Born–Infeld inspired modifications of gravity

In this paper, we study massive gravity in the presence of Born-Infeld nonlinear electrodynamics. First, we obtain metric function related to this gravity and investigate the geometry of the solutions and find that there is an essential singularity at the origin (r = 0). It will be shown that due to contribution of the massive part, the number, type and place of horizons may be changed. Next, we calculate the conserved and thermodynamic quantities and check the validation of the first law of thermodynamics. We also investigate thermal stability of these black holes in context of canonical ensemble. It will be shown that number, type and place of phase transition points are functions of different parameters which lead to dependency of stability conditions to these parameters. Also, it will be shown how the behavior of temperature is modified due to extension of massive gravity and strong nonlinearity parameter. Next, critical behavior of the system in extended phase space by considering cosmological constant as pressure is investigated. A study regarding neutral Einstein-massive gravity in context of extended phase space is done. Geometrical approach is employed to study the thermodynamical behavior of the system in context of heat capacity and extended phase space. It will be shown that GTs, heat capacity and extended phase space have consistent results. Finally, critical behavior of the system is investigated through use of another method. It will be pointed out that the results of this method is in agreement with other methods and follow the concepts of ordinary thermodynamics.

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Einstein-Born-Infeld-Massive Gravity: adS-Black Hole Solutions and their Thermodynamical properties

The recent discovery of the novel four-dimensional static and spherically symmetric Gauss–Bonnet black hole provides a promising bed to test Gauss–Bonnet gravity by using astronomical observations (Glavan et al. in PRL 124:081301, 2020). In this paper, we first obtain the rotating Gauss–Bonnet black hole solution by using the Newman–Janis algorithm and then study the shadow cast by the nonrotating and rotating candidate Gauss–Bonnet black holes. The result indicates that positive metric parameter $$\alpha $$
 shrinks the shadow, while negative one enlarges it. Meanwhile, both the distortion and ratio of two diameters of the shadow are found to increase with the metric parameter for certain spin. Comparing with the Kerr black hole, the shadow gets more distorted for $$\alpha $$
 and less distorted for negative one. Furthermore, we calculate the angular diameter of the shadow by making use of the observation of M87*. The result indicates that negative metric parameter $$\alpha $$
 in (−4.5, 0) is more favored. Since the negative energy appears for negative $$\alpha $$
 , our results extends the study of Gauss–Bonnet gravity. We believe further study on the four-dimensional rotating black hole may shed new light on Gauss–Bonnet gravity.

Testing the nature of Gauss–Bonnet gravity by four-dimensional rotating black hole shadow

We study a specific model of anisotropic strange stars in the modified |$f\left(R,\mathcal {T}\right)$|-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that |$f(R,\mathcal {T})=R+2\chi \mathcal {T}$|⁠, where R is Ricci scalar, |$\mathcal {T}$| is the trace of the energy–momentum tensor of matter, and χ is a coupling constant. To obtain our solution to the modified Einstein equations, we successfully apply the ‘embedding class one’ techniques. We also consider the case when the strange quark matter (SQM) distribution is governed by the simplified MIT bag model equation of state given by |$p_r=\frac{1}{3}\left(\rho -4B\right)$|⁠, where B is bag constant. We calculate the radius of the strange star candidates by directly solving the modified TOV equation with the observed values of the mass and some parametric values of B and χ. The physical acceptability of our solutions is verified by performing several physical tests. Interestingly, besides the SQM, another type of matter distribution originates due to the effect of coupling between the matter and curvature terms in the |$f\left(R,\mathcal {T}\right)$| gravity theory. Our study shows that with decreasing the value of χ, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for χ < 0 the |$f\left(R,\mathcal {T}\right)$| gravity emerges as a suitable theory for explaining the observed massive stellar objects like massive pulsars, super-Chandrasekhar stars, and magnetars, etc., which remain obscure in the standard framework of General Relativity.

Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $f\left(R,\mathcal {T}\right)$ gravity

The present work is focused on the investigation of the existence of compact structures describing anisotropic matter distributions within the framework of modified gravity theories, specifically $f(R,\mathcal{T}$) gravity theory. Additionally, we have taken $f(R,\mathcal{T})$ as a linear function of the Ricci scalar $R$ and the trace of the energy-momentum tensor $\mathcal{T}$ as $f(R,\mathcal{T})=R+2\ensuremath{\chi}\mathcal{T}$, where $\ensuremath{\chi}$ is a dimensionless coupling parameter, and the Lagrangian matter ${\mathcal{L}}_{m}=\ensuremath{-}\frac{1}{3}(2{p}_{t}+{p}_{r})$, to describe the complete set of field equations for the anisotropic matter distribution. We follow the embedding class I procedure using the Eisland condition to obtain a full space-time description inside the stellar configuration. Once the space-time geometry is specified, we determine the complete solution of modified Einstein equations by using the MIT bag model equation of state ${p}_{r}=\frac{1}{3}(\ensuremath{\rho}\ensuremath{-}4B)$ that describes the strange quark matter (SQM) distribution inside the stellar system, where $B$ denotes a bag constant. The physical validity of our anisotropic solution is confirmed by executing several physical tests. It is worth mentioning that with the help of the observed mass values for the various strange star candidates, we have predicted the exact radii by taking different values for $\ensuremath{\chi}$ and $B$. These predicted radii show a monotonic decreasing nature as the parameter $\ensuremath{\chi}$ is moved from $\ensuremath{-}0.8$ to 0.8 progressively. In this case, our anisotropic stellar system becomes more massive and transforms into more dense compact stars. We also perform a detailed graphical analysis of the compact star. As a result, for $\ensuremath{\chi}l0$, the current modified $f(R,\mathcal{T})$ gravity seems promising to explain the observed massive compact astrophysical objects, similar to magnetars, massive pulsars, and Chandrasekhar super white dwarfs, which are not justified in the framework of general relativity. Finally, we note that when $\ensuremath{\chi}=0$, general relativity results for anisotropic matter distributions are recovered.

