Spacetime Structure near Generic Horizons and Soft Hair

Area of Science:

• Theoretical physics
• General relativity
• Quantum gravity

Background:

• Black holes and cosmological horizons possess complex spacetime structures.
• Understanding horizon physics is crucial for unifying gravity and quantum mechanics.
• Previous studies hinted at emergent symmetries and soft quantum numbers at horizons.

Purpose of the Study:

• To explore the spacetime structure near nonextremal horizons in dimensions greater than two.
• To identify and characterize novel near-horizon algebras and their properties.
• To investigate the concept of
• soft hair
• and its implications for black hole thermodynamics and entropy.

Main Methods:

• Analysis of boundary conditions defining interactions with a thermal bath.
• Derivation of near-horizon algebras using dynamical variables.
• Construction of specific algebraic structures, including semidirect sums and nonlinear extensions.
• Application of these findings to black hole and cosmological horizons.

Main Results:

• Novel boundary conditions specify inequivalent horizon interactions.
• A new near-horizon algebra is found, a semidirect sum of diffeomorphisms and "spin-s supertranslations".
• For s=1, the first explicit near-horizon realization of the Bondi-Metzner-Sachs algebra is obtained.
• A nonlinear extension of the Heisenberg algebra is derived, generalizing previous results.
• Black holes and cosmological horizons can be equipped with "soft hair".

Conclusions:

• The study reveals a rich structure of spacetime near nonextremal horizons.
• "Soft hair" provides a new framework for understanding black hole thermodynamics and entropy.
• The discovered algebras offer insights into emergent symmetries and quantum properties of horizons.