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Register a new userEntropies and The First Laws of Black Hole Thermodynamics in Einstein-aether-Maxwell Theory
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Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and definitive entropy expressions at both Killing and universal horizons for some examples of exact black hole solutions, including 3-dimensional static charged quasi-BTZ black hole, two 4-dimensional static charged black holes and 3-dimensional rotating solution. At Killing horizons the entropies are exactly one quarter of the horizon area, but at universal horizons of 3-dimensional black holes, the entropies have a corrected term in addition to the one proportional to the horizon area.
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Exact black hole solutions in the Einstein-Maxwell-scalar theory are constructed. They are the extensions of dilaton black holes in de Sitter or anti de Sitter universe. As a result, except for a scalar potential, a coupling function between the scalar field and the Maxwell invariant is present. Then the corresponding Smarr formula and the first law of thermodynamics are investigated.
We consider whether the new horizon-first law works in higher-dimensional $f(R)$ theory. We firstly obtain the general formulas to calculate the entropy and the energy of a general spherically-symmetric black hole in $D$-dimensional $f(R)$ theory. For applications, we compute the entropies and the energies of some black hokes in some interesting higher-dimensional $f(R)$ theories.
We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordstrom black holes. They also possess a finite mass $M$ and electric charge $Q_e$, with $Q_e/M>1$. An exact wormhole solution with ungauged, massless fermions is also reported.
In this paper, we systematically study spherically symmetric static spacetimes in the framework of Einstein-aether theory, and pay particular attention to the existence of black holes (BHs). In the present studies we first clarify several subtle issues. In particular, we find that, out of the five non-trivial field equations, only three are independent, so the problem is well-posed, as now generically there are only three unknown functions, {$F(r), B(r), A(r)$, where $F$ and $B$ are metric coefficients, and $A$ describes the aether field.} In addition, the two second-order differential equations for $A$ and $F$ are independent of $B$, and once they are found, $B$ is given simply by an algebraic expression of $F,; A$ and their derivatives. To simplify the problem further, we explore the symmetry of field redefinitions, and work first with the redefined metric and aether field, and then obtain the physical ones by the inverse transformations. These clarifications significantly simplify the computational labor, which is important, as the problem is highly involved mathematically. In fact, it is exactly because of these, we find various numerical BH solutions with an accuracy that is at least two orders higher than previous ones. More important, these BH solutions are the only ones that satisfy the self-consistent conditions and meantime are consistent with all the observational constraints obtained so far. The locations of universal horizons are also identified, together with several other observationally interesting quantities, such as the innermost stable circular orbits (ISCO), the ISCO frequency, and the maximum redshift $z_{max}$ of a photon emitted by a source orbiting the ISCO. All of these quantities are found to be quite close to their relativistic limits.
We present several new exact solutions in five and higher dimensional Einstein-Maxwell theory by embedding the Nutku instanton. The metric functions for the five-dimensional solutions depend only on a radial coordinate and on two spatial coordinates for the six and higher dimensional solutions. The six and higher dimensional metric functions are convoluted-like integrals of two special functions. We find that the solutions are regular almost everywhere and some spatial sections of the solution describe wormhole handles. We also find a class of exact and nonstationary convoluted-like solutions to the Einstein-Maxwell theory with a cosmological constant.
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