Black holes in multi-fractional and Lorentz-violating models

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Cosmology

Background:

• General Relativity describes black holes with specific singularities and event horizons.
• Multi-fractional theories of gravity propose scale-dependent spacetime dimensions and fundamental lengths.
• Previous studies explored fractional calculus in gravity, but multi-fractional approaches offer unique geometric variations.

Purpose of the Study:

• To investigate static, radially symmetric black holes within multi-fractional theories of gravity using q-derivatives and weighted derivatives.
• To analyze modifications to black hole event horizons, singularities, and thermodynamics.
• To explore potential implications for the cosmological constant problem.

Main Methods:

• Formulation of black hole solutions in multi-fractional gravity with q-derivatives.
• Formulation of black hole solutions in multi-fractional gravity with weighted derivatives.
• Calculation of Hawking temperature and thermodynamic properties for both scenarios.
• Comparison with General Relativity and other Lorentz-violating models.

Main Results:

• The q-derivative scenario yields a shifted event horizon and an additional ring singularity for Schwarzschild black holes.
• The weighted derivative scenario results in a de Sitter-Schwarzschild black hole due to geometric features generating a cosmological constant.
• Black holes in the q-derivative case can be hotter and possess the ring singularity; weighted derivative cases exhibit de Sitter hair.

Conclusions:

• Multi-fractional theories of gravity significantly alter black hole structure and thermodynamics compared to General Relativity.
• The weighted derivative scenario offers a geometric origin for a de Sitter term, potentially addressing the cosmological constant problem.
• These findings highlight the impact of scale-dependent gravity on fundamental astrophysical objects and cosmological models.