Kerr-Sen Black Hole Research Articles

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Thermodynamic topology of Kerr-Sen black holes via Rényi statistics

In the present study, we investigate the topological properties of black holes in terms of Rényi statistics as an extension of the Gibbs-Boltzmann (GB) statistics, aiming to characterize the non-Boltzmannian thermodynamic topology of Kerr-Sen and dyonic Kerr-Sen black holes. Through this research, we discover that the topological number derived via Rényi statistics differs from that obtained through GB statistics. Interestingly, although the nonextensive parameter λ changes the topological number, the topological classification of the Kerr-Sen and dyonic Kerr-Sen black holes remains consistent under both GB and Rényi statistics. In addition, the topological numbers associated with these two types of black holes without cosmological constant using Rényi entropy processes are the same as the AdS cases of them by considering the GB entropy, as further evidenced by such a study found here. This indicates the cosmological constant has some potential connections with the nonextensive parameter from the perspective of thermodynamic topology.

Hawking radiation characteristics of Kerr–Sen black hole spacetime under Lorentz symmetry breaking

Hawking radiation characteristics of Kerr–Sen black hole spacetime under Lorentz symmetry breaking

Correction of Kerr-Sen Black Hole Temperature and Entropy by Lorentz Invariance Violation* *Supported by National Natural Science Foundation of China (Grant No.12373109) and the Natural Science Foundation of Shandong Province of China(Grant No.ZR202102220686).

In this paper, we modify the action of spin field in Kerr-Sen curved space-time through Lorentz invariance violation (LIV). The tunneling radiation rate of Fermion in the Kerr-Sen black hole and the correction of the black hole entropy are studied. In the curved space-time of the Kerr-Sen black hole, by considering the inclusion of LIV correction terms in the action of a spinor field, the modified form of the fermion dynamics equation, the tunneling radiation rate and Bekenstein-Hawking entropy of the black hole are obtained. In this paper, we further consider the modification of the results obtained under quantum perturbation theory and discuss the significance of the results obtained. We have used quantum perturbation theory to perform a more accurate correction of the above results.

Entropy inside the Kerr–Sen black holes

In this paper, we consider the Kerr–Sen black hole. Unlike the AdS black hole, it is actually an exact solution for the heterotic string theory in the low energy effective field theory in four dimensions. Starting from the black hole metric in the Boyer–Lindquist coordinates, we calculate the maximal interior volume by introducing the advanced time. Further, we present the rate of change of the interior volume with the advanced time on the radius of the black hole and observe that it has a maximal value for a specific value of the radius of the black hole. It is also shown from the graph that the maximal value increases with the increase of mass, and the position of the maxima shifts towards the large radius. Moreover, we calculate the rate of loss of mass due to Hawking radiation and interpret it graphically. Finally, we compute the interior entropy and show from its variations with mass and outer horizon radius of the black hole that in the interior, the entropy decreases with mass and becomes negative, whereas, in the exterior, the entropy increases with mass and remains positive. This is further proof of the argument that was proposed in Azuma and Subramanian (2020). In this investigation, an interesting feature is that the low-mass Kerr–Sen black hole behaves like a reversible process, whatever its outer horizon also reveals.

Hidden conformal symmetry for dyonic Kerr-Sen black hole and its gauged family

Motivated by advanced progress in the holographic theory between rotating black holes and CFT, we explore the conformal invariance on dyonic Kerr-Sen black hole and its gauged family. We consider a neutral massless scalar probe on the black holes’ background within the low-frequency limit and exhibit that the solution space possesses SL(2,R)times SL(2,R) isometry. The periodic identification of the azimuthal angle corresponds to the spontaneous conformal symmetry breaking by temperatures T_L,T_R. Using the computation of the central charges on Sakti and Burikham (Phys Rev D 106:106006, 2022) that we recalculate by considering the contributions of all associated fields, we successfully derive the Bekenstein-Hawking entropy from Cardy entropy formula. Furthermore, we also calculate the absorption cross-section from gravity side for generic non-extremal dyonic Kerr-Sen black hole and near-extremal gauged dyonic Kerr-Sen black hole. Our calculations show that those quantities are in a perfect match with the calculation from CFT. Therefore, our findings further support the duality between rotating black holes and CFTs.

