Naman Kumar

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that—within a fixed asymptotic charge sector—the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.

We show that the Weak Gravity Conjecture follows from semiclassical entropy consistency once null entropy variations are required to have a regular modular endpoint. The argument uses generalized entropy, the Quantum Null Energy Condition (QNEC), and the modular structure of null deformations. If all charged states are strictly subextremal, extremal charged horizons become one-sided endpoints of the semiclassical charged state space. On such horizons the non-extremal Kay–Wald/Bisognano–Wichmann identification of modular flow with Killing flow cannot be continued while preserving the same affine null-cut realization. The endpoint is therefore modularly terminal. Regular endpoint extendibility of the generalized entropy excludes such terminality, while QNEC and bounded null stress exclude the alternative of an upward entropy-curvature singularity. Hence a consistent semiclassical theory satisfying these entropy and regularity conditions must contain a charged state with q/m ≥ 1.

A bstract: The static tidal Love numbers of four-dimensional black holes vanish identically, unlike their nontrivial dynamical response at finite frequency. Recent work has provided three complementary descriptions of this phenomenon: an emergent SL(2, ℝ ) organization of static near-zone perturbations, a graded logarithmic and multi-zeta structure in Shell Effective Field Theory (Shell EFT), and an on-shell matching framework based on gravitational Raman scattering with renormalization group (RG) running. We show that these features arise from a common near-zone truncation mechanism. For a massless scalar field, horizon regularity selects a unique static solution forming a highest-weight-type representation, truncating the hypergeometric solution to a finite polynomial and eliminating the independent decaying branch at large radius. This excludes a static Wilson coefficient in the effective theory. We show that the same truncation operates in the static Regge-Wheeler and Zerilli equations for four-dimensional Schwarzschild black holes. Analytic continuation of the horizon-regular solution to small frequency — via the Coulomb-hypergeometric or Mano-Suzuki-Takasugi formalisms — preserves this truncation as an anchoring condition for the renormalized angular momentum parameter. The resulting low-frequency expansion is controlled by Gamma and hypergeometric functions, generating a graded algebra of logarithms and odd Riemann zeta values. Within this structure, no invariant of negative weight exists in the static sector, so the vanishing of the static Love number follows as a structural consequence. This explains the “zero-sum” rule of Shell EFT and why the self-induced RG flow in gravitational Raman scattering does not generate a static invariant.

A bstract: We study tidal Love numbers of static black holes in four-dimensional quadratic theory of gravity, extending the result of GR. We use worldline effective field theory (WEFT) methods to compute metric perturbations from one-point functions, treating the higher-derivative terms perturbatively. We show that insertions of scalar fields on the worldline induce non-zero tidal tails, and the corresponding Love number displays no RG running. The same conclusion holds for the insertions of tensor fields. Furthermore, for scalar dipole perturbations, we derive a Yukawa-deformed Frobenius solution and match the asymptotic behavior to fix the UV charge, finding agreement with EFT predictions of Wilson coefficients. Our work demonstrates that quadratic higher-curvature corrections induce non-zero but scale-independent tidal responses, offering a robust EFT framework to test deviations from GR in gravitational wave observations.