arXiv subjects

Sunil D. Maharaj

Publications and source records attributed to Sunil D. Maharaj.

At least 37 records · Page 2Linked to original sources

arXiv2022

Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent

We study the dynamics of test particle and stability of circular geodesics in the gravitational field of a non-commutative geometry inspired Schwarzschild black hole spacetime (NCSBH). The coordinate time Lyapunov exponent ($λ_{c}$) is crucial to investigate the stability of equatorial circular geodesics of massive and massless test particles. The stability or instability of circular orbits are discussed by analysing the variation of Lyapunov exponent with radius of these orbits for different values of non-commutative parameter ($α$). In the case of null circular orbits, the instability exponent is calculated and presented to discuss the instability of null circular orbits. Further, by relating parameters corresponding to null circular geodesics (i.e. angular frequency and Lyapunov exponent), the quasinormal modes (QNMs) for a massless scalar field perturbation in the eikonal approximation are evaluated, and also visualised by relating the real and imaginary parts. The nature of scalar field potential, by varying the non-commutative parameter ($α$) and angular momentum of perturbation ($l$), are also observed and discussed.

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arXiv2021

A semi-tetrad decomposition of the Kerr spacetime

In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the ergoregion. As a result we are able to explicitly write down the 1+1+2 Kerr quantities, and the evolution and propagation equations they satisfy. This formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner; and also to highlight the role of vorticity. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.

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arXiv2021

Nonsingular black hole chemistry

We study the nonsingular black hole in Anti de-Sitter background taking the negative cosmological constant as the pressure of the system. We investigate the horizon structure, and find the critical values $m_0$ and $\tilde{k}_0$, such that $m>m_0$ (or $\tilde{k}<\tilde{k}_0$) corresponds to a black solution with two horizons, namely the Cauchy horizon $x_-$ and the event horizon $x_+$. For $m=m_0$ (or $\tilde{k}=\tilde{k}_0$), there exist an extremal black hole with degenerate horizon $x_0=x_{\pm}$ and for $m \tilde{k}_0$), no black hole solution exists. In turn, we calculate the thermodynamical properties and by observing the behaviour of Gibb's free energy and specific heat, we find that this black hole solution exhibits first order (small to large black hole) and second order phase transition. Further, we study the $P-V$ criticality of system and then calculate the critical exponents showing that they are the same as those of the Van der Waals fluid.

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arXiv2021

Necessity of spacetime shear for cosmological gravitational waves

We show that a general but shear-free perturbation of homogeneous and isotropic universes are necessarily silent, without any gravitational waves. We prove this in two steps. First we establish that a shear free perturbation of these universes are acceleration-free and the fluid flow geodesics of the background universe maps onto themselves in the perturbed universe. This effect then decouples the evolution equations of the electric and magnetic parts of the Weyl tensor in the perturbed spacetimes and the magnetic part no longer contains any tensor modes. Although the electric part, that drives the tidal forces, do have tensor modes sourced by the anisotropic stress, these modes have homogeneous oscillations at every point on a time slice without any wave propagation. We also show the presence of vorticity vector waves that are sourced by the curl of heat flux. This analysis shows the critical role of the shear tensor in generating cosmological gravitational waves in an expanding universe.

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arXiv2021

On homothetic Killing vectors in stationary axisymmetric vacuum spacetimes

In this paper we consider homothetic Killing vectors in the class of stationary axisymmetric vacuum (SAV) spacetimes, where the components of the vectors are functions of the time and radial coordinates. In this case the component of any homothetic Killing vector along the $z$ direction must be constant. Firstly, it is shown that either the component along the radial direction is constant or we have the proportionality $g_{ϕϕ}\propto g_{ρρ}$, where $g_{ϕϕ}>0$. In both cases, complete analyses are carried out and the general forms of the homothetic Killing vectors are determined. The associated conformal factors are also obtained. The case of vanishing twist in the metric, i.e., $ω= 0$ is considered and the complete forms of the homothetic Killing vectors are determined, as well as the associated conformal factors.

