[Paper Review] TeV scale black holes thermodynamics with extra dimensions and quantum gravity effects

Kourosh Nozari, Prof.Asoc. Ledian Shahini|arXiv (Cornell University)|Jun 25, 2012

Noncommutative and Quantum Gravity Theories1 references3 citations

TL;DR

This paper investigates TeV-scale black hole thermodynamics in large extra dimensions, incorporating both a minimal length (via Generalized Uncertainty Principle) and a maximal momentum (from Doubly Special Relativity). It finds that including maximal momentum reduces the final temperature and increases entropy, lowering the minimum black hole mass and enhancing detectability at the LHC compared to models with only a minimal length cutoff.

ABSTRACT

TeV scale black hole thermodynamics in the presence of quantum gravity effects encoded in the existence of a minimal length and a maximal momentum is studied in a model universe with large extra dimensions.

Motivation & Objective

• To study the thermodynamic behavior of TeV-scale black holes in large extra dimensions under quantum gravity effects.
• To examine the combined impact of a minimal length and maximal momentum on black hole evaporation and remnant formation.
• To assess how these quantum gravity cutoffs affect the detectability of black holes at the LHC.
• To compare results with and without a maximal momentum cutoff, highlighting its physical significance.

Proposed method

• Formulates a generalized uncertainty principle (GUP) that includes both a minimal measurable length and a maximal momentum, derived from quantum gravity constraints.
• Applies the modified GUP to derive a corrected Hawking temperature expression in d-dimensional spacetime with large extra dimensions.
• Uses a Taylor expansion of the temperature expression around the GUP parameter α to extract thermodynamic quantities like entropy and heat capacity.
• Calculates the minimum black hole mass and maximum temperature at the final evaporation stage, comparing scenarios with and without maximal momentum.
• Derives expressions for entropy and heat capacity as functions of black hole mass and spacetime dimensionality d.
• Performs numerical analysis for various d (4 to 11) and α values (1 and 2/π), producing comparative plots and tables of key thermodynamic quantities.

Experimental results

Research questions

• RQ1 How does the inclusion of a maximal momentum cutoff affect the final temperature and mass of a TeV-scale black hole in large extra dimensions?
• RQ2 What is the role of spacetime dimensionality in determining the minimum mass and maximum temperature of black hole remnants?
• RQ3 How does the maximal momentum cutoff alter the entropy and heat capacity of evaporating black holes compared to the standard GUP with only a minimal length?
• RQ4 Does the presence of both minimal length and maximal momentum increase the likelihood of detecting TeV-scale black holes at the LHC?
• RQ5 How do the thermodynamic quantities (temperature, entropy, heat capacity) evolve during the final stages of black hole evaporation under the modified GUP?

Key findings

• Including a maximal momentum cutoff reduces the final temperature of evaporating black holes compared to models with only a minimal length, due to suppression of high-energy states.
• The minimum black hole mass (M_min) is lower when both minimal length and maximal momentum are included, increasing the probability of black hole production and detection at the LHC.
• For α = 1, M_min increases from 0.5 TeV (d=4) to 4.72 TeV (d=11) when only minimal length is considered, but drops to 0.32 TeV at d=11 when maximal momentum is added.
• When α = 2/π, M_min decreases to 0.12 TeV at d=11 with maximal momentum, indicating a significant enhancement in detectability across higher dimensions.
• Entropy increases relative to the minimal-length-only case when maximal momentum is included, due to the additional phase space suppression from the momentum cutoff.
• Heat capacity increases in magnitude when maximal momentum is included, indicating a more stable final remnant phase with enhanced thermodynamic response.