Modified Gravity Theories From the Barrow Hypothesis: Modified Einstein Equations

Table of Links

Abstract and 1 Introduction

2 Modified Einstein equations with the Jacobson’s approach

3 Quantum gravitational corrections to the Schwarzschild metric

4 Conclusions and References

2 Modified Einstein equations with the Jacobson’s approach

The Barrow hypothesis suggests that the entropy has the form

The general solution of (2.5) is

where Λ′ is the integration constant. This expression matches the result of [30]. Since our goal is to see what happens when ∆ is a radial function, thus we expand

where c is some constant. By doing a series expansion of (2.6), integrating by parts and collecting powers of ǫ, we find

The limit ǫ → 0 reduces to general relativity.