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We present a family of extensions of spherically symmetric Einstein-Lanczos-Lovelock gravity. The field equations are second order and obey a generalized Birkhoffs theorem. The Hamiltonian constraint can be written in terms of a generalized Misner-Sharp mass function that determines the form of the vacuum solution. The action can be designed to yield interesting non-singular black-hole spacetimes as the unique vacuum solutions, including the Hayward black hole as well as a completely new one. The new theories therefore provide a consistent starting point for studying the formation and evaporation of non-singular black holes as a possible resolution to the black hole information loss conundrum.
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We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoffs theorem. In complete analogy with spherically symmetric Einstein-Lanczos-Lovelock gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black-hole spacetimes than previously available.
We investigate static and rotating charged spherically symmetric solutions in the framework of $f({cal R})$ gravity, allowing additionally the electromagnetic sector to depart from linearity. Applying a convenient, dual description for the electromagnetic Lagrangian, and using as an example the square-root $f({cal R})$ correction, we solve analytically the involved field equations. The obtained solutions belong to two branches, one that contains the Kerr-Newman solution of general relativity as a particular limit and one that arises purely from the gravitational modification. The novel black hole solution has a true central singularity which is hidden behind a horizon, however for particular parameter regions it becomes a naked one. Furthermore, we investigate the thermodynamical properties of the solutions, such as the temperature, energy, entropy, heat capacity and Gibbs free energy. We extract the entropy and quasilocal energy positivity conditions, we show that negative-temperature, ultracold, black holes are possible, and we show that the obtained solutions are thermodynamically stable for suitable model parameter regions.
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.
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.
We systematically study the field equations of $f(mathbb Q)$ gravity for spherically symmetric and stationary metric-affine spacetimes. Such spacetimes are described by a metric as well as a flat and torsionless affine connection. In the Symmetric Teleparallel Equivalent of GR (STEGR), the connection is pure gauge and hence unphysical. However, in the non-linear extension $f(Q)$, it is promoted to a dynamical field which changes the physics. Starting from a general metric-affine geometry, we construct the most general static and spherically symmetric forms of the metric and the affine connection. We then use these symmetry reduced geometric objects to prove that the field equations of $f(Q)$ gravity admit GR solutions as well as beyond-GR solutions, contrary to what has been claimed in the literature. We formulate precise criteria, under which conditions it is possible to obtain GR solutions and under which conditions it is possible to obtain beyond-GR solutions. We subsequently construct several perturbative corrections to the Schwarzschild solution for different choices of $f(Q)$, which in particular include a hair stemming from the now dynamical affine connection. We also present an exact beyond-GR vacuum solution. Lastly, we apply this method of constructing spherically symmetric and stationary solutions to $f(T)$ gravity, which reproduces similar solutions but without a dynamical connection.
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