Energy formula, surface geometry and energy extraction for Kerr-Sen black hole

We evaluate the surface energy ( $$\mathcal {E}_{s}^{\pm }$$ ), rotational energy ( $$\mathcal { E}_{r}^{\pm }$$ ) and electromagnetic energy ( $$\mathcal { E}_{em}^{\pm }$$ ) for a Kerr-Sen black hole (BH) having the event horizon ( $$\mathcal { H}^{+}$$ ) and the Cauchy horizon ( $$\mathcal { H}^{-}$$ ). Interestingly, we find that the sum of these three energies is equal to the mass parameter i.e. $$\mathcal { E}_{s}^{\pm }+\mathcal { E}_{r}^{\pm }+\mathcal { E}_{em}^{\pm }=\mathcal { M}$$ . Moreover in terms of the scale parameter $$(\zeta _{\pm })$$ , the distortion parameter ( $$\xi _{\pm }$$ ) and a new parameter $$(\sigma _{\pm })$$ which corresponds to the area ( $$\mathcal { A}_{\pm }$$ ), the angular momentum (J) and the charge parameter (Q), we find that the mass parameter in a compact form $$\mathcal { E}_{s}^{\pm }+\mathcal { E}_{r}^{\pm }+\mathcal { E}_{em}^{\pm }=\mathcal { M} =\frac{\zeta _{\pm } }{2} \sqrt{\frac{1+2\,\sigma _{\pm }^2}{1-\xi _{\pm }^2}}$$ which is valid through all the horizons ( $$\mathcal { H}^{\pm }$$ ). We also compute the equatorial circumference and polar circumference which is a gross measure of the BH surface deformation. It is shown that when the spinning rate of the BH increases, the equatorial circumference increases while the polar circumference decreases. We show that there exist two classes of geometry separated by $$\xi _{\pm }=\frac{1}{2}$$ in Kerr-Sen BH. In the regime $$\frac{1}{2}<\xi _{\pm }\le \frac{1}{\sqrt{2}}$$ , the Gaussian curvature is negative and there exist two polar caps on the surface. While for $$\xi _{\pm }<\frac{1}{2}$$ , the Gaussian curvature is positive and the surface will be an oblate deformed sphere. Furthermore, we compute the exact expression of rotational energy that should be extracted from the BH via Penrose process. The maximum value of rotational energy which is extractable should occur for extremal Kerr-Sen BH i.e. $$\mathcal { E}_{r}^{+} =\left( \sqrt{2}-1\right) \sqrt{\frac{J}{2}}$$ .

Connections between the Shadow Radius and the Quasinormal Modes of Kerr-Sen Black Hole

The correspondence between the shadow radius and the real part of the quasinormal modes (QNMs) of a Kerr–Sen black hole is studied. By using the equation of the shadow radius of Kerr–Sen black hole and the angular separation constant of the QNMs, the expression of QNMs related to shadow radius is established in the eikonal limit. We found that, our formula can reduce to the previous result of Kerr black hole when Kerr-Sen parameter b sets to zero.

Dual CFT on a dyonic Kerr-Sen black hole and its gauged and ultraspinning counterparts

We demonstrate that rotating dyonic black holes in Einstein-Maxwell-Dilaton-Axion (EMDA) theory is holographically dual with 2D conformal field theory. We first investigate the duality on dyonic Kerr-Sen black hole with non-vanishing dilaton and axion charges. The near-horizon geometry of extremal dyonic Kerr-Sen spacetime possesses the $SL(2,R) \times U (1)$ isometry allowing to employ the asymptotic symmetry group method to find the corresponding central charge. We find two different branches of the mass which correspond to CFT with two different central charges $c_L=12am_+$ and $c_L=12am_-$. The exact agreement between the Bekenstain-Hawking entropy and entropy from CFT is then found also in two different branches of extremal entropy. Furthermore, we demonstrate that this duality is robust insofar for non-zero AdS length. We show that the duality holds for both dyonic Kerr-Sen-AdS black hole and its ultraspinning counterpart. In both cases, we obtain the expected entropy from CFT which matches exactly with the Bekenstein-Hawking entropy. Since dyonic and axion charges are proportional to $1/m$, we note that there are possibly more than two branches of the central charge for non-zero AdS length in terms of mass. When we turn off dyonic charge, the axion charge vanishes showing the results of Kerr-Sen-AdS black hole. Moreover, when we assume the equal electromagnetic charges, it recovers the results when the dilaton charge vanishes. In the end, we compare the results of dyonic Kerr-Sen-AdS black hole and its ultraspinning counterpart to those of the dyonic Kerr-Newman-AdS black hole and the ultraspinning counterpart. Depending on the dyonic charge parameters, it is found that extremal ultraspinning dyonic Kerr-Sen-AdS black hole is not always superentropic.

