Abstract We study the SL(2) transformation properties of spherically symmetric perturbations of the Bertotti-Robinson universe and identify an invariant μ that characterizes the backreaction of these linear solutions. The only backreaction allowed by Birkhoff’s theorem is one that destroys the AdS 2 × S 2 boundary and builds the exterior of an asymptotically flat Reissner-Nordström black hole with Q = M 1 − μ / 4 $$ Q=Msqrt{1-mu /4} $$ . We call such backreaction with boundary condition change an anabasis. We show that the addition of linear anabasis perturbations to Bertotti-Robinson may be thought of as a boundary condition that defines a connected AdS 2 ×S 2. The connected AdS 2 is a nearly-AdS 2 with its SL(2) broken appropriately for it to maintain connection to the asymptotically flat region of Reissner-Nordström. We perform a backreaction calculation with matter in the connected AdS 2 × S 2 and show that it correctly captures the dynamics of the asymptotically flat black hole.
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机译：摘要我们研究了Bertotti-Robinson Universe的球形对称扰动的SL（2）转换特性，并识别表征这些线性解决方案反应的不变μ。 Birkhoff的定理允许的唯一反应是破坏广告2×S 2边界的反应，并建立了Q = M 1 - μ/ 4 $$ Q = M SQRT {1---建立了渐近平面reissner-nordström黑洞的外部。 mu / 4} $$。我们用边界条件调整了这种反应改变了一只anabasis。我们表明，向Bertotti-Robinson添加线性AnaBasis扰动可以被认为是限定连接的广告2×S2的边界条件。连接的ADS 2是近广告2，其SL（2）适当地破坏它维持与Reissner-Nordström的渐近平坦区域的连接。我们在连接的广告2×S 2中以物质进行了反应计算，并表明它正确地捕获了渐近平面黑洞的动态。
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