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Register a new userThermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields
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We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.
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After considering the quantum corrections of Einstein-Maxwell theory, the effective theory will contain some higher-curvature terms and nonminimally coupled electromagnetic fields. In this paper, we study the first law of black holes in the gravitational electromagnetic system with the Lagrangian $math{L}(g_{ab}, R_{abcd}, F_{ab})$. Firstly, we calculate the Noether charge and the variational identity in this theory, and then generically derive the first law of thermodynamics for an asymptotically flat stationary axisymmetrical symmetric black hole without the requirement that the electromagnetic field is smooth on the bifurcation surface. Our results indicate that the first law of black hole thermodynamics might be valid for the Einstein-Maxwell theory with some quantum corrections in the effective region.
In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einsteins theory as an intrinsic property of gravitation.
We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordstrom geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $Psi_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $chi$ which relates the perturbations of the radiative Maxwell scalars $varphi_2$ and the Weyl scalar $Psi_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhars book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordstrom spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal.
The isothermal Tolman condition and the constancy of the Klein potentials originally expressed for the sole gravitational interaction in a single fluid are here generalized to the case of a three quantum fermion fluid duly taking into account the strong, electromagnetic, weak and gravitational interactions. The set of constitutive equations including the Einstein-Maxwell-Thomas-Fermi equations as well as the ones corresponding to the strong interaction description are here presented in the most general relativistic isothermal case. This treatment represents an essential step to correctly formulate a self-consistent relativistic field theoretical approach of neutron stars.
We study several aspects of the extended thermodynamics of BTZ black holes with thermodynamic mass $M=alpha m + gamma frac{j}{ell}$ and angular momentum $J = alpha j + gamma ell m$, for general values of the parameters $(alpha, gamma)$ ranging from regular ($alpha=1, gamma=0$) to exotic ($alpha=0, gamma=1$). We show that there exist two distinct behaviours for the black holes, one when $alpha > gamma$ (mostly regular), and the other when $gamma < alpha$ (mostly exotic). We find that the Smarr formula holds for all $(alpha, gamma)$. We derive the corresponding thermodynamic volumes, which we find to be positive provided $alpha$ and $gamma$ satisfy a certain constraint. The dependence of pressure on volume is unremarkable and strictly decreasing when $alpha > gamma$, but a maximum volume emerges for large $Jgg T$ when $gamma > alpha$; consequently an exotic black hole of a given horizon circumference and temperature can exist in two distinct anti de Sitter backgrounds. We compute the reverse isoperimetric ratio, and study the Gibbs free energy and criticality conditions for each. Finally we investigate the complexity growth of these objects and find that they are all proportional to the complexity of the BTZ black hole. Somewhat surprisingly, purely exotic BTZ black holes have vanishing complexity growth.
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