与黑洞类似，Buchdahl 星无法被极值化
Like Black holes, Buchdahl stars cannot be extremalized
AI总结：
本研究验证了非极端Buchdahl星无法通过试验粒子吸积极值化，与黑洞规律一致，并指出其极端极限大于1的特性或为极端黑洞形成的唯一可能途径。
摘要：
早在文献\textit{Dadhich97}中就已证明，非极端黑洞无法通过试验粒子的绝热吸积转变为极端黑洞。Buchdahl 星是不含视界的最致密天体，其定义为$\Phi(R) = 4/9$，而黑洞的定义为$\Phi(R) = 1/2$，其中$\Phi(R)$是粒子所经历的引力势：对静态天体为径向下落情形，对旋转天体为轴向情形。在这篇短注中，我们研究了Buchdahl星的极值化问题，证明其与黑洞遵循相同的结论，即非极端Buchdahl星无法通过试验粒子吸积实现极值化。此外，由于Buchdahl星（BS）的极端极限大于1，它可能通过中性、无自旋吸积促进极端黑洞的形成，这或许是极端黑洞形成的唯一途径。
英文摘要：
It was shown long back in \cite{Dadhich97} that a non-extremal black hole cannot be converted into an extremal one by test particle adiabatic accretion. The Buchdahl star is the most compact object without horizon and is defined by $Φ(R) = 4/9$, while black hole by $Φ(R) = 1/2$. Here $Φ(R)$ is the gravitational potential experienced by a particle, radially falling for static and axially for the rotating object. In this short note we examine the question of extremalization of the Buchdhal star and show that the same result holds good as for the black hole. That is, a non-extremal Buchdahl star cannot be extremalized by test particle accretion. Further since extremal limit for BS is $>1$, it could facilitate formation of extremal black holes by neutral and spinless accretion. That is perhaps the only way they could be formed.
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