Gravitational Waves Constrain F(R) Gravity & Black Hole Entropy Area Formula

Scientists are refining our understanding of black hole entropy with new research into corrections to the Bekenstein-Hawking area formula, potentially bridging the gap between theoretical physics and gravitational wave observations. Rohit Das, Parthasarathi Majumdar, and Debadrita Mukherjee, all from the School of Physical Sciences at the Indian Association for the Cultivation of Science, investigate these ‘inverse area’ corrections within the framework of F(R) gravity , a modification of Einstein’s general relativity , utilising the Wald formula and insights from Jacobson, Kang and Myers. Their work establishes constraints on the parameters of F(R) gravity by demanding consistency with the Hawking Area Theorem, as validated by recent gravitational wave detections of binary black hole mergers, offering a crucial test of modified gravity theories and a deeper insight into the fundamental nature of black holes,

Experiments. . Requiring absolute consistency between the coefficients of these corrections and gravitational wave observations validating the Hawking Area Theorem for binary black hole coalescences, researchers aimed to constrain the parameters defining F(R) gravity. To facilitate comparison, the work also computed inverse area corrections for black holes within general relativity, utilising a modified Wheeler’s “It from Bit” approach informed by tenets of Loop Quantum Gravity. The team calculated the entropy by applying the Wald entropy function, initially formulated as involving integration of a ‘N other charge’ over the bifurcation of a Killing horizon.
However, leveraging the generalization demonstrated by Jacobson et al, they integrated the conserved N other current over any two-dimensional cross-section of the horizon, specifically employing a spatial foliation. This methodological innovation proved particularly useful for estimating inverse power-law corrections to the area formula for stationary spherical black holes in modified gravity theories. Restricting attention to spherically symmetric, static black hole solutions of F(R) gravity, the researchers integrated over 2-spheres S as cross-sections. For large areas, corresponding to astrophysical black holes observed via gravitational waves from binary black hole coalescences, the Wald-Jacobson-Kang-Myers Entropy function admitted a Taylor expansion in inverse powers of the horizon cross-sectional area.

Coefficients within this expansion were determined by derivatives of F(R) with respect to R, evaluated at R|S = 0. Identifying the leading term with the black hole area formula for F(R) gravity, the remaining expansion terms were recast as inverse powers of the black hole entropy. The study then established an absolute consistency criterion, linking corrections to the area formula with gravitational wave observations, thereby restricting higher-order derivatives of F(R) with respect to R at R|S = 0, effectively defining parameters of the modified gravity theory. Furthermore, the correction terms to the area formula were resummed, yielding a concise form for the restrictions on F(R) parameters implied by consistency with gravitational wave data. Specifically, for spherically symmetric, static black hole solutions of F(R) gravity, the integration cross-sections were 2-spheres, and for large areas, the entropy function admits a Taylor expansion in inverse powers of the horizon cross-section area. The coefficients of this expansion are determined by derivatives of F(R) with respect to R at R|S = 0.

Results demonstrate. The team further showed that these correction terms to the BHAF can be resummed, leading to a concise form of the restrictions on F(R) parameters implied by consistency with gravitational wave observations. Measurements confirm that the calculation of the first sub-leading inverse area correction to the BHAF, using Wheeler’s ‘It From Bit’ argument modified by Loop Quantum Gravity, provides a valuable comparison point. The work establishes a clear link between theoretical calculations of black hole entropy and observational data from gravitational wave astronomy, offering a powerful new approach to testing modified gravity theories.