Kerr Sen 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.

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

Analysis of the Geodesic Motions of Massive Particles in Kerr–Sen–AdS4 Spacetime

We consider geodesic motions in Kerr–Sen–AdS4 spacetime. We obtain equations of motion for light rays and test particles. Using parametric diagrams, we show some regions where radial and latitudinal geodesic motions are allowed. We analyze the impact of parameters related to the dilatonic scalar on the orbit and find that it will result in more rich and complex orbital types.

Dual CFT on Nariai limit for Kerr–Sen–dS black holes

In this work, we study the Kerr–Sen–de Sitter black hole (BH) in the Nariai limit where the event and cosmological horizon coincide. We show that the near-horizon Kerr–Sen–de Sitter black hole in Nariai limit is a fiber over AdS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} with an appropriate coordinate transformation, instead of fiber over dS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}. Hence, we can compute the associated central charge and CFT temperature by using the Kerr/CFT method. It is remarkably exhibited that through Cardy’s growth of states, the Bekenstein–Hawking entropy on cosmological horizon is reproduced. Moreover, we show that the radial equation of the quantum scalar field in J- and Q-pictures on this charged rotating background in Nariai limit can be portrayed in quadratic Casimir operator form with SL(2,R)×SL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SL(2,R)\ imes SL(2,R)$$\\end{document} isometry. We also compute the corresponding thermodynamic quantities from CFT to find the absorption cross-section and real-time correlator in J-picture. In Q-picture, we do not find a well-defined CFT description. We then extend the study of quantum scalar field in Nariai limit for Kerr–Newman–dS black hole solution and show that the hidden conformal symmetry on this black hole’s background in J- and Q-pictures is well-defined.

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.

Thermodynamic overview and heat engine efficiency of Kerr–Sen–AdS black hole

This paper reflects a study on the thermodynamic features of charged rotating Kerr–Sen–AdS black holes discussed with an extended phase space, where the negative cosmological constant is accounted for pressure. Thermal stability/instability and dependency of the phase transition points on the parameters of a black hole have been discussed further. The authors have systematically studied the throttling process of the black hole considering its mass is identified by its enthalpy. Moreover, the phenomenon of Joule–Thomson expansion has been explored, and inversion temperature for the black hole has been investigated using a numerical approach. Next, a heat engine is constructed by considering the black hole as a working object and subsequently, its efficiency is calculated by considering a rectangular heat cycle in the [Formula: see text]–[Formula: see text] plane. Then the effects of the black hole parameters on its efficiency and their respective roles are studied, followed by a careful comparison of the efficiency with that of a Carnot engine so that the second law of thermodynamics holds true.

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.

Energy extraction via magnetic reconnection in Lorentz breaking Kerr–Sen and Kiselev black holes

Black holes can accumulate a large amount of energy, responsible for highly energetic astrophysical phenomena. Although the Blandford–Znajek is considered to date the leading mechanism for powering jets and GRBs, recently fast magnetic reconnection (MR) of the magnetic field was proposed as a new way to extract energy. In this paper, we investigate this phenomena in a bumblebee Kerr–Sen BH, which differentiates from standard Kerr solution via a Lorentz symmetry breaking parameter ell and an electric charge one b. We find that the presence of the charge parameter strongly changes the simple Kerr case, making this extraction mechanism possible even for not extremely rotating black holes (asim 0.7). We also show that, under appropriate circumstances, MR is more efficient compared to the Blandford–Znajek mechanism. We finally compare these results with dark energy (quintessence) black-hole solutions. In this case, we find that a Kerr black hole is indistinguishable from a rotational Kiselev one, whatever the energy-matter that surrounds it (including ordinary matter, such as dust and radiation).

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.

