Abstract
Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR.
Highlights
In this paper we studied the noncommutative geometry inspired black hole solutions in Rastall gravity
If requiring the spacetime is asymptotically Minkowskian, we found Schwarzschild solution in Rastall gravity
The noncommutative geometry inspired Schwarzschild black hole (NCSBH) in general relativity (GR) is a kind of regular black hole
Summary
Where λ is the Rastall parameter and κ is the Rastall gravitational coupling constant. Eqs. When λ = 0, the traditional GR and the covariant conservation of the energy-momentum tensor are both recovered with the parameter κ = 8π G. We will consider a special case with κλ = 1/2 and correspondingly κ = 4π G In this case, the gravitational field equation turns into. We will consider a fluid-type matter source with the energy-momentum tensor μ ν satisfying μ ν. The integration constant C0 should be zero This is just the well-known Schwarzschild solution outside the source, which is the solution in vacuum. This result is expectable, because Rastall gravity is equivalent to GR in the vacuum case
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