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Register a new userMass and spin of a Kerr black hole in modified gravity and a test of the Kerr black hole hypothesis
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In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter $alpha$ affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red- and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured red- and blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.
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Christodoulou and Rovelli have shown that the maximal interior volume of a Schwarzschild black hole linearly grows with time. Recently, their conclusion has been extended to the Reissner{-}Nordstr$ddot{text{o}}$m and Kerr black holes. Meanwhile, the entropy of interior volume in a Schwarzschild black hole has also been calculated. Here, a new method calculating the entropy of interior volume of the black hole is given and it can be used in more general cases. Using this method, the entropy associated with the volume of a Kerr black hole is calculated and it is found that the entropy is proportional to the Bekenstein-Hawking entropy in the early stage of black hole evaporation. Using the differential form, the entropy of interior volume in a Schwarzschild black hole is recalculated. It is shown that the proportionality coefficient between the entropy and the Bekenstein-Hawking entropy is half of that given in the previous literature. Moreover, the black hole information paradox is brought up again and discussed.
For the Schwarzschild black hole the Bekenstein-Hawking entropy is proportional to the area of the event horizon. For the black holes with two horizons the thermodynamics is not very clear, since the role of the inner horizons is not well established. Here we calculate the entropy of the Reissner-Nordstrom black hole and of the Kerr black hole, which have two horizons. For the spherically symmetric Reissner-Nordstrom black hole we used several different approaches. All of them give the same result for the entropy and for the corresponding temperature of the thermal Hawking radiation. The entropy is not determined by the area of the outer horizon, and it is not equal to the sum of the entropies of two horizons. It is determined by the correlations between the two horizons, due to which the total entropy of the black hole and the temperature of Hawking radiation depend only on mass $M$ of the black hole and do not depend on the black hole charge $Q$. For the Kerr and Kerr-Newman black holes it is shown that their entropy has the similar property: it depends only on mass $M$ of the black hole and does not depend on the angular momentum $J$ and charge $Q$.
In this paper, the shadows cast by non-rotating and rotating modified gravity black holes are investigated. In addition to the black hole spin parameter $a$ and the inclination angle $theta$ of observer, another parameter $alpha$ measuring the deviation of gravitational constant from the Newton one is also found to affect the shape of the black hole shadow. The result shows that, for fixed values of $a/M$ and $theta$, the size and perimeter of the shadows cast by the non-rotating and rotating black holes significantly increase with the parameter $alpha$, while the distortions decrease with $alpha$. Moreover, the energy emission rate of the black hole in high energy case is also investigated, and the result shows that the peak of the emission rate decreases with the parameter $alpha$.
Binary black hole may form near a supermassive black hole. The background black hole (BH) will affect the gravitational wave (GW) generated by the binary black hole. It is well known that the Penrose process may provide extra energy due to the ergosphere. In the present paper we investigate the energy amplification of the gravitational wave by a Kerr black hole background. In particular and different from the earlier studies, we compare the energies of the waves in the cases with and without a nearby Kerr BH. We find that only when the binary black hole is moving relative to the Kerr background can the GW energy be amplified. Otherwise, the energy will be suppressed by the background Kerr black hole. This finding is consistent with the inequality found by Wald for Penrose process. Taking into account realistic astrophysical scenarios, we find that the Kerr black hole background can amplify the GW energy by at most 5 times.
An exact Kerr-like solution has been obtained recently in Einstein-bumblebee gravity model where Lorentz symmetry is spontaneously broken. In this paper, we investigate the superradiance instability of the Kerr-like black hole under the perturbation of a massive scalar field. We find the Lorentz breaking parameter $L$ affects superradiance regime but not the regime of the bound states. We calculate the bound state spectrum via the continued-fraction method and show the influence of $L$ on the maximum binding energy and the damping rate. The superradiance instability could occur since the superradiance condition and the bound state condition could be both satisfied. Compared with Kerr black hole, the nature of the superradiance instability of this black hole depends non-monotonously not only on the rotation speed of the black hole $a$ and the product of the black hole mass $M$ and the field mass $mu$, but also on the Lorentz breaking parameter $L$. Through the Monte Carlo method, we find that for $l=m=1$ state the most unstable mode occurs at $L=-0.79637$, $a/M=2.213$ and $Mmu=0.439$, with the maximum growth rate of the field $omega_{I}M=1.676times10^{-6}$, which is about 10 times of that in Kerr black hole.
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