Holographic cosmology from the first law of thermodynamics and the generalized uncertainty principle

2009/11/30 by James E. Lidsey · 29 citations
Physics and Astronomy · #Astrophysics #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Holographic principle #Holography #Laws of thermodynamics #Non-equilibrium thermodynamics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Second law of thermodynamics #Statistical physics #Theoretical physics #Thermodynamics #Uncertainty principle #astro-ph.CO #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.88.103519

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 88(10) (American Physical Society) · Extended discussion post-Planck results; In press, Physical Review D

arxiv created 2013/09/30 · openalex publication_date 2013/11/14 · arxiv updated 2013/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The cosmological Friedmann equation sourced by the trace anomaly of a conformal field theory that is dual to the five-dimensional Schwarzschild-AdS geometry can be derived from the first law of thermodynamics if the apparent horizon of the boundary spacetime acquires a logarithmically corrected Bekenstein-Hawking entropy. It is shown that such a correction to the entropy can arise when the generalized uncertainty principle (GUP) is invoked. The necessary condition for such a thermodynamic derivation directly relates the GUP parameter to the conformal anomaly. It is consistent with the existence of a gravitational cutoff at a scale l_uv\ensuremath\gtrsim√(n)l₄ for a theory containing n light species. The absolute minimum in position uncertainty can be identified with the scale at which gravity becomes effectively five dimensional.

Citations

• Entropy of the Schwarzschild black hole and the string–black-hole correspondence
• The algebraic structure of the generalized uncertainty principle
• Power of black hole physics: seeing through the vacuum landscape
• First Law of Thermodynamics and Friedmann Equations of Friedmann–Robertson–Walker Universe
• Holographic Reconstruction of Spacetime¶and Renormalization in the AdS/CFT Correspondence
• The four laws of black hole mechanics
• Thermodynamics of Spacetime: The Einstein Equation of State
• Trace anomaly driven inflation
• Black holes and large N species solution to the hierarchy problem
• Black hole explosions?
• Quantum tunneling beyond semiclassical approximation
• Relativistic Equations for Adiabatic, Spherically Symmetric Gravitational Collapse
• Particle creation by black holes
• An Alternative to Compactification
• Brane new world
• Quantum Groups, Gravity, and the Generalized Uncertainty Principle
• Generalized second law of thermodynamics in black-hole physics
• Black hole bound on the number of species and quantum gravity at CERN LHC
• Black Holes and Entropy
• Lecture Notes on Holographic Renormalization
• Gravity on a brane in infinite-volume extra space
• QUANTUM GRAVITY AND MINIMUM LENGTH
• The large N limit of superconformal field theories and supergravity

Cited by

• Proca theory of four-dimensional regularized Gauss-Bonnet gravity and black holes with primary hair