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arXiv2021

Noncommutative inspired black holes in regularised 4D Einstein-Gauss-Bonnet theory

Low energy limits of string theory indicated that the standard gravity action should be modified to include higher-order curvature terms, in the form of dimensionally continued Gauss-Bonnet densities. If one includes only quadratic curvature terms then the resulting theory is Einstein-Gauss-Bonnet (EGB) gravity valid only in $D>4$ dimensions. Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit, of EGB gravity, and the resulting regularized $4D$ EGB gravities have nontrivial gravitational dynamics. We obtain a static spherically symmetric noncommutative (NC) geometry inspired black hole solution with Gaussian mass distribution as a source in the regularized $4D$ EGB and also analyze their properties. The metric of the NC inspired $4D$ EGB black hole smoothly interpolates between a de Sitter core around the origin and $4D$ EGB metric as $r/\sqrtθ \to \infty$. Owing to the NC and GB term corrected black hole, the thermodynamic quantities have also been altered. The phase transitions for the local thermodynamic stability, in the theory, is outlined by a discontinuity of specific heat $C_{+}$ at a critical radius $r_+=r_C$, and $C_{+}$ changes from infinitely negative to infinitely positive and then down to a finite positive for the smaller $r_+$. The thermal evaporation process leads to a thermodynamic stable extremal black hole with vanishing temperature.

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arXiv2020

Matter shear and vorticity in conformally flat spacetimes

In this paper we consider conformally flat perturbations on the Friedmann Lemaitre Robertson Walker (FLRW) spacetime containing a general matter field. Working with the linearised field equations, we unearth some important geometrical properties of matter shear and vorticity and how they interact with the thermodynamical quantities in the absence of any free gravity powered by the Weyl curvature. As there are hardly any physically realistic rotating exact conformally flat solutions in general relativity, these covariant and gauge invariant results bring out transparently the role of vorticity in the linearised regime. Most interestingly, we demonstrate that the matter shear obeys a transverse traceless tensor wave equation, and the vorticity obeys a vector wave equation in this regime. These shear and vorticity waves replace the gravitational waves in the sense that they causally carry the information about local change in the curvature of these spacetimes.

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arXiv2020

Phase transition of AdS black holes in 4D EGB gravity coupled to nonlinear electrodynamics

Einstein-Gauss-Bonnet (EGB) gravity is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in $ D > 4$ dimensions and EGB gravity is topologically invariant in $4D$. Recently several ways have been proposed for regularizing, a $ D \to 4 $ limit of EGB, for nontrivial gravitational dynamics in $ 4D $. Motivated by the importance of anti-de Sitter gravity/conformal field theory correspondence (AdS/CFT), we analyze black holes with AdS asymptotic to regularized $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED) field. For a static spherically symmetric \textit{ansatz} the field equations are solved exactly, using two different approaches, for a NED Lagrangian to obtain an identical solution$-$namely NED charged AdS black holes in $4D$ EGB gravity which retains several known solutions. Owing to the NED charge corrected EGB black holes, the thermodynamic quantities are also modified, and the entropy does not obey the usual area law. We calculate the heat capacity and Helmholtz free energy, in terms of horizon radii, to investigate both local and global thermodynamic stability of black holes. We observe a secondary Hawking-Page transition between the smaller thermally favoured black hole and thermal AdS space. Our results show that the behaviour of Hawking's evaporation abruptly halts at shorter radii regime such that the black holes do have a thermodynamically stable remnant with vanishing temperature.

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arXiv2020

Matching conditions in Locally Rotationally Symmetric spacetimes and radiating stars

We recast the well known Israel-Darmois matching conditions for Locally Rotationally Symmetric (LRS-II) spacetimes using the semitetrad 1+1+2 covariant formalism. This demonstrates how the geometrical quantities including the volume expansion, spacetime shear, acceleration and Weyl curvature of two different spacetimes are related at a general matching surface inheriting the symmetry, which can be timelike or spacelike. The approach is purely geometrical and depends on matching the Gaussian curvature of 2-dimensional sheets at the matching hypersurface. This also provides the constraints on the thermodynamic quantities on each spacetime so that they can be matched smoothly across the surface. As an example we regain the Santos boundary conditions and model of a radiating star matched to a Vaidya exterior in general relativity.

