Black hole entropy, flat directions and higher derivatives

Higher order derivative corrections to the Einstein--Maxwell action are considered and an explicit form is found for the corrections to the entropy of extremal black holes. We speculate on the properties of these corrections from the point of view of small black holes and in the case when the classical black hole potential exhibits flat directions. A particular attention is paid to the issue of stability of several solutions, including large and small black holes by using properties of the Hessian matrix of the effective black hole potential. This is done by using a model independent expression for such matrix derived within the entropy function formalism.Comment: 21 pages, PACS numbers: 04.50.Gh, 04.70.Dy, 04.65.+

Corrections to the statistical entropy of five dimensional black holes

We compute the statistical entropy of the three charge (D1-D5-p) five dimensional black hole to sub-leading order in a large charge expansion. We find an agreement with the macroscopic calculation of the Wald entropy in R^2 corrected supergravity theory. The two calculations have a overlapping regime of validity which is not the Cardy regime. We use this result to clarify the 4d-5d lift for black holes on Taub-NUT space. In particular, we compute sub-leading corrections to the formula S^{4d} = S^{5d}. In the microscopic analysis, this correction arises from excitations bound to the Taub-NUT space. In the macroscopic picture, the difference is accounted by a mechanism present in a higher derivative theory wherein the geometry of the Taub-NUT space absorbes some of the electric charge.Comment: 25 pages. Few changes and improvements. To be published in JHE

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Insights into the high-energy γ-ray emission of Markarian 501 from extensive multifrequency observations in the Fermi era

We report on the γ-ray activity of the blazar Mrk 501 during the first 480 days of Fermi operation. We find that the average Large Area Telescope (LAT) γ-ray spectrum of Mrk 501 can be well described by a single power-law function with a photon index of 1.78 ± 0.03. While we observe relatively mild flux variations with the Fermi-LAT (within less than a factor of two), we detect remarkable spectral variability where the hardest observed spectral index within the LAT energy range is 1.52 ± 0.14, and the softest one is 2.51 ± 0.20. These unexpected spectral changes do not correlate with the measured flux variations above 0.3 GeV. In this paper, we also present the first results from the 4.5 month long multifrequency campaign (2009 March 15-August 1) on Mrk 501, which included the Very Long Baseline Array (VLBA), Swift, RXTE, MAGIC, and VERITAS, the F-GAMMA, GASP-WEBT, and other collaborations and instruments which provided excellent temporal and energy coverage of the source throughout the entire campaign. The extensive radio to TeV data set from this campaign provides us with the most detailed spectral energy distribution yet collected for this source during its relatively low activity. The average spectral energy distribution of Mrk 501 is well described by the standard one-zone synchrotron self-Compton (SSC) model. In the framework of this model, we find that the dominant emission region is characterized by a size ≲0.1 pc (comparable within a factor of few to the size of the partially resolved VLBA core at 15-43 GHz), and that the total jet power (≃1044 erg s-1) constitutes only a small fraction (∼10-3) of the Eddington luminosity. The energy distribution of the freshly accelerated radiating electrons required to fit the time-averaged data has a broken power-law form in the energy range 0.3 GeV-10 TeV, with spectral indices 2.2 and 2.7 below and above the break energy of 20 GeV. We argue that such a form is consistent with a scenario in which the bulk of the energy dissipation within the dominant emission zone of Mrk 501 is due to relativistic, proton-mediated shocks. We find that the ultrarelativistic electrons and mildly relativistic protons within the blazar zone, if comparable in number, are in approximate energy equipartition, with their energy dominating the jet magnetic field energy by about two orders of magnitude. © 2011. The American Astronomical Society

Unraveling the Complex Behavior of Mrk 421 with Simultaneous X-Ray and VHE Observations during an Extreme Flaring Activity in 2013 April

© 2020. The American Astronomical Society. All rights reserved. We report on a multiband variability and correlation study of the TeV blazar Mrk 421 during an exceptional flaring activity observed from 2013 April 11 to 19. The study uses, among others, data from GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT), Swift, Nuclear Spectroscopic Telescope Array (NuSTAR), Fermi Large Area Telescope, Very Energetic Radiation Imaging Telescope Array System (VERITAS), and Major Atmospheric Gamma Imaging Cherenkov (MAGIC). The large blazar activity and the 43 hr of simultaneous NuSTAR and MAGIC/VERITAS observations permitted variability studies on 15 minute time bins over three X-ray bands (3-7 keV, 7-30 keV, and 30-80 keV) and three very-high-energy (VHE; >0.1 TeV) gamma-ray bands (0.2-0.4 TeV, 0.4-0.8 TeV, and >0.8 TeV). We detected substantial flux variations on multi-hour and sub-hour timescales in all of the X-ray and VHE gamma-ray bands. The characteristics of the sub-hour flux variations are essentially energy independent, while the multi-hour flux variations can have a strong dependence on the energy of the X-rays and the VHE gamma-rays. The three VHE bands and the three X-ray bands are positively correlated with no time lag, but the strength and characteristics of the correlation change substantially over time and across energy bands. Our findings favor multi-zone scenarios for explaining the achromatic/chromatic variability of the fast/slow components of the light curves, as well as the changes in the flux-flux correlation on day-long timescales. We interpret these results within a magnetic reconnection scenario, where the multi-hour flux variations are dominated by the combined emission from various plasmoids of different sizes and velocities, while the sub-hour flux variations are dominated by the emission from a single small plasmoid moving across the magnetic reconnection layer