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Equation of state for Buchdahl star and black hole

Naresh Dadhich
Dec 2022
摘要
It turns out that the Buchdahl star, the most compact object without horizon,is defined by the potential $\Phi(R) = 4/9$ and black hole by $\Phi(R) = 1/2$,where $\Phi(R) = (MR-Q^2/2R)/(R^2+a^2)$ for the Kerr-Newman charged androtating object. Equivalently in terms of gravitational and non-gravitationalenergy, the former is defined when gravitational energy is half ofnon-gravitational energy while the latter when the two are equal. In thisletter we wish to point out that the latter characterization implies that theBuchdahl star is a Virial star as its equilibrium is maintained by averagekinetic energy being half of potential energy, and consequently the equation ofstate $p= \frac{1}{2} \rho$ and sound velocity, $v_s^2 = 1/2$. Similarly thiswould predict an equation of state for black hole $p = \rho$ and $v_s^2=1$.
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