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| Bousso bound | |
|---|---|
| Name | Bousso bound |
| Field | Theoretical physics |
| Introduced | 1999 |
| Introduced by | Raphael Bousso |
| Related | Holographic principle, General relativity, Quantum field theory |
Bousso bound The Bousso bound is a conjectured entropy bound in theoretical physics that relates entropy flux through null hypersurfaces to the area of their bounding surfaces. It refines ideas from the holographic principle, connects to results in general relativity, and motivates relations between black hole thermodynamics, quantum field theory, and string theory. The bound has influenced work on AdS/CFT correspondence, cosmology, and formulations of quantum gravity.
The Bousso bound was proposed by Raphael Bousso in the context of attempts to make the holographic principle precise in arbitrary spacetimes, drawing on insights from Bekenstein's entropy bound, Hawking's area theorem, and the Bekenstein–Hawking relation for black holes. It aims to generalize entropy bounds previously considered in flat spacetime, de Sitter space, and near Schwarzschild metric horizons, integrating concepts from Penrose-type causal structure, the Raychaudhuri equation, and the notion of light-sheets. Influences include work by ’t Hooft, Susskind, and later developments in the AdS/CFT correspondence by Maldacena.
The bound is stated for a spacelike two-surface S embedded in a Lorentzian manifold satisfying the NEC or variants like the averaged NEC considered in semiclassical contexts. From S one constructs four families of null hypersurfaces, called light-sheets, generated by future- or past-directed null geodesic congruences with nonpositive expansion determined by the Raychaudhuri equation. The conjecture asserts that the entropy flux through any such light-sheet L is bounded by one quarter of the area A(S) measured in Planck units, echoing the area law for black hole entropy and relating to entropy bounds discussed by Bekenstein and constraints in von Neumann entropy contexts. Specific technical statements invoke causal structure theorems used in work by Penrose and energy conditions explored in studies by Hawking and Ellis.
Motivation arises from paradoxes in black hole thermodynamics and thought experiments involving collapse, evaporation, and information flow that engaged researchers such as Preskill, Page, and ’t Hooft. The Bousso bound provides a covariant, local formulation compatible with causal properties central to Penrose and constraints from semiclassical analyses by Hartle and Thorne. It is interpreted as an expression of a deeper holographic bookkeeping principle linking area in Planck scale geometry to degrees of freedom counted by entropy measures pertinent to quantum field theory on curved backgrounds, a viewpoint reinforced by results in AdS/CFT correspondence by Maldacena and entropy inequalities studied by Holevo and Everett-inspired quantum information approaches.
Rigorous proofs exist in restricted settings: for weakly gravitating systems in asymptotically flat or asymptotically anti-de Sitter spacetimes, arguments leverage techniques from quantum field theory regularization, the generalized second law as articulated by Bekenstein and Hawking, and light-cone quantization methods related to work by Mandelstam. Semiclassical derivations invoke the generalized covariant entropy conjecture and use entropy inequalities akin to the strong subadditivity of entropy proved in quantum information theory by researchers influenced by Lieb and Ruskai. More formal proofs in specialized backgrounds were provided by collaborators including Raphael Bousso and others, building on mathematical tools from differential geometry used by Yau and causal methods employed by Geroch.
The bound constrains entropy carried into regions of cosmological models like FLRW universes considered by Starobinsky and impacts analysis of entropy in de Sitter space relevant to inflationary scenarios of Guth and Linde. It informs bounds on information flow in black hole evaporation debates involving Hawking and Preskill, and it shapes constraints in holographic reconstructions central to Maldacena's AdS/CFT correspondence. The bound has been used in studies of entropy inequalities in condensed matter physics via holographic entanglement entropy proposals by Kachru-adjacent researchers and in quantum information contexts examined by Charles Bennett-class investigators.
Generalizations relax classical energy conditions, replacing the NEC with averaged or quantum-inequality-inspired versions developed by Ford, and incorporate quantum corrections via the generalized entropy concept used by Borde-related approaches and researchers like Jacobson who connected thermodynamics to Einstein equations. Extensions include quantum-covariant entropy bounds, the Quantum Focussing Conjecture proposed in literature influenced by Raphael Bousso and collaborators, and holographic entropy inequalities in AdS/CFT correspondence contexts explored by Belinski-adjacent teams. Work by authors such as Page and Gibbons examined implications for cosmological horizons in de Sitter space and for generalized second law scenarios considered by Bekenstein and Hawking.
Criticisms focus on regimes where classical energy conditions fail, such as in quantum fields studied by Schwinger-style analyses or exotic matter proposals influenced by Thorne-type traversable wormhole discussions. Open problems include rigorous formulation in full quantum gravity frameworks like loop quantum gravity or nonperturbative string theory constructions studied by Witten and Sen, precise relation to information retrieval in black hole evaporation debated by Preskill and Mathur, and establishing universally valid quantum energy conditions akin to those proposed by Friedrichs and Fewster. Further work is needed to reconcile the bound with counterexamples in semiclassical regimes and to integrate it with dynamical spacetime proposals by Rovelli and Smolin.