Study of anisotropic strange stars in f (R ,T ) gravity: An embedding approach under the simplest linear functional of the matter-geometry coupling

A new theory of gravity called Eddington-inspired Born–Infeld (EiBI) gravity was recently proposed by Banados and Ferreira. This theory leads to some exciting new features, such as free of cosmological singularities. In this paper, we first obtain a charged EiBI black hole solution with a nonvanishing cosmological constant when the electromagnetic field is included in. Then based on it, we study the strong gravitational lensing by the asymptotic flat charged EiBI black hole. The strong deflection limit coefficients and observables are shown to closely depend on the additional coupling parameter $$\kappa $$
 in the EiBI gravity. It is found that, compared with the corresponding charged black hole in general relativity, the positive coupling parameter $$\kappa $$
 will shrink the black hole horizon and photon sphere. Moreover, the coupling parameter will decrease the angular position and relative magnitudes of the relativistic images, while increase the angular separation, which may shine new light on testing such gravity theory in near future by the astronomical instruments.

/pdf/black-hole-solution-and-strong-gravitational-lensing-in-44kc7x0jqb.pdf

Black hole solution and strong gravitational lensing in Eddington-inspired Born–Infeld gravity

In this paper, we study numerically the quasi-equatorial lensing by the stationary, axially-symmetric black hole in Kerr-Taub-NUT spacetime in the strong field limit. The deflection angle of light ray and other strong deflection limit coefficients are obtained numerically and they are found to be closely dependent on the NUT charge n and spin a. We also compute the magnification and the positions of the relativistic images. The caustics are studied and the results show that these caustics drift away from the optical axis, which is quite different from the Schwarzschild black hole case. Moreover, the intersections of the critical curves on the equatorial plane are obtained and it is shown that they increase with the NUT charge. These results show that there is a significant effect of the NUT charge on the strong gravitational lensing.

Strong field limit analysis of gravitational lensing in Kerr-Taub-NUT spacetime

A novel four-dimensional Einstein-Gauss-Bonnet gravity was formulated by Glavan and Lin (Phys. Rev. Lett. 124:081301, 2020), which is intended to bypass the Lovelock’s theorem and to yield a non-trivial contribution to the four-dimensional gravitational dynamics. However, the validity and consistency of this theory has been called into question recently. We study a static and spherically symmetric black hole charged by a Born–Infeld electric field in the novel four-dimensional Einstein–Gauss–Bonnet gravity. It is found that the black hole solution still suffers the singularity problem, since particles incident from infinity can reach the singularity. It is also demonstrated that the Born-Infeld charged black hole may be superior to the Maxwell charged black hole to be a charged extension of the Schwarzschild-AdS-like black hole in this new gravitational theory. Some basic thermodynamics of the black hole solution is also analyzed. Besides, we regain the black hole solution in the regularized four-dimensional Einstein–Gauss–Bonnet gravity proposed by Lu and Pang (arXiv:2003.11552).

/pdf/born-infeld-black-holes-in-4d-einstein-gauss-bonnet-gravity-4mfm8ypulk.pdf

Born–Infeld black holes in 4D Einstein–Gauss–Bonnet gravity

This work tries to find out thick brane solutions in braneworld scenarios described by a real scalar field in the presence of a scalar-kinetic term F(X, )=Xm with a single extra dimension, where stands for the standard kinetic term and m=0, 1, 2...??. We mainly consider bent branes, namely de Sitter and anti-de Sitter four-dimensional slices. The solutions of a flat brane are obtained when taking the four-dimensional cosmological constant ?4?0. When the parameter m=0, these solutions turn to those of the standard scenario. The localization and spectrum of graviton on these branes are also analyzed.

http://iopscience.iop.org/article/10.1209/0295-5075/90/51001/pdf

Scalar-kinetic branes

A new theory of gravity called Eddington-inspired Born-Infeld (EiBI) gravity was recently proposed by Banados and Ferreira. This theory leads to some exciting new features, such as free of cosmological singularities. In this paper, we first obtain a charged EiBI black hole solution with a nonvanishing cosmological constant when the electromagnetic field is included in. Then based on it, we study the strong gravitational lensing by the asymptotic flat charged EiBI black hole. The strong deflection limit coefficients and observables are shown to closely depend on the additional coupling parameter $\kappa$ in the EiBI gravity. It is found that, compared with the corresponding charged black hole in general relativity, the positive coupling parameter $\kappa$ will shrink the black hole horizon and photon sphere. Moreover, the coupling parameter will decrease the angular position and relative magnitudes of the relativistic images, while increase the angular separation, which may shine new light on testing such gravity theory in near future by the astronomical instruments.

/pdf/black-hole-solution-and-strong-gravitational-lensing-in-dkic45he2q.pdf

Ke Yang

Papers

Black hole solution and strong gravitational lensing in Eddington-inspired Born–Infeld gravity

Strong field limit analysis of gravitational lensing in Kerr-Taub-NUT spacetime

Born–Infeld black holes in 4D Einstein–Gauss–Bonnet gravity

Scalar-kinetic branes

Black hole solution and strong gravitational lensing in Eddington-inspired Born-Infeld gravity