1
    "The kinetic energy of an object does not gravitate, only the rest mass." This is not quite accurate. If you consider a group of objects in their center of mass frame, then the gravitational field of this group will be bigger if the individual objects are moving. – TimRias Feb 20 '20 at 10:52
  • Thanks a lot , but I'm only in 12th grade and very interested in astrophysics. I have never come across the equation above , kindly recommend a good book for me and explain your answer theoretically as I don't know the maths behind . Thank you very much again . – Tushar Sharma Feb 20 '20 at 10:52
  • 1
    -1: The kinetic energy of the object does gravitate. For instance the asymptotic mass of an isolated matter system in linearized gravity is proportional to the integral of $T^{tt} =\rho u^t u^t$ and $u^t$ is larger when the dust is moving faster. – Void Feb 20 '20 at 11:24
  • @mmeent That's only true when the components are moving with different velocities, in which case it again contributes to the total mass $E_{\rm tot}^2-p_{\rm tot}^2$. – Eric David Kramer Feb 20 '20 at 12:39
  • @TusharSharma The Einstein equation expresses how matter curves space and gravitates. You can think of the length of space as being $1-\frac{GM}{c^2r}$, and $R$ is roughly the second derivative of this. $R$ is in turn equal to $G$ times the mass density. – Eric David Kramer Feb 20 '20 at 12:42
  • @Void $u^t$ is exactly the gamma factor in the question. If what you're saying is true then my whole answer is wrong. Could you write an answer explaining? What about the argument that I wrote? – Eric David Kramer Feb 20 '20 at 12:44
  • @EricDavidKramer The argument you wrote focussed only on the trace of $R$. There is more to the gravitational field than just that. – TimRias Feb 20 '20 at 12:55