论文标题
黑洞的静态响应的隐藏对称性：爱情数字的应用
Hidden symmetry of the static response of black holes: Applications to Love numbers
论文作者
论文摘要
我们表明，Schwarzschild黑洞周围的任何静态线性扰动都享有一组保守的电荷，形成了中央扩展的SchrödingerAlgebrash（1）= SL $（2，\ Mathbb {r}）\ ltimes \ ltimes \ Mathcal \ Mathcal {H} $。中央电荷由黑洞质量给出，在近摩尼子差异对称性的黑洞熵上呼应结果。这些保守的电荷产生的有限对称转换对应于静态场和坐标的共形变换。这种新结构使人们可以通过基于对称的方法讨论测试场近似中Schwarzschild黑洞的静态响应。首先，我们表明（水平的）对称性保护了Hui等人最近展出的爱情数字消失的对称性，称为HJPSS对称性，与SchrödingerGroup的SL $（2，\ Mathbb {r}）$发电机相吻合。然后，证明了HJPSS对称性的选择，这要归功于整个schrödinger对称性的自发断裂，直至简单的Abelian子组。后者可以理解为保护地平线测试场的规律性的对称性。在4维情况下，这为消失的Schwarzschild爱情编号提供了对称保护。我们的结果微不足道地扩展到Kerr案。
We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh(1) = sl$(2,\mathbb{R}) \ltimes \mathcal{H}$. The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al, dubbed the HJPSS symmetry, coincides with one of the sl$(2,\mathbb{R})$ generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case.
