ETD

• amplification
• black holes
• effective field theory
• extremal
• general relativity
• Reissner–Nordström
• scaling exponent
• tidal forces

Massive fields are expected to decouple, generating corrections to GR suppressed by powers of the ratio of the fields' wavelengths to the horizon radius. At an extremal black hole horizon the suppression survives, the decoupling does not. Static deformations of the near-horizon geometry scale as powers with scaling exponent gamma, fixed by the field equations. In GR gamma is integer, and the leading mode has gamma=2. Since the tidal forces measured by an infalling observer scale with gamma-2, they remain finite. EFT operators shift the exponent of this mode. Negative shift makes the tidal forces diverge near-horizon. Previous work established this mechanism for extremal Kerr, that develops a singular horizon even though curvature invariants remain finite. At 4-derivative EFT order, by contrast, the exponents of polar deformation of 4-dimensional extremal RN remain unshifted. This thesis extends the analysis to 6- and 8-derivative EFT corrections. The 6-derivative operator lowers the tidal exponent only when their coefficient is positive. In one-loop matching dominated by the lightest integrated-out state, this occurs when that state is bosonic. This sign condition is opposite to that found for Kerr. The 8-derivative operators give a sign-definite contribution thanks to standard positivity bounds associated with a unitary and causal ultraviolet completion. Subject to these bounds, the parity-even exponent shifts downward, whereas the parity-odd exponent shifts upward.