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arXiv2020

Clouds of strings in $4D$ Einstein-Gauss-Bonnet black holes

Recently it has been shown that the Einstein-Gauss-Bonnet (EGB) gravity, by rescaling the coupling constant as $α/(D-4)$ and taking the limit $D \rightarrow 4$ at the level of the equations of motion, becomes nontrivially ghost-free in $4D$ - namely the novel $4D$ EGB gravity. We present an exact charged black hole solution to the theory surrounded by clouds of string (CS) and also analyze their thermodynamic properties to calculate exact expressions for the black hole mass, temperature, and entropy. Owing to the corrected black hole due to the background CS, the thermodynamic quantities have also been corrected except for the entropy, which remains unaffected by a CS background. However, as a result of the novel $4D$ EGB theory, the Bekenstein-Hawking area law turns out to be corrected by a logarithmic area term. The heat capacity $C_+$ diverges at a critical radius $r=r_C$, where incidentally the temperature has a maximum, and the Hawking-Page transitions even in absence of the cosmological term and $C_+ > 0$ for $r_+ < r_C$ allowing the black hole to become thermodynamically stable. In addition, the smaller black holes are globally preferred with negative free energy $F_+<0$. Our solution can also be identified as a $4D$ monopole-charged EGB black hole. We regain results of spherically symmetric black hole solutions of general relativity and that of novel $4D$ EGB, respectively, in the limits $α\to 0$ and $a=0$.

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arXiv2020

Quasinormal modes, shadow and greybody factors of 5D electrically charged Bardeen black holes

We study quasinormal modes (QNMs) in 5D electrically charged Bardeen black holes spacetime by considering the scalar and electromagnetic field perturbations. The black holes spacetime is an exact solution of Einstein gravity coupled to nonlinear electrodynamics in five dimensions, which has nonsingular behavior. To calculate QNMs, we use the WKB approximation method up to sixth order. Due to the presence of electric charge $q_e > 0$, both the scalar and electromagnetic field perturbations decay more slowly when compared to the Schwarzschild-Tangherlini black holes. We discover that the scalar field perturbations oscillate more rapidly when compared to the electromagnetic field perturbations. In terms of damping, the scalar field perturbations damp more quickly. Graphically we show that the transmission (reflection) coefficients decrease (increase) with an increase in the magnitude of the electric charge $q_e$. The emission of gravitational waves allows spacetime to undergo damped oscillations due to the nonzero value of the imaginary part, which is always negative. The imaginary part of the QNMs frequencies is continuously decreasing with an increase in the magnitude of the electric charge $q_e$ for a given mode ($l,n$). A connection between the QNMs frequencies and the black hole shadow, as well as the geometric cross-section in the eikonal limit, is also described.

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arXiv2020

Radiating black holes in the novel 4D Einstein-Gauss-Bonnet gravity

Recently Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] formulated a novel Einstein-Gauss-Bonnet gravity in which the Gauss-Bonnet coupling has been rescaled as $α/(D-4)$ and the $4D$ theory is defined as the limit $D \rightarrow 4$, which preserves the number degrees of freedom thereby free from the Ostrogradsky instability. We present exact spherically symmetric nonstatic null dust solutions in the novel 4D Einstein-Gauss-Bonnet gravity that bypasses the Lovelock theorem. Our solution represents radiating black holes and regains, in the limit $α\rightarrow 0$, the famous Vaidya black hole of general relativity (GR). We discuss the horizon structure of black hole solutions to find that the three horizon-like loci that characterizes its structure, viz. $AH$, $EH$ and $ TLS $ have the relationship $r_{EH} < r_{AH} = r_{TLS}$. The charged radiating black holes in the theory, generalizing Bonnor-Vaidya black holes, are also considered. In particular our results, in the limit $α\rightarrow 0$, reduced exactly to \emph{vis-$\grave{a}$-vis} 4D black holes of GR.

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arXiv2020

Anisotropic generalization of Vaidya-Tikekar superdense star

We study superdense relativistic stars with anisotropic matter distributions with spheroidal spatial hypersurfaces. We propose a methodology to make an anisotropic generalization of the Vaidya-Tikekar superdense star model. The anisotropic Einstein field equations can be solved in terms of hypergeometric functions for our choice of gravitational potential and anisotropy. Particular parameter choices allow us to generate models of anisotropic stars in terms of elementary functions. Also, isotropic stars can be generated in the limit of vanishing anisotropy. In particular, we obtain the well known superdense models of Tikekar which are isotropic and have specific spheroidal geometries. The impact of anisotropy on the gross physical behaviour of a compact star is studied.

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arXiv2020

An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz [{\it Astrophys. Astron.} {\bf 3} (1982) 325] for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya-Tikekar parameter, $k$, indicating deviation form sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions required for a relativistic charged fluid sphere as an interior to a charged star. We also obtain and discuss charged analogue of the Buchdahl compactness bound.