Extension of thermodynamics of the Kerr–Sen black hole under general uncertainty principle along with first-order corrected entropy

A four-dimensional solution of the classical equation of motion in the low-energy effective field theory for heterotic string theory is chosen. Popularly, this is known as Kerr–Sen black hole. Thermodynamic picture for this particular black hole is constructed. Applying the generalized uncertainty principle (GUP), the first-order correction of it in connection with the thermal heat capacity (THC) and due to conformal field theory (CFT) background are studied. All the cases are pointing towards an unstable thermodynamic phase of the concerned black holes. Phase transitions are located by studying where signs of the heat capacity are changing. Unlike the black holes embedded in AdS space, first-order corrected entropy is found to be unphysical. Photons by tunneling rate are calculated. A comparative study of the effect of generalized uncertainty principle parameter [Formula: see text] along with the black holes’ parameters on the thermodynamics of the black hole is presented.

Supergravity black holes, Love numbers, and harmonic coordinates

To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of alternative theories with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such viable, alternative theories, based on metrics arising from ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged rotating black hole, when the scalar field is either time independent or in the low-frequency, near-zone limit, with a view to calculating the Love numbers of tidal perturbations, and of obtaining harmonic coordinates for the background metric. For a four-parameter family of charged asymptotically flat rotating black hole solutions of ungauged supergravity theory known as STU black holes, which includes Kaluza-Klein black holes and the Kerr-Sen black hole as special cases, we find that all time-independent solutions, and hence the harmonic coordinates of the metrics, are identical to those of the Kerr solution. In the low-frequency limit we find the scalar fields exhibit the same $SL(2,R)$ symmetry as holds in the case of the Kerr solution. We point out extensions of our results to a wider class of metrics, which includes solutions of Einstein-Maxwell-Dilaton theory.

Connections between the Shadow Radius and the Quasinormal Modes of Kerr-Sen Black Hole

The correspondence between the shadow radius and the quasi-normal modes of the Kerr-Sen black hole is studied. By using the equation of the shadow radius of the Kerr-Sen black hole and the angular separation constant of the quasi-normal modes, the expression of the real part of quasi-normal modes related to the shadow radius is obtained. We found that in the eikonal limit, our formula coincides with the previous result. Moreover, we also calculate the energy emission rate of the Kerr-Sen black hole, it turns out that the peak energy emissivity is inversely correlated with the charge parameter.

A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity

The purpose of this paper is to enhance the conventional Komar integral to asymptotically anti-de Sitter (AdS) black holes. In order to do so, we first obtain a potential that is the linear combination of the usual Komar potential with two third-order derivative terms generated by the action of the d’Alembertian operator and the exterior derivative upon a Killing vector. Then this higher-order corrected potential is extended to the Einstein gravity with a negative cosmological constant, yielding the potential that is the linear combination of the usual Komar one with it acted on by the d’Alembertian. It is demonstrated that the surface integral of the improved Komar potential can serve as a formula for conserved charges of asymptotically AdS spacetimes. Finally, to illustrate such a formula, we make use of it to compute the mass and the angular momentum of Schwarzschild-AdS black holes, regular AdS black holes, asymptotically AdS Kerr-Sen black holes, Kerr-NUT-AdS black holes, and Kerr-AdS black holes in arbitrary dimensions. The results are in agreement with the ones in the literature.

Parameters estimation and strong gravitational lensing of nonsingular Kerr-Sen black holes

The recent time witnessed a surge of interest in strong gravitational lensing by black holes is due to the Event Horizon Telescope (EHT) results, which suggest comparing the black hole lensing in both general relativity and heterotic string theory. That may help us to assess the phenomenological differences between these models. Motivated by this, we consider gravitational lensing by the nonsingular Kerr-Sen black holes, which encompass Kerr black holes as a particular case, to calculate the light deflection coefficients p and q in strong-field limits, while the former increases with increasing parameters k and charge b, later decrease. We also find a decrease in the light deflection angle αD, angular position θ∞ decreases more slowly and impact parameter for photon orbits um more quickly, but angular separation s increases more rapidly with parameters b and k. We compare our results with those for Kerr black holes, and also the formalism is applied to discuss the astrophysical consequences in the case of the supermassive black holes NGC 4649, NGC 1332, Sgr A* and M87*. In turn, we also investigate the shadows of the nonsingular Kerr-Sen black holes and show that they are smaller and more distorted than the corresponding Kerr black holes and nonsingular Kerr black holes shadows. The inferred circularity deviation Δ C≤ 0.10, for the M87* black hole shadow, put constraints on the nonsingular Kerr-Sen black hole parameters (a, k) and (a, b). The maximum shadow angular diameter for b=0.30M and k=0.30M are, respectively, θd=35.3461 μas and θd=35.3355 μas. We also estimate the parameters associated with nonsingular Kerr-Sen black holes using the shadow observables.

