Higher Order Corrections to Black Hole Entropy

A scheme for calculating corrections to all orders to the entropy of any thermodynamic system due to statistical fluctuations around equilibrium has been developed. It is then applied to the BTZ black hole, AdS-Schwarzschild black Hole and Schwarzschild black Hole in a cavity. The scheme that we present is a model-independent scheme and hence universally applicable to all classical black holes with positive specific heat. It has been seen earlier that the microcanonical entropy of a system can be more accurately reproduced by considering a logarithmic correction to the canonical entropy function. The higher order corrections will be a step further in calculating the microcanonical entropy of a black hole.Comment: 9 pages, Revised version to appear in Classical and Quantum Gravit

The Ysz--Yx Scaling Relation as Determined from Planck and Chandra

SZ clusters surveys like Planck, the South Pole Telescope, and the Atacama Cosmology Telescope, will soon be publishing several hundred SZ-selected systems. The key ingredient required to transport the mass calibration from current X-ray selected cluster samples to these SZ systems is the Ysz--Yx scaling relation. We constrain the amplitude, slope, and scatter of the Ysz--Yx scaling relation using SZ data from Planck, and X-ray data from Chandra. We find a best fit amplitude of \ln (D_A^2\Ysz/CY_X) = -0.202 \pm 0.024 at the pivot point CY_X=8\times 10^{-5} Mpc^2. This corresponds to a Ysz/Yx-ratio of 0.82\pm 0.024, in good agreement with X-ray expectations after including the effects of gas clumping. The slope of the relation is \alpha=0.916\pm 0.032, consistent with unity at \approx 2.3\sigma. We are unable to detect intrinsic scatter, and find no evidence that the scaling relation depends on cluster dynamical state

Interpreting the strongly lensed supernova iPTF16geu: time delay predictions, microlensing, and lensing rates

We present predictions for time delays between multiple images of the gravitationally lensed supernova, iPTF16geu, which was recently discovered from the intermediate Palomar Transient Factory (iPTF). As the supernova is of Type Ia where the intrinsic luminosity is usually well-known, accurately measured time delays of the multiple images could provide tight constraints on the Hubble constant. According to our lens mass models constrained by the {\it Hubble Space Telescope} F814W image, we expect the maximum relative time delay to be less than a day, which is consistent with the maximum of 100 hours reported by Goobar et al. but places a stringent upper limit. Furthermore, the fluxes of most of the supernova images depart from expected values suggesting that they are affected by microlensing. The microlensing timescales are small enough that they may pose significant problems to measure the time delays reliably. Our lensing rate calculation indicates that the occurrence of a lensed SN in iPTF is likely. However, the observed total magnification of iPTF16geu is larger than expected, given its redshift. This may be a further indication of ongoing microlensing in this system.Comment: 5 pages, 3 figures, 1 table, ApjL accepted, minor but important correction