{"arxiv_id":"gr-qc/0612089","incoming":{"papers":32,"sentences":50,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1105.3659","title":"Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field","url":"/paper/1105.3659","section":"First Law of Thermodynamics","sentence":"In this section we follow Ref. [ref] to find a higher dimensional form of the Misner-Sharp energy [ref] inside the horizon of the static spherically symmetric black hole in $f(R)$ gravity.","intent_p":0.89,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":2,"sentences":4,"quotes":[{"arxiv_id":"2411.09276","title":"Is The Internal Entropy of F(R)-Gravity Really An Entropy?","url":"/paper/2411.09276","section":"Internal Entropy","sentence":"Reproducing this approach we aim to inspect the internal part of entropy functional and compare the result with the one obtained by other approaches [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1407.1698","title":"Thermodynamic approach to field equations in Lovelock gravity and f(R) gravity revisited","url":"/paper/1407.1698","section":"Introduction","sentence":"[ref] , the procedure of ref.","intent_p":0.84,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":11,"sentences":12,"quotes":[{"arxiv_id":"2411.09276","title":"Is The Internal Entropy of F(R)-Gravity Really An Entropy?","url":"/paper/2411.09276","section":"Introduction","sentence":"Ever since the thermodynamics of $F(R)$-Gravity was studied [ref] , the additional effects, arising from the higher order members of the function $F(R)$, were identified as disipative nature of gravity caused by a new entropy member — internal entropy [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"2204.09496","title":"Non-flat and non-Extensive Thermodynamic Effects of M{\\o}ller tetradic theory of gravitation on cosmology","url":"/paper/2204.09496","section":"Thermodynamic behavior of the dust and radiation cases","sentence":"In general, the apparent horizon is not constant but changes with time [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"0705.3882","title":"Viscous Spacetime Fluid and Higher Curvature Gravity","url":"/paper/0705.3882","section":"Introduction","sentence":"The problem of entropy production for $f(R)$ gravity has been extensively discussed in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2304.08348","title":"Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition","url":"/paper/2304.08348","section":"Introduction","sentence":"Although the FRW universe has many well-known properties, including the existence of an apparent horizon [ref] , Hawking temperature and radiation [ref] , Bekenstein-Hawking entropy, quasi-local Misner-Sharp energy [ref] , and the unified first law [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"2001.11357","title":"Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein's and Jordan's frames","url":"/paper/2001.11357","section":"Introduction","sentence":"And their physical properties are discussed in, e.g., [ref] .","intent_p":0.94,"contests_p":null}]}],"unlabelled_sentences":33},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/gr-qc/0612089"}}