论文标题
较高尺寸的电动球形物质壳：熵，热力学稳定性和黑洞极限
Electrically charged spherical matter shells in higher dimensions: Entropy, thermodynamic stability, and the black hole limit
论文作者
论文摘要
我们通过在壳上施加热力学的第一定律来研究$ d $尺寸中静态电荷球形薄壳的热力学特性。外壳在Radius $ r $中，内部的时空是Minkowski，而SpaceTime则是Reissner-Nordström。我们可以通过给出两个额外的状态方程，一个用于温度，另一个用于静电电势，从而完全描述了壳热力学。我们选择温度的状态方程式作为重力半径$ r _+$带有指数$ a $的功率定律，因此$ a = 1 $ case赋予具有黑洞热力学特性的外壳的温度，而对于静电电位，我们选择了Reissner-NordströmblackBlack black Black hole spacemente的状态特征。发现外壳的熵与$ a _+^a $成比例，其中$ a _+$是对应于$ r _+$的重力区域，带有$ a> 0 $。然后，我们能够执行黑洞限制$ r = r _+$，找到smarr公式，并恢复$ d $ d $二维的reissner-nordström黑洞的热力学。我们研究了所选状态方程的壳的固有热力学稳定性。我们以$ 0 <a \ leq \ frac {d-3} {d-2} $的价格获得，所有外壳的配置在热力学上都是稳定的，$ \ frac {d-3} {d-3} {d-2} {d-2} <a <1 <a <1 $稳定性取决于质量和电荷，除了$ a> $ a> $ a> $ a> $ a> a shell的范围外，它是不稳定的，其范围是不稳定的，其范围是不稳定的。 稳定的。我们根据实验室变量重写稳定条件。我们发现，这些壳的稳定性的足够条件是当等温电敏感性$χ_{p，t} $是正面的，当该数量是无限的时，边际稳定性发生，并且对于具有负电易感性的配置而产生的不稳定性。
We study the thermodynamic properties of a static electrically charged spherical thin shell in $d$ dimensions by imposing the first law of thermodynamics on the shell. The shell is at radius $R$, inside it the spacetime is Minkowski, and outside it the spacetime is Reissner-Nordström. We obtain that the shell thermodynamics is fully described by giving two additional reduced equations of state, one for the temperature and another for the electrostatic potential. We choose the equation of state for the temperature as a power law in the gravitational radius $r_+$ with exponent $a$, such that the $a=1$ case gives the temperature of a shell with black hole thermodynamic properties, and for the electrostatic potential we choose an equation of state characteristic of a Reissner-Nordström black hole spacetime. The entropy of the shell is found to be proportional to $A_+^a$, where $A_+$ is the gravitational area corresponding to $r_+$, with $a>0$. We are then able to perform the black hole limit $R=r_+$, find the Smarr formula, and recover the thermodynamics of a $d$-dimensional Reissner-Nordström black hole. We study the intrinsic thermodynamic stability of the shell with the chosen equations of state. We obtain that for $0<a\leq \frac{d-3}{d-2}$ all the configurations of the shell are thermodynamically stable, for $\frac{d-3}{d-2}<a<1$ stability depends on the mass and electric charge, and for $a>1$ all the configurations are unstable, except for the shell at its own gravitational radius, which is marginally stable. We rewrite the stability conditions in terms of laboratory variables. We find that the sufficient condition for the stability of these shells is when the isothermal electric susceptibility $χ_{p,T}$ is positive, marginal stability happening when this quantity is infinite, and instability arising for configurations with a negative electric susceptibility.
