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Register a new userUniversal $p$-form black holes in generalized theories of gravity
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We explore how far one can go in constructing $d$-dimensional static black holes coupled to $p$-form and scalar fields before actually specifying the gravity and electrodynamics theory one wants to solve. At the same time, we study to what extent one can enlarge the space of black hole solutions by allowing for horizon geometries more general than spaces of constant curvature. We prove that a generalized Schwarzschild-like ansatz with an arbitrary isotropy-irreducible homogeneous base space (IHS) provides an answer to both questions, up to naturally adapting the gauge fields to the spacetime geometry. In particular, an IHS-Kahler base space enables one to construct magnetic and dyonic 2-form solutions in a large class of theories, including non-minimally couplings. We exemplify our results by constructing simple solutions to particular theories such as $R^2$, Gauss-Bonnet and (a sector of) Einstein-Horndeski gravity coupled to certain $p$-form and conformally invariant electrodynamics.
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We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct $d$-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor and its covariant derivatives of arbitrary order. Namely, we show that, apart from containing two arbitrary functions $a(r)$ and $f(r)$ (essentially, the $g_{tt}$ and $g_{rr}$ components), in any such theory the line-element may admit as a base space {em any} isotropy-irreducible homogeneous space. Technically, this ensures that the field equations generically reduce to two ODEs for $a(r)$ and $f(r)$, and dramatically enlarges the space of black hole solutions and permitted horizon geometries for the considered theories. We then exemplify our results in concrete contexts by constructing solutions in particular theories such as Gauss-Bonnet, quadratic, $F(R)$ and $F$(Lovelock) gravity, and certain conformal gravities.
Recent results of arXiv:1907.08788 on universal black holes in $d$ dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to virtually any metric theory of gravity in vacuum.
In this work, we consider that in energy scales greater than the Planck energy, the geometry, fundamental physical constants, as charge, mass, speed of light and Newtonian constant of gravitation, and matter fields will depend on the scale. This type of theory is known as Rainbow Gravity. We coupled the nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function $M(r,epsilon)$, such that we may formulate new classes of spherically symmetric regular black hole solutions, where the curvature invariants are well-behaved in all spacetime. The main differences between the General Relativity and our results in the the Rainbow gravity are: a) The intensity of the electric field is inversely proportional to the energy scale. The higher the energy scale, the lower the electric field intensity; b) the region where the strong energy condition (SEC) is violated decrease as the energy scale increase. The higher the energy scale, closer to the radial coordinate origin SEC is violated.
Gravity is believed to have deep and inherent relation to thermodynamics. We study phase transition and critical behavior in the extended phase space of asymptotic anti de-Sitter (AdS) black holes in Einstein-Horndeski gravity. We demonstrate that the black hole in Einstein-Horndeski gravity undergo phase transition and P-V criticality mimicking the van der Waals gas-liquid system. The key approach in our study is to introduce a more reasonable pressure instead of previous pressure $P=-Lambda/8pi$ related to cosmological constant $Lambda$, and this proper pressure is given insight from the asymptotical behaviour of this black hole. Moreover, we also first obtain P-V criticality in the two cases with $Lambda=0$ and $Lambda>0$ in our paper, which implicates that the cosmological constant $Lambda$ may be not a necessary pressure candidate for black holes at the microscopic level. We present critical exponents for these phase transition processes.
We analyse the classical configurations of a bootstrapped Newtonian potential generated by homogeneous spherically symmetric sources in terms of a quantum coherent state. We first compute how the mass and mean wavelength of these solutions scale in terms of the number of quanta in the coherent state. We then note that the classical relation between the ADM mass and the proper mass of the source naturally gives rise to a Generalised Uncertainty Principle for the size of the gravitational radius in the quantum theory. Consistency of the mass and wavelength scalings with this GUP requires the compactness remains at most of order one even for black holes, and the corpuscular predictions are thus recovered, with the quantised horizon area expressed in terms of the number of quanta in the coherent state. Our findings could be useful for analysing the classicalization of gravity in the presence of matter and the avoidance of singularities in the gravitational collapse of compact sources.
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