Quasi-homogeneous black hole thermodynamics

Although the fundamental equations of ordinary thermodynamic systems are known to correspond to first-degree homogeneous functions, in the case of non-ordinary systems like black holes the corresponding fundamental equations are not homogeneous. We present several arguments, indicating that black holes should be described by means of quasi-homogeneous functions of degree different from one. In particular, we show that imposing the first-degree condition leads to contradictory results in thermodynamics and geometrothermodynamics of black holes. As a consequence, we show that in generalized gravity theories the coupling constants like the cosmological constant, the Born-Infeld parameter or the Gauss-Bonnet constant must be considered as thermodynamic variables

Predictive Modeling of the Non-Profit Sector in the US

The Non-Profit Sector contributes almost $1 trillion to the US economy, representing 5.4% of GDP, and generating over 12 million jobs in 2017. Yi (2010) suggests that a better understanding of the factors that affect fundraising should be of great interest to policy makers, and fundraisers. However, the workings of the sector are subject of much debate. Matsunaga, Yamauchi and Okuyama (2010) relate its size to the Theory of Government Failure. Sokolowski (2013) proposes that government funding does have a positive effect on revenues. Curry, Rodin and Carlson (2012) suggested they swing with GDP, but, Berman, Brooks and Murphy (2006) contend that macroeconomic variables do not affect short-run dynamics. List (2011) found that non-profit revenues react more to economic upswings than downturns. And the National Philanthropic Trust (2016) relates ups and downs to certain events and public awareness. Wallace (2016) points to the fact that predictive modeling has focused big-donor analytics, aimed at the identification of potential donors. We set out instead to define a working model. After locating complete time series for an emblematic segment, the environmental cause, Factor Analysis allowed us to pinpoint independent variables. We found that Non-Profit Revenues (NPR) depend largely on Public Awareness, as measured by TV coverage, and Disposable Personal Income (DPI), specifically: NPR = -4401.542 + 528.327(DPI) +23.121(TVCoverage) +

Pioneer's Anomaly and the Solar Quadrupole Moment

The trajectories of test particles moving in the gravitational field of a non-spherically symmetric mass distribution become affected by the presence of multipole moments. In the case of hyperbolic trajectories, the quadrupole moment of an oblate mass induces a displacement of the trajectory towards the mass source, an effect that can be interpreted as an additional acceleration directed towards the source. Although this additional acceleration is not constant, we perform a general relativistic analysis in order to evaluate the possibility of explaining Pioneer's anomalous acceleration by means of the observed Solar quadrupole moment, within the range of accuracy of the observed anomalous acceleration. We conclude that the Solar quadrupole moment generates an acceleration which is of the same order of magnitude of Pioneer's constant acceleration only at distances of a few astronomical units.Comment: Typos corrected, references adde

Matching conditions in relativistic astrophysics

We present an exact electrovacuum solution of Einstein-Maxwell equations with infinite sets of multipole moments which can be used to describe the exterior gravitational field of a rotating charged mass distribution. We show that in the special case of a slowly rotating and slightly deformed body, the exterior solution can be matched to an interior solution belonging to the Hartle-Thorne family of approximate solutions. To search for exact interior solutions, we propose to use the derivatives of the curvature eigenvalues to formulate a $C^3-$matching condition from which the minimum radius can be derived at which the matching of interior and exterior spacetimes can be carried out. We prove the validity of the $C^3-$matching in the particular case of a static mass with a quadrupole moment. The corresponding interior solution is obtained numerically and the matching with the exterior solution gives as a result the minimum radius of the mass configuration

Multipole structure of compact objects

We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of compact objects. We focus on the interpretation of exact solutions of Einstein's equations in terms of their multipole moments structure. In view of the lack of physical interior solutions, we propose an alternative approach in which higher multipoles should be taken into account