Cosmological constant effect on charged and rotating black hole shadows

Motivated by recent astrophysical observations, we investigate the shadow behaviors of four-dimensional charged rotating black holes with a cosmological constant. This study is made in terms of a reduced moduli space parameterized by the charge and the rotation parameters. For fixed observers, we analyse in some details the shadow behaviors and the corresponding naked singularities of Kerr–Newman and Kerr–Sen four-dimensional black holes in Anti-de Sitter backgrounds. Then, a comparative discussion is provided by computing the geometrical observables and the energy emission rate.

Implications of Einstein–Maxwell dilaton–axion gravity from the black hole continuum spectrum

ABSTRACT String inspired models can serve as potential candidates to replace general relativity (GR) in the high-energy/high-curvature regime where quantum gravity is expected to play a vital role. Such models not only subsume the ultraviolet nature of gravity but also exhibit promising prospects in resolving issues like dark matter and dark energy, which cannot be adequately addressed within the framework of GR. The Einstein–Maxwell dilaton–axion (EMDA) theory that is central to this work is one such string inspired model arising in the low energy effective action of the heterotic string theory with interesting implications in inflationary cosmology and in the late-time acceleration of the Universe. It is therefore important to survey the role of such a theory in explaining astrophysical observations, e.g. the continuum spectrum of black holes which is expected to hold a wealth of information regarding the background metric. The Kerr–Sen space–time corresponds to the exact, stationary, and axisymmetric black hole solution in EMDA gravity, possessing dilatonic charge and angular momentum originating from the axionic field. In this work, we compute the theoretical spectrum from the accretion disc around quasars in the Kerr–Sen background assuming the thin accretion disc model due to Novikov and Thorne. This is then used to evaluate the theoretical estimates of optical luminosity for a sample of eighty Palomar Green quasars which are subsequently compared with the available observations. Our results based on χ2 analysis indicate that the dilaton parameter r2 ∼ 0.2 is favoured by optical observations of quasars which is further corroborated by other error estimators e.g. the Nash–Sutcliffe efficiency, the index of agreement and their modified versions. We further report that strong dilaton charges (r2 > 1.6) are disfavoured by quasar optical data and the spins associated with the quasars are also estimated.

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.

Shadows of charged rotating black holes: Kerr–Newman versus Kerr–Sen

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope (EHT) observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr–Newman (KN) solution, and the other within the context of low-energy heterotic string theory, the Kerr–Sen (KS) solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions.

Observational signature of a near-extremal Kerr-Sen black hole in the heterotic string theory

We analytically study the optical appearance of an isotropically emitter orbiting near the horizon of a near-extremely rotating Kerr-Sen (KS) black hole which is an electrically charged black hole arising in heterotic string theory. We study the influence of the Sen charge on the observational quantities, including the image position, flux and redshift factor. Moreover, we compare the results with those for a near-extremal Kerr-Newman (KN) black hole, which is the charged rotating black hole in general relativity. We find quantitative corrections of the signatures of these charged black holes (both KS and KN) compare to that of a neutral Kerr black hole. This may serve as distinctive features of different black holes for future tests by the Event Horizon Telescope.

String effect on the relative time delay in the Kerr–Sen black hole

A well known solution of heterotic string theory is the spinning Kerr–Sen black hole (KSBH) characterized by a string parameter ξ. Kerr black hole is recovered at ξ=0. The purpose of this paper is to investigate the effect of ξ on a new diagnostic of relative time delay (RTD) to see how the latter deviates from that in general relativity. Assuming KSBH as the spinning lens partner in PSR–BH binary systems, which provide the best laboratory for testing the time delay predictions, we study here the RTD up to third PPN order in 1∕r in the thin-lens approximation. We work out a useful generalization of the RTD formulas applicable to the experimentally viable finite distance lens scales, while terms higher than the zeroth order are shown to contain the effect of ξ. We shall also relate RTD to the observable image magnification factor determined by β∕θE, where β is the angular separation between the source and the observer and θE is the ”Einstein angle” determined by an ”effective” non-aligned static lens equivalent to the original aligned spinning lens. Numerical estimates for two typical binary lens systems show μsec level delay at the zeroth order consistent with predictions in the literature. However, the string effect at higher orders is too tiny to be measurable even in the far future leading to the conclusion that the stringy and general relativity BHs are yet observationally indistinguishable.

