Hamilton-Jacobi Formulation of the Thermodynamics of Einstein-Born-Infeld-AdS Black Holes

A Hamilton-Jacobi formalism for thermodynamics was formulated by Rajeev [Ann. Phys. 323, 2265 (2008)] based on the contact structure of the odd dimensional thermodynamic phase space. This allows one to derive the equations of state of a family of substances by solving a Hamilton-Jacobi equation (HJE). In the same work it was applied to chargeless non-rotating black holes, and the use of Born-Infeld electromagnetism was proposed to apply it to charged black holes as well. This paper fulfills this suggestion by deriving the HJE for charged non-rotating black holes using Born-Infeld theory and a negative cosmological constant. The most general solution of this HJE is found. It is shown that there exists solutions which are distinct from the equations of state of the Einstein-Born-Infeld-AdS black hole. The meaning of these solutions is discussed.Comment: 5 pages, 2 figure

Constraining scalar-tensor theories using neutron star mass and radius measurements

We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter $\beta$ for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is not able to effectively constrain the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more effectively to test alternative theories in general.Comment: 19 pages, 13 figure

Loss of hyperbolicity and tachyons in generalized Proca theories

Various groups recently demonstrated that the time evolution of simplest self-interacting vector fields, those with self-interaction potentials, can break down after a finite duration in what is called loss of hyperbolicity. We establish that this is not an isolated issue, and other generalizations of the Proca theory suffer from the same problem. Specifically, we show that vector field theories with derivative self-interactions have a similar pathology. For this, we derive the effective metric that governs the dynamics, and show that it can change signature during time evolution. We also show that, generalized Proca theories may suffer from tachyonic instabilities as well, which lead to another form of unphysical behavior.Comment: 10 pages, 4 figure