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arXiv2020

Ergosphere and shadow of a rotating regular black hole

The spacetime singularities in classical general relativity predicted by the celebrated singularity theorems are formed at the end of gravitational collapse. Quantum gravity is the expected theory to resolve the singularity problem, but we are now far from it. Therefore attention has shifted to models of regular black holes free from the singularities. A spherically symmetric regular toy model was obtained by Dymnikova (1992) which we demonstrate as an exact solution of Einstein's field equations coupled to nonlinear electrodynamics for a Lagrangian with parameter $b$ related to magnetic charge. We construct rotating counterpart of this solution which encompasses the Kerr black hole as a special case when charge is switched off ($b=0$). Event Horizon Telescope has released the first image of supermassive black hole M87$^*$, revealing the structure near black hole horizon. The rotating regular black hole's shadow may be useful to determine strong field regime. We investigate ergosphere and black hole shadow of rotating regular black hole to infer that their sizes are sensitive to charge $b$ and have a richer chaotic structure. In particular, rotating regular black hole possess larger size, but less distorted shadows when compared with Kerr black holes. We find one to one correspondence between ergosphere and shadow of the black hole.

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arXiv2020

Rotating five-dimensional electrically charged Bardeen regular black holes

We derive a rotating counterpart of the five-dimensional electrically charged Bardeen regular black holes spacetime by employing the Giampieri algorithm on static one. The associated nonlinear electrodynamics source is computed in order to justify the rotating solution. We thoroughly discuss the energy conditions and the other properties of the rotating spacetime. The black hole thermodynamics of the rotating spacetime is also presented. In particular, the thermodynamic quantities such as the Hawking temperature and the heat capacity are calculated and plotted to see the thermal behavior. The Hawking temperature profile of the black hole implies that the regular black holes are thermally colder than its singular counterpart. On the other hand, we find that the heat capacity has two branches: the negative branch corresponds to the unstable phase and the positive branch corresponds to that of the stable phase for a suitable choice of the physical parameters characterizing the black holes.

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arXiv2020

Non-existence of expansion-free dynamical stars with rotation and spatial twist

Extending a previous work by the same authors, we investigate the existence of expansion-free dynamical stars with non-zero spatial twist and rotation and show that such stars cannot exist. Firstly, it is shown that a rotating expansion-free dynamical star with zero twist cannot exist. This is due to the fact that such stars cannot radiate and they are shear-free, in which case the energy density $ρ$ is time independent. Secondly, we prove that a non-rotating expansion-free dynamical star with non-zero spatial twist also cannot exist, as either the strong energy condition must be violated, i.e. $ρ+3p<0$, or the star must be shear-free in which case the star is static ($Θ=Ω=Σ=0$). Finally, if we insist that the rotation and spatial twist are simultaneously non-zero, then the star cannot be shear-free in which case we obtain a quadratic polynomial equation in $ϕ$ and $Σ$ with no real solutions. Therefore such stars cannot exist.

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arXiv2019

Bardeen-like regular black holes in $5D$ Einstein-Gauss-Bonnet gravity

We find an exact spherically symmetric regular Bardeen-like solutions by considering the coupling between Einstein-Gauss-Bonnet theory and nonlinear electrodynamics (NED) in five-dimensional spacetime. These solutions, with an additional parameter $g$ apart from the mass $M$, represent black holes with Cauchy and event horizons, extremal black holes with degenerate horizons or no black holes in the absence of the horizons, and encompasses as a special case Boulware-Deser black holes which can be recovered in the absence of magnetic charge ($g=0$). Owing to the NED corrected black hole, the thermodynamic quantities have also been modified and we have obtained exact analytical expressions for the thermodynamical quantities such the Hawking temperature $T_+$, the entropy $S_+$, the specific heat $C_+$, and the Gibbs free energy $F_+$. The heat capacity diverges at a critical radius $r=r_C$, where incidentally the temperature has a maximum, and the Hawking-Page transitions even in absence of the cosmological term. The thermal evaporation process leads to eternal remnants for sufficiently small black holes and evaporates to a thermodynamic stable extremel black hole remnants with vanishing temperature. The heat capacity becomes positive $C_+ > 0$ for $r_+ < r_C$ allowing black hole to become thermodynamically stable, in addition the smaller black holes are globally stable with positive heat capacity $C_+ > 0$ and negative free energy $F_+<0$. The entropy $ S $ of a 5D Bardeen black hole is not longer a quarter of the horizon area $A$, i.e., $S \neq A/4$.

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