Periodic Orbits Around Kerr Sen Black Holes**Supported by the National Natural Science Foundation of China under Grant Nos. 11447168, 11247013, and Hunan Provincial Natural Science Foundation of China under Grant Nos. 12JJ4007 and 2015JJ2085

We investigate periodic orbits and zoom-whirl behaviors around a Kerr Sen black hole with a rational number q in terms of three integers (z,w,v), from which one can immediately read off the number of leaves (or zooms), the ordering of the leaves, and the number of whirls. The characteristic of zoom-whirl periodic orbits is the precession of multi-leaf orbits in the strong-field regime. This feature is analogous to the counterpart in the Kerr space-time. Finally, we analyze the impact of the charge parameter b on the zoom-whirl periodic orbits. Compared to the periodic orbits around the Kerr black hole, it is found that typically lower energies are required for the same orbits in the Kerr Sen black hole.

Particles collision near Kerr–Sen Dilaton-Axion black hole

Here, we consider axially symmetric, stationary, rotating and charged Kerr–Sen Dilaton-Axion black hole as particle accelerator. We find the effective potential and discuss the circular orbit of a particle. We investigate the center of mass energy of two colliding neutral particles with different rest masses falling from rest at infinity to near the non-extremal horizons (event horizon and Cauchy horizon) and extremal horizon of the Kerr–Sen Dilaton-Axion black hole. Analogous to the Compton process, we discuss the collision of a particle and a massless photon. Finally, we find the center of mass energy due to the collision of two photons in the background of Kerr–Sen Dilaton-Axion black hole.

Charged scalar fields in a Kerr–Sen black hole: exact solutions, Hawking radiation, and resonant frequencies * * H.S.V. is funded by the CNPq through the research Project (150640/2018-8). V.B.B. is partially supported by the CNPq through the research Project (305835/2016-5)

In this study, we consider charged massive scalar fields around a Kerr–Sen spacetime. The radial and angular parts of the covariant Klein–Gordon equation are solved in terms of the confluent Heun function. From the exact radial solution, we obtain the Hawking radiation spectrum and discuss its resonant frequencies. The massless case of the resonant frequencies is also examined.

Over-spinning Kerr–Sen black holes with test fields

In this work, we investigate validity of the weak form of the cosmic censorship conjecture in the interaction of Kerr–Sen black holes with neutral test fields. Previous studies of the Klein–Gordon equation on Kerr–Sen background imply that superradiance occurs for scalar fields. We show that scalar fields can overspin a nearly extremal black hole into a naked singularity, but the modes that could overspin an extremal black hole are not absorbed due to superradiance. From Kerr analogy one can naively expect superradiance to be absent for fermionic fields. In such a case overspinning becomes generic and also applies to extremal Kerr–Sen black holes. This robust violation of cosmic censorship cannot be fixed by backreaction effects which are ignored in this work. These results are analogous to the Kerr case.

Observing the contour profile of a Kerr–Sen black hole

In this paper, the shadow and the corresponding naked singularity cast by a Kerr–Sen black hole are studied. It is found that the shadow of a rotating black hole would be a dark zone surrounded by a deformed circle, and the shadow is distorted more away from a circle when the black hole approaches the extremal case. Besides, it is shown that the mean radius of the shadow decreases and distortion parameter increases with the increasing of charge, respectively. However, the mean radius and the distortion parameter vary complicatedly with the change of spin parameter. In the beginning, both observables decrease rapidly with the increasing of specific angular momentum, nevertheless, they increase slightly in the latter part. These results show that there would be a significant effect of the spin on the shadows, which would be of great importance for probing the nature of the black hole.