Signatures of Einstein-Maxwell dilaton-axion gravity from the observed jet power and the radiative efficiency

The Einstein-Maxwell dilaton-axion (EMDA) gravity arises in the low energy effective action of the heterotic string theory and provides a simple framework to explore the signatures of the same. The dilaton and the axion fields inherited in the action from string compactifications have interesting consequences in inflationary cosmology and in explaining the present accelerated expansion of the universe. It is therefore worthwhile to search for the footprints of these fields in the available astrophysical observations. Since Einstein gravity is expected to receive quantum corrections in the high curvature domain, the near horizon regime of black holes seems to be the ideal astrophysical laboratory to test these deviations from general relativity. Exact, stationary and axisymmetric black hole solution in EMDA gravity corresponds to the Kerr-Sen spacetime which carries dilaton charge, while the angular momentum is sourced by the axion field. The ballistic jets and the peak emission of the continuum spectrum from the accretion disk are believed to be launched very close to the event horizon and hence should bear the imprints of the background spacetime. We compute the jet power and the radiative efficiency derived from the continuum spectrum in the Kerr-Sen background and compare them with the corresponding observations of microquasars. Our analysis reveals that Kerr black holes are more favored compared to Kerr-Sen black holes with dilaton charges.

Escape probability of particle from Kerr-Sen black hole

Assuming that a particle source is at rest in a locally non-rotating frame on the equatorial plane of the Kerr-Sen black hole, we investigate the escape of the massless particle and massive particle from the black hole to spatial infinity. We calculate the escape probabilities of the emitted particles. We find that the angular momentum of the Kerr-Sen black hole boosts the escape probabilities near the horizon of the extreme Kerr-Sen black hole; however the angular momentum of the Kerr-Sen black hole suppresses the escape probabilities near the horizon of the non-extreme Kerr-Sen black hole. We also discover that the horizon limit of the Kerr-Sen black hole is not the most difficult position to escape for a particle in certain conditions.

Analysis and research on superradiant stability of Kerr-sen Black Hole

Kerr-Sen black holes have stretchon parameters and hidden conformal symmetries. The superradiation stability and steady-state resonance are worth further study. This is the research motivation of this paper.In that article, a new variable y is added here to expand the results of the above article. When$\sqrt{2a^2}/{r^2_+}< \omega< m\varOmega_H+q\varPhi_H$,so the Kerr-sen black hole is superradiantly stable at that time,similar to the superradiation result of the Kerr-Newman black hole.

Emission of photons near the horizon of Kerr-Sen black holes

We investigate the escape probabilities of the photons near the horizon of the Kerr-Sen black hole. We find that the escape probabilities of the photons are nonzero in the event horizon limit of the extreme Kerr-Sen black hole if the light sources are near the equator. We show that the escape probability of a photon increases with the radial position of the light source. It is also uncovered that the escape probability decreases if the light source with constant radius moves from the equatorial plane to the pole. Besides, we discover that the escape probability of a photon in the Carter frame is always greater than the one in the locally non-rotating frame, except on the pole, where they are equal.

On phase transition behaviors of Kerr–Sen black hole

We investigate phase transitions and critical behaviors of the Kerr–Sen black hole in four dimensions. Computing the involved thermodynamical quantities including the specific heat and using the Ehrenfest scheme, we show that such a black hole undergoes a second-order phase transition. Adopting a new metric form derived from the Gibss free energy scaled by a conformal factor associated with extremal solutions, we calculate the geothermodynamical scalar curvature recovering similar phase transitions. Then, we obtain the scaling laws and the critical exponents, matching perfectly with mean field theory.

Pair production of scalars around near-extremal Kerr-Sen black holes

We investigate the charged scalar pair production near the horizon of a near-extremal Kerr-Sen black holes. The condition for pair production to occur has relation to the violation of Breitenlohner–Freedman bound in an hbox {AdS}_2 space. The method employed in this work has been used to show the pair production in the near-horizon of a near-extremal Kerr–Newman black hole and its non-rotating case as well. We also discuss the static limit of our result.