Modified Gravity Theories From the Barrow Hypothesis: Modified Einstein Equations

Authors: (1) Ankit Anand, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India; (2) Ruben Campos Delgado, Bethe Center for Theoretical Physics, Physikalisches Institut der Universit¨at Bonn, Nussallee 12, 53115 Bonn, Germany. 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. This paper is available on arxiv under CC BY 4.0 Deed license. Authors: (1) Ankit Anand, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India; (2) Ruben Campos Delgado, Bethe Center for Theoretical Physics, Physikalisches Institut der Universit¨at Bonn, Nussallee 12, 53115 Bonn, Germany. Authors: Authors: (1) Ankit Anand, Department of Physics, Indian Institute of Technology Madras, Chennai 600 036, India; (2) Ruben Campos Delgado, Bethe Center for Theoretical Physics, Physikalisches Institut der Universit¨at Bonn, Nussallee 12, 53115 Bonn, Germany. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Modified Einstein equations with the Jacobson’s approach 2 Modified Einstein equations with the Jacobson’s approach 3 Quantum gravitational corrections to the Schwarzschild metric 3 Quantum gravitational corrections to the Schwarzschild metric 4 Conclusions and References 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. This paper is available on arxiv under CC BY 4.0 Deed license. This paper is available on arxiv under CC BY 4.0 Deed license. available on arxiv