A cloud of dust (pressureless matter, ) has

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

The Geometry of Gravity, Ch The stress-energy tensor and relativistic continua

Problem

A cloud of dust (pressureless matter,

p=0

) has, in its own rest frame, proper energy density

\rho_0 = 2.0\times10^{17}\ \mathrm{J\,m^{-3}}

. An observer sees the cloud streaming past along the

x

axis at

v = 0.8c

. ((a)) Compute

T^{00}

T^{0x}

and

T^{xx}

as measured by this observer, and identify the two physical effects that each factor of

\gamma

T^{00}

represents. ((b)) Compute

T^\mu{}_\mu

in the boosted frame and check it against the rest-frame value. ((c)) Test this dust against the weak and dominant energy conditions.

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