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Register a new userAction growth for black holes in modified gravity
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The general form of the action growth for a large class of static black hole solutions in modified gravity which includes $F(R)$-gravity models is computed. The cases of black hole solutions with non vanishing Ricci curvature are also considered, generalizing the results previously found and valid only for constant curvature black holes. An argument is put forward to provide a physical interpretation of the results.
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A covariant modified gravity (MOG) is formulated by adding to general relativity two new degrees of freedom, a scalar field gravitational coupling strength $G= 1/chi$ and a gravitational spin 1 vector field $phi_mu$. The $G$ is written as $G=G_N(1+alpha)$ where $G_N$ is Newtons constant, and the gravitational source charge for the vector field is $Q_g=sqrt{alpha G_N}M$, where $M$ is the mass of a body. Cosmological solutions of the theory are derived in a homogeneous and isotropic cosmology. Black holes in MOG are stationary as the end product of gravitational collapse and are axisymmetric solutions with spherical topology. It is shown that the scalar field $chi$ is constant everywhere for an isolated black hole with asymptotic flat boundary condition. A consequence of this is that the scalar field loses its monopole moment radiation.
The Complexity=Action conjecture is studied for black holes in Warped AdS$_3$ space, realized as solutions of Einstein gravity plus matter. The time dependence of the action of the Wheeler-DeWitt patch is investigated, both for the non-rotating and the rotating case. The asymptotic growth rate is found to be equal to the Hawking temperature times the Bekenstein-Hawking entropy; this is in agreement with a previous calculation done using the Complexity=Volume conjecture.
In the context of the recently proposed type-II minimally modified gravity theory, i.e. a metric theory of gravity with two local physical degrees of freedom that does not possess an Einstein frame, we study spherically symmetric vacuum solutions to explore the strong gravity regime. Despite the absence of extra degrees of freedom in the gravity sector, the vacuum solutions are locally different from the Schwarzschild or Schwarzschild-(A)dS metric in general and thus the Birkhoff theorem does not hold. The general solutions are parameterized by several free functions of time and admit regular trapping and event horizons. Depending on the choice of the free functions of time, the null convergence condition may be violated in vacuum. Even in the static limit, while the solutions in this limit reduce to the Schwarzschild or Schwarzschild-(A)dS solutions, the effective cosmological constant deduced from the solutions is in general different from the cosmological value that is determined by the action. Nonetheless, once a set of suitable asymptotic conditions is imposed so that the solutions represent compact objects in the corresponding cosmological setup, the standard Schwarzschild or Schwarzschild-(A)dS metric is recovered and the effective cosmological constant agrees with the value inferred from the action.
Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of vector-tensor theories of modified gravity, valid for arbitrary values of the rotation parameter. The new configuration is characterised by parametrically large deviations from the Kerr-Newman geometry, controlled by non-minimal couplings between vectors and gravity. It has an oblate horizon in Boyer-Lindquist coordinates, and it can rotate more rapidly and have a larger ergosphere than black holes in General Relativity (GR) with the same asymptotic properties. We analytically investigate the features of the innermost stable circular orbits for massive objects on the equatorial plane, and show that stable orbits lie further away from the black hole horizon with respect to rotating black holes in GR. We also comment on possible applications of our findings for the extraction of rotational energy from the black hole.
We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -mu^2/4 +c_2 m^2$ in the four dimensional case, where $mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.
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