Superrotation Charge and Supertranslation Hair on Black Holes (1611.09175v2)

Abstract: It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass $M$, momentum $\vec P$, angular momentum $\vec J$ and boost charge $\vec K$, an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gauge expression is derived for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.

• The paper shows that black holes possess infinite supertranslation hair and novel superrotation charges, extending classical properties and addressing aspects of the information paradox.
• It employs gravitational perturbation analysis and Bondi-gauge expressions to reveal how asymmetric shock waves induce supertranslations on black hole horizons.
• The work broadens the BMS symmetry framework in classical and quantum gravity, paving the way for potential experimental validation through gravitational memory effects.

Superrotation Charge and Supertranslation Hair on Black Holes

The paper "Superrotation Charge and Supertranslation Hair on Black Holes" by Stephen W. Hawking, Malcolm J. Perry, and Andrew Strominger explores the new avenues in the classical Einstein gravity relating to the properties of black holes. The work explores how black holes, aside from having the conventional ADM characteristics such as mass $M$, momentum $P$, angular momentum $J$, and boost charge $K$, also possess an infinite suite of supertranslation hair. This paper extends the analysis to include the superrotation charges, with significant implications for both classical and quantum gravity theories.

The authors examine how black holes can be differentiated by their classical superrotation charges, typically measured at infinity. This investigation stems from the paradigm that all black holes are not only defined by few observable quantities but also by the extensive suite of conserved charges arising from the asymptotic symmetries at null infinity in gravitational theories—as characterized by the Bondi-Metzner-Sachs (BMS) group. This leads to novel conceptual extensions such as the non-trivial modifications of the classical phase space due to large diffeomorphisms involving supertranslations and superrotations.

Central to the paper is the demonstration that black holes can be supertranslated by introducing asymmetric shock waves. The authors derive a Bondi-gauge expression for the linearized horizon supertranslation charge, revealing its capacity to induce supertranslations on the linearized phase space of gravitational perturbations. These findings potentially resolve specific aspects of the black hole information paradox by establishing that conservation of the supertranslation charges binds outgoing Hawking radiation and the black hole's internal structure through quantum correlations.

The paper's numerical results highlight that, upon supertranslating a Schwarzschild black hole, it bears distinct superrotation charges, even though these transformations do not augment supertranslation charges due to the group's abelian nature. The classical framework used here may have profound implications given the superrotation charges' role as identifiers of different black hole configurations, offering a measurable prediction for these conserved quantities, suggesting a possible experimental verification mechanism through observables like the gravitational memory effect.

From a theoretical perspective, the introduction and detailed examination of superrotation and supertranslation charges transplant a refined layer onto the BMS group symmetry structures, broadening the classical relativity framework. This extension to incorporate infinite-dimensional symmetries suggests a richer phase space landscape in gravitational contexts, potentially allowing for a more nuanced understanding of black hole microstates and their interaction with the surrounding spacetime.

The potential for future development is notable, with immediate implications for uncovering a more unified description of the asymptotic behavior of spacetimes that may directly impact quantum gravity theories. The paper of how these aspects might interplay in non-perturbative quantum gravity scenarios could unveil new methodologies to approach classical and semiclassical formulations cohesively.

In conclusion, this paper elevates our understanding of black holes beyond the historical no-hair conjecture by introducing and validating the concept of supertranslation hair and their accompanying superrotation charges. These intricate symmetries not only further challenge the canonical perceptions of black hole uniqueness but also offer a potential resolution to various perceived theoretical conflicts, adding depth to the analysis of black hole quantum states and their semiclassical treatments. Future work should aim to integrate these insights within a broader quantum gravity framework, further exploring black hole entropy, and possibly linking them with holographic principle propositions.